[0001] The technical field relates generally to signal processing, and more particularly to systems and methods for increasing instantaneous bandwidth in a vector signal analyzer or a vector signal generator. DESCRIPTION OF THE RELATED ART

[0002] Instantaneous bandwidth is an important banner specification for all radio frequency (RF) vector signal analyzers (VSAs) and RF vector signal generators (VSGs). The desire of the industry is to increase the bandwidth as much as possible without sacrificing dynamic range. In many cases, the limiting factor in achieving the largest possible bandwidth is the sample rate of the analog-to-digital converters (ADCs) and digital-to-analog converters (DACs). While ADC and DAC vendors are always working to increase the converter rates, there still exists a desire in many applications for bandwidths that exceed the capabilities of state-of-the-art ADCs and DACs. There are several different methods within the industry for achieving larger bandwidths, each with their own disadvantages.

[0003] The prior methods for creating larger instantaneous bandwidths that do not intentionally sacrifice resolution fall into two categories: (1) Time- Interleaving (time) and (2) Quadrature Mixing (phase). Both of these methods are industry standards for increasing bandwidth.

[0004] Time-Interleaving uses converters that have larger bandwidths than their sample rates allow. For ADCs, this is made possible by placing faster sample-and-hold circuits on the front- end than the ADC backend is capable of digitizing. Then, by taking N ADCs and staggering them in time by the ADC sample period divided by N, the samples can be interleaved together to create an effective larger sample rate. This method introduces errors resulting from inaccuracies in staggering the time alignment and from differences in the magnitude and phase between the various ADCs. Therefore, several online and offline DSP correction algorithms have been created to combat these effects. In general, it is difficult to achieve more than 8 bits of dynamic range without DSP correction. With offline DSP correction, this can be improved to better than 12 bits of dynamic range but can be very sensitive to temperature. Online methods typically have to assume something about the input signal, and other negative effects occur when those assumptions are broken.

[0005] Quadrature mixing uses a quadrature down-converter or up-converter to mix an RF signal into or from two signals, an in-phase signal and a quadrature-phase signal. In the case of a down-converter, the RF signal is mixed with a sinusoid to create the in-phase signal and the same RF signal is mixed with a sinusoid that is 90 degrees out of phase with the in-phase sinusoid to create the quadrature phase signal. Finally, each of these two analog signals is digitized with ADCs. These two signals are typically represented as a single complex signal, where the in-phase signal represents the real part and the quadrature-phase part of the signal represents the imaginary part. As a result, the positive frequency bandwidth is independent of the negative frequency bandwidth. Thus the net effect is a doubling of the bandwidth. Using this method, the full resolution of the data converters is preserved. However, this method typically creates a DC leakage spur and an image spur. In addition, the method only scales to two converts.

[0006] Thus, there exists a need for mechanisms capable of achieving the goal of larger instantaneous or modulation bandwidths from smaller bandwidths without the scalability and image rejection issues of the quadrature mixing technique and without the inaccuracies present for time interleaving methods.

SUMMARY

[0007] Methods and systems are disclosed for processing a signal using a plurality of vector signal analyzers (VSAs). In a presented method, each of the plurality of VSAs may be provided with a respective component signal comprising a copy of a respective frequency band of an input signal. The combination of the respective frequency bands may comprise an aggregate frequency band having an aggregate center frequency. Each respective frequency band may have a respective region of overlap with at least one other respective frequency band. Each respective frequency band may also have a respective center frequency with a respective frequency offset from the aggregate center frequency. Each of the VSAs may be phase-locked and time- synchronized with respect to the other VSAs.

[0008] Each of the VSAs may process the provided respective component signal. The processing may comprise digitizing, interpolating, frequency-shifting, filtering, and adjusting the gain and phase of the respective component signal. The digitizing may comprise shifting the respective center frequency of the respective frequency band to baseband, and sampling at least a portion of the respective component signal corresponding to the respective measurement band. The frequency- shifting may comprise shifting the respective component signal such that the respective center frequency is offset from baseband by the respective frequency offset. The filtering the respective component signals may be configured to cause a sum of the component signals to have a unity frequency response within each region of overlap. The filtering may be performed using a digital half-band filter. The adjusting gain and phase of the respective component signals may be configured to cause the sum of the component signals to have a continuous frequency response over the aggregate frequency band.

[0009] The method may further comprise summing the respective component signals to obtain a composite signal.

[0010] A system is presented for processing a signal. The apparatus may comprise a signal splitter configured to receive an analog signal, and output a plurality of copies of the analog signal. The system may further comprise a plurality of output ports, each of the communication ports configured to provide to a respective vector signal analyzer (VSA) a respective copy of the modulated signal. The system may further comprise a plurality of input ports, each of the input ports configured to receive from the respective VSA a respective digital signal. Each respective digital signal may comprise a digitized version of a respective frequency band of the analog signal. Each respective frequency band may have a region of overlap with at least one other frequency band received by another of the communication ports. Each respective frequency band may also have a respective center frequency having a respective frequency offset from an aggregate center frequency of an aggregate frequency band. The aggregate frequency band may comprise the combination of the frequency bands of the received digital signals. The respective VSA may be phase-locked and time- synchronized with respect to the VSAs of the other input ports.

[0011] The system may further comprise a plurality of parallel signal processing pathways. Each of the parallel signal processing pathways may be configured to receive a respective digital signal from one of the input ports, and digitize, interpolate, frequency-shift, filter, and adjust the gain and phase of the respective digital signal according to the method described above.

[0012] The system may further comprise a summing unit configured to sum the outputs of the plurality of parallel signal processing pathways to obtain a composite signal. [0013] A method is provided for calibrating a signal processing system including at least a first VSA and a second VSA. The method may comprise providing a first component signal to the first VSA and providing a second component signal to the second VSA. The first component signal may comprise a first frequency band within an aggregate frequency band of an input signal, and the second component signal may comprise a second frequency band within the aggregate frequency band of the input signal. The aggregate frequency band may have an aggregate center frequency. The first frequency band may have a first center frequency at a first frequency offset from the aggregate center frequency, and the second frequency band may have a second center frequency at a second frequency offset from the aggregate center frequency. The second frequency band may have a region of overlap with the first frequency band, the region of overlap containing a calibration tone. The second VSA may be phase-locked and time-synchronized with respect to the first VSA.

[0014] The method may further comprise digitizing, interpolating, frequency-shifting, and filtering each of the first and second component signals, according to the method described above. The method may further comprise computing a complex calibration constant based on a magnitude ratio and a phase difference. The magnitude ratio may be determined by a magnitude of the calibration tone measured by the first VSA and a magnitude of the calibration tone measured by the second VSA. The phase difference may be determined by a phase of the calibration tone measured by the first VSA and a phase of the calibration tone measured by the second VSA.

[0015] The method may further comprise storing the complex calibration constant in memory. The complex calibration constant may be useable to correct phase and gain mismatch between the first VSA and the second VSA. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] A better understanding of the present inventions can be obtained when the following detailed description is considered in conjunction with the following drawings:

[0017] Figure 1 is a block diagram illustrating an embodiment of a system for performing spectral stitching in a receive path;

[0018] Figure 2 is a block diagram illustrating an embodiment of parallel vector signal analyzers (VSAs); [0019] Figures 3 a, 3b, and 3c illustrate exemplary embodiments of respective frequency bands within an aggregate frequency band with and without calibration tones;

[0020] Figure 4 illustrates the signal response of a half-band filter;

[0021] Figure 5 is a block diagram illustrating another embodiment of a system for performing spectral stitching in a receive path;

[0022] Figures 6a and 6b illustrate measurements of a calibration tone, as performed by two VSAs before and after phase and magnitude adjustment, represented in the time domain;

[0023] Figure 7 is a block diagram illustrating an embodiment of a system for performing spectral stitching in a transmit path; and

[0024] Figure 8 is a block diagram illustrating an embodiment of a digital signal processing block for use in the system of Figure 7.

[0025] While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings and are herein described in detail. It should be understood, however, that the drawings and detailed description thereto are not intended to limit the invention to the particular form disclosed, but on the contrary, the intention is to cover all modifications, equivalents and alternatives falling within the spirit and scope of the present invention as defined by the appended claims. Note that the various section headings in the following Detailed Description are for organizational purposes only and are not meant to be used to limit the claims.

DETAILED DESCRIPTION

[0026] Incorporation by Reference

[0027] The following references are incorporated by reference as if fully and completely disclosed herein:

[0028] U.S. Patent Application No. 2013/0343490, filed June 20, 2012, entitled "Synchronizing Receivers in a Signal Acquisition System", invented by Wertz et al.;

[0029] U.S. Pat. No. 7,624,294, issued on Nov. 24, 2009, entitled "Synchronizing Measurement Devices Using Trigger Signals", invented by Craig M. Conway; and

[0030] U.S. Pat. No. 7,315,791, issued on Jan. 1, 2008, entitled "Application Programming Interface for Synchronizing Multiple Instrumentation Devices", invented by Kosta Ilic et al.

[0031] Terminology [0032] The following is a glossary of terms used in the present application:

[0033] Memory Medium - Any of various types of memory devices or storage devices. The term "memory medium" is intended to include an installation medium, e.g., a CD-ROM, floppy disks 105, or tape device; a computer system memory or random access memory such as DRAM, DDR RAM, SRAM, EDO RAM, Rambus RAM, etc.; a non- volatile memory such as a Flash, magnetic media, e.g., a hard drive, or optical storage; registers, or other similar types of memory elements, etc. The memory medium may comprise other types of memory as well or combinations thereof. In addition, the memory medium may be located in a first computer in which the programs are executed, or may be located in a second different computer which connects to the first computer over a network, such as the Internet. In the latter instance, the second computer may provide program instructions to the first computer for execution. The term "memory medium" may include two or more memory mediums which may reside in different locations, e.g., in different computers that are connected over a network.

[0034] Programmable Hardware Element - includes various hardware devices comprising multiple programmable function blocks connected via a programmable interconnect. Examples include FPGAs (Field Programmable Gate Arrays), PLDs (Programmable Logic Devices), FPOAs (Field Programmable Object Arrays), and CPLDs (Complex PLDs). The programmable function blocks may range from fine grained (combinatorial logic or look up tables) to coarse grained (arithmetic logic units or processor cores). A programmable hardware element may also be referred to as "reconfigurable logic".

[0035] Computer System - any of various types of computing or processing systems, including a personal computer system (PC), mainframe computer system, workstation, network appliance, Internet appliance, personal digital assistant (PDA), television system, grid computing system, or other device or combinations of devices. In general, the term "computer system" can be broadly defined to encompass any device (or combination of devices) having at least one processor that executes instructions from a memory medium.

[0036] Local Oscillator (LO) - a circuit configured to generate a periodic signal at a specified frequency and amplitude. The periodic signal may be a pure sinusoid, and its frequency and/or amplitude may be programmable. The periodic signal may or may not be phase or frequency locked to another periodic signal. [0037] Overview

[0038] Time interleaving uses time as the mechanism to increase the bandwidth while quadrature mixing uses phase as its mechanism. The present "spectral stitching" approach uses frequency as its mechanism to achieve larger instantaneous bandwidths. The spectral stitching approach may be applied to both signal receivers, such as RF (radio frequency) receivers, for example, and signal generators, such as RF generators, for example, as discussed below. As used herein, the term "RF" is intended to include the full spectrum of communication frequencies, and includes at least radio and microwave frequencies.

[0039] Embodiments of the present invention may be realized in any of various forms. For example, in some embodiments, the present invention may be realized as a computer- implemented method, a computer-readable memory medium, or a computer system. In other embodiments, the present invention may be realized using one or more custom-designed hardware devices such as ASICs. In other embodiments, the present invention may be realized using one or more programmable hardware elements such as FPGAs.

[0040] In some embodiments, a computer-readable memory medium may be configured so that it stores program instructions and/or data, where the program instructions, if executed by a computer system, cause the computer system to perform a method, e.g., any of a method embodiments described herein, or, any combination of the method embodiments described herein, or, any subset of any of the method embodiments described herein, or, any combination of such subsets.

[0041] In some embodiments, a computer system may be configured to include a processor (or a set of processors) and a memory medium, where the memory medium stores program instructions, where the processor is configured to read and execute the program instructions from the memory medium, where the program instructions are executable to implement any of the various method embodiments described herein (or, any combination of the method embodiments described herein, or, any subset of any of the method embodiments described herein, or, any combination of such subsets). The computer system may be realized in any of various forms. For example, the computer system may be a personal computer (in any of its various realizations), a workstation, a computer on a card, an application-specific computer in a box, a server computer, a client computer, a hand-held device, a tablet computer, a wearable computer, etc. [0042] Receive Path

[0043] In a receive path, spectral stitching may be performed by using a plurality N of vector signal analyzers (VSAs) to digitize an analog input receive (RX) signal, such as an RF signal, where each VSA handles a respective frequency band of the signal. Together the respective frequency bands comprise an aggregate frequency band of interest. The outputs of the N VSAs may therefore be recombined to form a composite signal having a bandwidth on the order of N times the bandwidth of each individual VSA, thus covering the entire aggregate frequency band. The aggregate frequency band may be a region of interest within the input RX signal.

[0044] Figure 1 illustrates a block diagram of an embodiment of a system 100 for performing spectral stitching in a signal path receiving an inputRX signal. As shown in Figure 1, the system 100 includes three VSAs 108a-c. Other embodiments may include another number N of VSAs. It should be appreciated that the terms "VSA" and "vector signal analyzer," as used herein, may encompass any type of signal analyzer, digitizer, receiver, or other device capable of converting, or configured to convert, an analog input signal to a digital output signal.

[0045] One or more calibration tones may be added to the inputRX signal to aid in calibrating the plurality of VSAs, as discussed below. In some embodiments, the one or more calibration tones may be generated by calibration tone generator 104, and added to the input signal by a power combiner 102. In other embodiments, the one or more calibration tones may be added to the input signal using a simple two-port mux, or using any other signal combining technique known in the art. In some embodiments, the system 100 may include multiple calibration tone generators, which may require the power combiner 102 to have more than two inputs. The one or more calibration tones may be generated and added to the input signal while the system 100 is operating in a calibration mode, as discussed below. Thus, in normal operation, the power combiner 102 may not add the one or more calibration tones to the input signal.

[0046] A copy of at least a portion of the inputRX signal may be provided to each of the VSAs 108a-c. This may be accomplished by splitting the input signal, such as by using a power splitter 106, having N outputs.

[0047] The output of each VSA 108a-c may be provided to a summing unit 110. The output of the summing unit 110 is a composite signal representing the sum of the output of each of the VSAs 108a-c. [0048] As mentioned previously, each of the VSAs 108a-c may handle a different frequency band of the inputRX signal. To ensure continuity across the full aggregate frequency band, the different frequency bands handled by the respective VSAs 108a-c should overlap. Thus, in order for the sum of the outputs of the VSAs 108a-c to accurately represent a digitized version of the aggregate frequency band of the inputRX signal, the outputs of the VSAs 108a-c may be further processed to provide continuity through the regions of overlap. Each of the VSAs 108a-c may therefore comprise signal processing capabilities beyond those traditionally included in a VSA. In some embodiments, each of the VSAs 108a-c may not comprise a stand-alone VSA. For example, each of the VSAs 108a-c may be implemented as a signal processing path on a programmable hardware element, multiprocessor system, etc.

[0049] Figure 2 illustrates a block diagram providing further detail of an embodiment of the VSAs 108a-c. Specifically, blocks 202a-210a represent details of an embodiment of VSA 108a, blocks 202b-210b represent details of an embodiment of VSA 108b, and blocks 202c-210c represent details of an embodiment of VSA 108c. Summing unit 110 is also included in Figure 2 for context.

[0050] At each of the digitize blocks 202a-c, a component signal comprising a respective frequency band of the inputRX signal may be digitized. Each of the digitize blocks 202a-c may include functionality included in a traditional VSA.

[0051] In some embodiments, each of the digitize blocks 202a-c may receive a copy of the entire inputRX signal, e.g. from the signal splitter 106. In other embodiments, each of the digitize blocks 202a-c may receive only a respective portion of the inputRX signal. Because each of the VSAs 108a-c may handle a different frequency band of the inputRX signal, each of the digitize blocks 202a-c may digitize a respective component signal comprising a respective frequency band, each respective frequency band identified by a respective center frequency.

[0052] Figure 3a illustrates an exemplary embodiment of frequency bands as received by the digitize blocks 202a-c, represented in the frequency domain. In this example, frequency band 302 represents the frequency band of the digitize block 202a (i.e. VSA 108a), frequency band 304 represents the frequency band of the digitize block 202b (i.e. VSA 108b), and frequency band 306 represents the frequency band of the digitize block 202c (i.e. VSA 108c). The region covered by frequency bands 304-306 together represents the aggregate frequency band identified by an aggregate center frequency. Each respective center frequency is offset from the aggregate center frequency by a respective frequency offset. In some circumstances a respective center frequency may be offset from the aggregate center frequency by 0 Hz, as in the example of frequency band 304.

[0053] The frequency bands may overlap to avoid gaps within the aggregate frequency band. For example, the region 308 represents a region of overlap between frequency band 302 and frequency band 304 (i.e. between the respective component signals of VSAs 108a and 108b), and the region 310 represents the region of overlap between frequency band 304 and frequency band 306 (i.e. between the respective component signals of VSAs 108b and 108c).

[0054] The digitizing performed by each of the digitize blocks 202a-c may comprise performing I/Q demodulation on the respective component signal to produce a pair of analog I (in-phase) and Q (quadrature) signals.

[0055] The digitizing performed by each of the digitize blocks 202a-c may also comprise frequency-shifting the respective component signal (or the I/Q signal pair) such that the respective center frequency is shifted to baseband. Each of the digitize blocks 202a-c may then filter out portions of the shifted signal that are outside the respective frequency band, e.g. by using a low-pass filter. Alternatively, each of the digitize blocks 202a-c may frequency- shift the received inputRX signal to a position other than baseband (or forego frequency-shifting), and filter the shifted signal using a band-pass filter.

[0056] In one embodiment, each of the digitize blocks 202a-c may comprise a respective local oscillator (LO) operating at the respective center frequency. The respective LO may be used, for example, in frequency- shifting the respective center frequency to baseband. The LOs of the digitize blocks 202a-c may have a fixed phase difference relative to each other. For example, the LOs may be locked to a common reference, such that the relative phases between the devices will remain fixed.

[0057] The digitizing performed by each of the digitize blocks 202a-c may further comprise complex sampling the filtered signal, as known in the art. The VSAs 108a-c may be time- synchronized, such that the respective signals may be sampled simultaneously in each of the digitize blocks 202a-c. Alternatively, the respective signals may be sampled at a consistent offset of time. In this case, the consistent offset may be measured and corrected. Each of the digitize blocks 202a-c may output a complex (I/Q) signal. [0058] At filter blocks 204a-c, the respective component signals may be filtered. Because the respective frequency bands of the respective component signals overlap in frequency, as shown in Figure 3, the overlap regions should be filtered to prevent power spikes, or other artificial increases in magnitude, in the overlap regions when the respective signals are summed by summing unit 110. In other words, the respective component signals should be filtered such that their sum appears continuous. Specifically, the respective component signals may be filtered such that the sum of overlapping signals provides a unity response at all points within the aggregate frequency band. More generally, this continuous-sum filtering may be configured in any manner such that the summed signals approximate the result that would be achieved if the entire aggregate frequency band had been digitized by a single VSA having sufficient bandwidth to digitize the entire aggregate frequency band.

[0059] Various filter shapes may be used to accomplish this. For example, Figure 4 illustrates the response of a half -band filter, where the solid trace 402 represents a filter response for a first VSA and the dotted trace 404 represents a filter response for a second VSA with an overlapping frequency band. In Figure 4, the crossover point is located at 30MHz where there is a 10MHz crossover region. While a half-band filter inherently has the needed spectral characteristics to filter overlapping frequency bands to sum together to produce unity gain, it forces the crossover point to occur at the sampling frequency divided by four, fs/4. In other embodiments, this crossover may be moved further out in frequency using other filter methods, e.g., to increase the effectiveness of the natural instantaneous bandwidth of each device.

[0060] The filtering illustrated as filter blocks 204a-c may happen at any of various points in the VSA. For example, the filtering may occur after the interpolate blocks 206a-c. Alternatively, some embodiments may perform the filtering of the filter blocks 204a-c within the digitize blocks 202a-c, e.g., concurrently with the low-pass filtering of the digitize blocks 202a-c. In this case, the filtering may be performed by an analog filter prior to complex sampling of the filtered signal.

[0061] At interpolate blocks 206a-c, each respective component signal may be interpolated. The interpolation factor should be set such that each respective interpolate block 206 interpolates the respective component signal to at least the effective I/Q rate required for the "stitched" data's bandwidth. For example, in one embodiment, the effective I/Q rate may be required to be at least the Nyquist rate of the respective component signal. In another embodiment, a higher rate (e.g., 1.25 times the Nyquist rate) may be selected. [0062] At frequency shift blocks 208a-c, each respective component signal may be shifted into the proper location in frequency relative to the other devices. As a result, each device will frequency shift its interpolated spectrum to a different location. Specifically, each respective component signal may be shifted such that its respective center frequency is offset from baseband by the respective frequency offset by which it was originally offset from the aggregate center frequency. Thus, the entire aggregate frequency band is frequency shifted to center at baseband.

[0063] For example, in the case that there are three VSAs each using half -band filters with an VQ rate of 120MHz, then the cross-over points will be located at positive and negative 30MHz. This means that the three respective center frequencies may be shifted to [-60MHz, OHz, 60MHz]. Thus, the respective frequency bands should be defined such that the respective frequency offsets are [-60MHz, OHz, 60MHz] relative to the aggregate center frequency.

[0064] If the digitize blocks 202a-c previously shifted the respective center frequencies to baseband, then VSA 108a may, in this example, frequency shift its spectrum to the left by 60MHz, VSA 108b may shift by OHz, and VSA 108c may frequency shift its spectrum to the right by 60MHz. In other words, each respective center frequency may be shifted by its respective frequency offset. In embodiments in which the respective frequencies were shifted by the digitize blocks 202a-c to a frequency other than baseband, then the respective center frequencies may be shifted by some value other than the respective frequency offsets.

[0065] At the gain and phase correction blocks 210a-c, the magnitude and phase of each respective component signal may be adjusted to make the spectrum continuous through the regions of overlap. This gain and phase correction may comprise a complex multiply of each of one or more of the respective component signals with a respective calibration constant. Determining a calibration constant for each of the gain and phase correction blocks 210a-c is discussed below.

[0066] Where the VSAs 108a-c are not time- synchronized, but have a constant delay relative to each other, the gain and phase correction blocks 210a-c may be further configured to measure and correct the delay.

[0067] Figure 5 illustrates a block diagram of an embodiment of a second system 500 for performing spectral stitching in a signal path receiving an inputRX signal. As shown in Figure 5, the system 500 includes three VSAs 508a-c. Other embodiments may include another number N of VSAs. [0068] In Figure 5, the power combiner 102, the calibration tone generator 104, and the power splitter 106 may operate as described with regard to Figure 1. The VSAs 508a-c may be standard VSAs as known in the art, without the additional signal processing capabilities of VSAs 108a-c. Instead, the additional signal processing functions may be performed by a separate digital signal processing block 510. For example, the digital signal processing block 510 may perform the functions of filtering, interpolating, frequency shifting, and gain and phase correction, as discussed with regard to Figure 2, blocks 204-210, for each of the VSAs 508a-c. For example the digital signal processing block 510 may comprise a separate signal processing path for processing the output of each of the VSAs 508a-c. The digital signal processing block 510 may further comprise a summing function, which may function in a manner similar to the summing unit 110.

[0069] The system 500 presents an advantage over the system 100, in that the system 500 may allow a user to utilize standard, off-the-shelf VSAs. For example, system 500 may be realized in the form of a signal processing chassis comprising the digital signal processing block 510, and optionally further comprising one or more of the power combiner 102, the calibration tone generator 104, and the power splitter 106. The signal processing chassis may further comprise slots to accept a plurality of VSAs, which may be standard, off-the-shelf VSAs. The signal processing chassis may be configured to operate with a variable number of VSAs, according to the preferences of the user. Further, the VSAs may differ in bandwidth, resolution, or other characteristics, according to the preferences of the user.

[0070] Determining VSA Calibration Constants

[0071] In order to adjust the magnitudes and phases of the respective signals in the receive path to provide continuity through the regions of overlap, the relative magnitudes and phases between the respective signals without adjustment may be determined. This may be performed by injecting a calibration tone at each crossover point, or region of overlap, of the respective frequency bands. The calibration tone may then be measured and compared by the VSAs. Differences and/or ratios between the measurements by different VSAs of the magnitude and phase of the calibration tone may be used to determine calibration constants for each of the VSAs.

[0072] For example, to determine calibration constants for a system such as the system 100 shown in Figures 1-2, or the system 500 shown in Figure 5, the system may be set to a calibration mode. The calibration mode will be discussed herein with respect to the system 100 shown in Figures 1-2. However, the same principles may be applied to other embodiments, such as the system 500.

[0073] As shown in Figure 1, the power combiner 102 may be used to combine the input signal with one or more calibration tones from the calibration tone generator 104. A calibration tone may comprise a real tone at a single known frequency falling within a region of overlap. A calibration tone may also have a known magnitude. In some embodiments, a calibration tone may be injected at a single region of overlap at a time, with each region of overlap being treated sequentially. In other embodiments, calibration tones may be injected at multiple, or all, regions of overlap simultaneously. The combined signal may then be used as the input to the splitter 106 where each of the splitter's outputs may be the input to one of N VSAs, such as VSAs 108a-c.

[0074] At the N VSAs, each of the N-l regions of overlap may comprise a respective calibration tone, as shown in Figure 3b (either simultaneously or sequentially). As illustrated, calibration tone 312 may be generated within region of overlap 308 (i.e. within the respective signals of VSAs 108a and 108b), and calibration tone 314 may be generated within region of overlap 310 (i.e. within the respective signals of VSAs 108b and 108c).

[0075] At blocks 202-208, each respective signal may be digitized, filtered, interpolated, and frequency shifted, as discussed above with regard to Figure 2. However, the gain and phase correction block 210 may operate differently in the calibration mode. Specifically, the gain and phase correction block 210 may measure the respective calibration tone within each region of overlap. For example, the gain and phase correction block 210a (of VSA 108a) may measure the calibration tone 312, since it falls within the respective frequency band 302, which is processed by the VSA 108a. The gain and phase correction block 210b (of VSA 108b) may also measure the calibration tone 312, since it also falls within the respective frequency band 304, which is processed by the VSA 108b.

[0076] Figure 6a illustrates exemplary results of measurements of the calibration tone 312, as performed by the VSAs 108a and 108b, represented in the time domain. As illustrated, the in- phase (I) and quadrature (Q) components of the calibration tone 312 as measured by the VSA 108 a have a phase and magnitude that are different from the phase and magnitude of the I and Q components of the calibration tone 312 as measured by the VSA 108b. This may result from normal differences in the hardware, temperature, etc. of the VSAs 108a and 108b. In this condition, the sum of the respective signals output by the VSAs 108a and 108b will not be continuous through the region of overlap, because of the mismatch in phase and magnitude.

[0077] Using the measurements of the calibration tone within each region of overlap, respective calibration constants may be determined, for use in realigning the respective signals through each region of overlap. For example, for each respective VSA, a complex calibration constant may be determined that, when complex multiplied by a calibration tone measured by that respective VSA, will result in an output calibration tone having a phase and magnitude matching an output calibration tone of an adjacent VSA. Figure 6b illustrates output calibration tones of VSAs 108a and 108b. The output calibration tones shown in Figure 6b represent the signals shown in Figure 6a after being multiplied by the determined calibration constants.

[0078] In one embodiment, the magnitudes of the calibration tones generated by the calibration tone generator 104 may be known. The calibration constants may therefore be determined such that the output calibration tones have a magnitude matching the generated calibration tones. In another embodiment, the calibration constants may merely be determined such that the output calibration tones produced by adjacent VSAs have the same magnitude.

[0079] For example, calibration tone 312 may be measured by both VSA 108a and VSA 108b. Calibration tone 314 may be measured by both VSA 108b and VSA 108c. The output signal of VSA 108a will include an output calibration tone corresponding to calibration tone 312. The output signal of VSA 108b will include output calibration tones corresponding to calibration tone 312 and calibration tone 314. The output signal of VSA 108c will include an output calibration tone corresponding to calibration tone 314.

[0080] A first calibration constant may optionally be determined for VSA 108a such that complex multiplication of the first calibration constant with the output signal of VSA 108a results in the output calibration tone corresponding to calibration tone 312 having a magnitude matching the known magnitude of calibration tone 312.

[0081] A second calibration constant may be determined for VSA 108b such that complex multiplication of the second calibration constant with the output signal of VSA 108b results in the output calibration tone corresponding to calibration tone 312 having a phase matching the phase of the output calibration tone of VSA 108a. The second calibration constant may further be determined such that the output calibration tone corresponding to calibration tone 312 has a magnitude matching the known magnitude of calibration tone 312 and/or the magnitude of the output calibration tone of VSA 108a corresponding to calibration tone 312. In one embodiment, a calibration constant determined to cause the output calibration tone of 108b to match the phase and magnitude of the output calibration tone of VSA 108a may be determined by performing a complex division of the calibration tone 312 as measured by VSA 108a by the calibration tone 312 as measured by VSA 108b. Because the complex multiplication of the second calibration constant is performed with the entire output signal of VSA 108b, the output calibration tone of VSA 108b corresponding to calibration tone 314 is also adjusted.

[0082] A third calibration constant may be determined for VSA 108c such that complex multiplication of the third calibration constant with the output signal of VSA 108c results in the output calibration tone corresponding to calibration tone 314 having a phase matching the phase of the adjusted output calibration tone of VSA 108b corresponding to calibration tone 314. The third calibration constant may further be determined such that the output calibration tone corresponding to calibration tone 314 has a magnitude matching the known magnitude of calibration tone 314, and/or the magnitude of the output calibration tone of VSA 108b corresponding to calibration tone 314.

[0083] The calibration constants for each of the VSAs should be determined, or re-determined, each time the phases of the VSAs change relative to each other. For example, the relative phases of the VSAs may change if the relative phases of the LOs of the VSAs change. This may occur, e.g., if the LO frequencies of one or more VSAs change and the one or more VSAs are relocked. In some VSAs, the phase of the LO can be made to be deterministic. If this is the case, then a calibration constant may be determined once and stored for each frequency of the VSA. The stored calibration constant may then be recalled at some future time without the need for recalibration.

[0084] Transmit Path

[0085] In a transmit path, spectral stitching may be performed by using a plurality N of vector signal generators (VSGs) to generate an output analog transmit (TX) signal, such as an RF signal, where each VSG handles a respective frequency band of the signal. Together the respective frequency bands comprise an aggregate frequency band of interest. The outputs of the N VSAs may therefore be combined to form a composite signal having a bandwidth on the order of N times the bandwidth of each individual VSG, thus covering the entire aggregate frequency band. [0086] Figure 7 illustrates a block diagram of an embodiment of a system 700 for performing spectral stitching in a signal path generating an output analog signal. As shown in Figure 7, the system 700 includes three VSGs 704a-c. Other embodiments may include another number N of VSGs. It should be appreciated that the terms "VSG" and "vector signal generator," as used herein, may encompass any type of signal generator, transmitter, or other device capable of converting, or configured to convert, a digital input signal to an analog output signal.

[0087] A digital input signal, illustrated in Figure 7 as the "TX Signal", may be provided to the system. The input TX Signal may comprise a complex digital signal having a bandwidth that is larger than the bandwidth of each respective VSG. Therefore, each of the VSGs 704a-c may be provided with a respective component signal comprising at least a portion of the input TX Signal. Specifically, each component signal may comprise a respective frequency band of the input TX Signal, and each of the VSGs 704a-c may process the respective frequency band. Each respective frequency band may have a respective center frequency having a respective frequency offset from an aggregate center frequency of the aggregate frequency band.

[0088] To ensure continuity across the full aggregate frequency band, the respective frequency bands should overlap. Thus, in order for the outputs of the VSGs 704a-c to be recombined to accurately represent an analog version of the aggregate frequency band of the digital input signal, the component signals may be further processed to provide continuity through the regions of overlap. Each of the VSGs 704a-c may therefore comprise signal processing capabilities beyond those traditionally included in a VSG. Alternatively, such further processing may be performed by signal processing circuitry outside of the VSGs 704a-c, such as by the digital signal processing (DSP) block 702, which is described more fully below. Such an embodiment would allow a user to implement the present invention using standard off-the-shelf VSGs. In other embodiments, each of the VSGs 704a-c may not comprise a stand-alone VSG. For example, each of the VSGs 704a-c may be implemented as a signal processing path on a programmable hardware element, multiprocessor system, etc.

[0089] Once the further processing has been performed, e.g. by the DSP block 702 or by each of the VSGs 704a-c, each of the VSGs 704a-c may convert the respective component signal to an analog signal. Each of the VSGs 704a-c may also up-convert the respective component signal such that the aggregate center frequency is located at a desired carrier frequency, and each respective center frequency is offset from the desired carrier frequency by the respective frequency offset.

[0090] The combiner 706 may comprise a power combiner with a plurality of inputs, or may comprise any other hardware for combining analog signals, as known in the art. The combiner 706 may receive as inputs the outputs of the VSGs 704a-c, and may output a composite signal comprising a combination of its inputs.

[0091] A power splitter 708 may provide copies of the composite signal as an output of the system, i.e. as "TX Out" shown in Figure 7, and also to a calibration receiver 710. The calibration receiver 710 may be used to receive one or more calibration tones for use in determining calibration constants for one or more of the VSGs 704a-c, as discussed below. The calibration receiver 710 may be phase locked to the VSGs 704a-c.

[0092] Figure 8 is a block diagram illustrating the DSP block 702 in greater detail. The DSP block 702 may comprise a plurality of parallel processing paths, each of which may process one of the respective component signals. In some embodiments, the DSP block 702 may be separate from the VSGs 704a-c, as shown in Figure 7. In other embodiments, a respective one of the parallel processing paths of the DSP block 702 may be included in each of the VSGs 704a-c. For example, blocks 802a, 804a, 806a, and 808a may be included in VSG 704a; blocks 802b, 804b, 806b, and 808b may be included in VSG 704b; and blocks 802c, 804c, 806c, and 808c may be included in VSG 704c.

[0093] In some embodiments, each of the frequency shift blocks 802a-c may receive a copy of the entire digital input signal. In other embodiments, each of the frequency shift blocks 802a-c may receive only a respective portion of the digital input signal comprising a respective frequency band.

[0094] Figure 3a illustrates an exemplary embodiment of frequency bands as received by the frequency shift blocks 802a-c, represented in the frequency domain. In this example, frequency band 302 represents the frequency band of the frequency shift block 802a (i.e. VSG 704a), frequency band 304 represents the frequency band of the frequency shift block 802b (i.e. VSG 704b), and frequency band 306 represents the frequency band of the frequency shift block 802c (i.e. VSG 704c). The region covered by frequency bands 304-306 together represents the aggregate frequency band identified by an aggregate center frequency. Each respective center frequency is offset from the aggregate center frequency by a respective frequency offset. In some circumstances a respective center frequency may be 0 Hz, as in the example of frequency band 304.

[0095] The frequency bands may overlap to avoid gaps within the aggregate frequency band. For example, the region 308 represents a region of overlap between frequency band 302 and frequency band 304 (i.e. between the respective component signals of VSGs 704a and 704b), and the region 310 represents the region of overlap between frequency band 304 and frequency band 306 (i.e. between the respective component signals of VSGs 704b and 704c).

[0096] At the frequency shift blocks 802a-c, each of the respective component signals may be shifted to baseband. Where the aggregate frequency band is initially at baseband, this means that each respective component signal is frequency-shifted by the negative of the respective frequency offset. For example, if the respective frequency offset of the respective component signal being processed by the frequency shift block 802c is 60MHz, then the frequency shift block 802c would frequency shift the respective component signal by -60MHz.

[0097] At the decimate blocks 804a-c, each respective component signal may be decimated to a rate that is less than or equal to the maximum sample rate of the corresponding VSG. This decimation may comprise merely dropping samples. Alternatively, this decimation may comprise alias-protected decimation, utilizing an alias protection filter.

[0098] The filter blocks 806a-c are similar to the filter blocks 204a-c of Figure 2. Because the respective frequency bands of the respective component signals overlap in frequency, as shown in Figure 3, the overlap regions should be filtered to prevent power spikes in the overlap regions when the respective signals are combined by the combiner 706. In other words, the respective component signals should be filtered such that their sum appears continuous. Specifically, the respective component signals may be filtered such that the sum of overlapping signals provides a unity response at all points within the aggregate frequency band.

[0099] Various filter shapes may be used to accomplish this. For example, Figure 4 illustrates the response of a half -band filter, where the solid trace 402 represents a filter response for a first VSG and the dotted trace 404 represents a filter response for a second VSG with an overlapping frequency band. In Figure 4, the crossover point is located at 30MHz where there is a 10MHz crossover region. While a half-band filter inherently has the needed spectral characteristics to filter overlapping frequency bands to sum together to produce unity gain, it forces the crossover point to occur at the sampling frequency divided by four, fs/4. In other embodiments, this crossover may be moved further out in frequency using other filter methods, e.g., to increase the effectiveness of the natural instantaneous bandwidth of each device.

[00100] At the gain and phase correction blocks 808a-c, the magnitude and phase of each respective component signal may be adjusted to make the spectrum continuous through the regions of overlap. This gain and phase correction may comprise a complex multiply of each of one or more of the respective component signals with a respective calibration constant. Determining a calibration constant for each of the gain and phase correction blocks 808a-c is discussed below.

[00101] Determining VSG Calibration Constants

[00102] In order to adjust the magnitudes and phases of the respective signals in the transmit path to provide continuity through the regions of overlap, the relative magnitudes and phases between the respective signals without adjustment may be determined using one or more calibration tones. This may be performed in multiple ways.

[00103] For example, to determine calibration constants for a system such as the system 700 shown in Figures 7-8, the system 700 may be set to a calibration mode, which may operate according to one of the following approaches.

[00104] In a first approach, a calibration tone may be added to the input TX Signal within a region of overlap of the respective frequency band of the first VSG and the respective frequency band of a second, adjacent VSG. The calibration tone may be generated by a digital calibration tone generator (not shown), which may be comprised within the DSP block 702, or may be a separate component. The calibration tone may be added to the input TX Signal using a switch, a multiplexer, or by using any other method known in the art. Preferably, the calibration tone may be generated at the center of the region of overlap. For example, the calibration tone generator may generate a calibration tone 312 within the region 308, as shown in Figure 3b. The respective outputs of the VSG 704a and the VSG 704b will thus each include a representation of the calibration tone. With the output of the VSG 704b turned off or disabled, the magnitude and phase of the representation of the calibration tone 312 present in the output of the VSG 704a may be measured by the calibration receiver 710. The output of the first VSG may then be turned off or disabled, and the output of the second VSG may be enabled. For example, the VSG 704b may be enabled. The representation of the calibration tone 312 present in the output of the VSG 704b may then be measured by the calibration receiver 710. Where the calibration receiver 710 is phase-locked with the VSGs 704a and 704b throughout the time when the two measurements are made, a relative phase difference of the VSGs 704a and 704b may be determined by comparing the phases of the two representations of the calibration tone 312, as measured by the calibration receiver 710. A relative magnitude difference of the VSGs 704a and 704b may also be determined by comparing the magnitudes of the two representations of the calibration tone 312. A calibration constant may then be determined for one or more of the VSGs 704a and 704b, based on the determined relative phase difference and the determined relative magnitude difference. This method may be repeated for each of the regions of overlap.

[00105] In a second approach, an iterative method may be used to determine the relative magnitude and phases. In this method, both the VSG 704a and the VSG 704b may each simultaneously generate an output comprising a representation of the calibration tone 312. Then, the magnitude and phase of the VSG 704b may be iteratively adjusted, seeking to force the respective representations of the calibration tone 312 present in the respective outputs of VSG1 and VSG2 to deconstructively interfere. In other words, the magnitude and phase of the representation of the calibration tone 312 present in the output of the VSG 704b may be iteratively adjusted until the total output power at the frequency of the representation of the calibration tone 312 is minimized. The calibration constant may then be determined by negating the VSG 704b result to rotate it by 180 degrees. This procedure may then be repeated for each overlap region. While this second approach would take longer than the direct measurement of the first approach, this second approach does not require the calibration receiver 710 to be phase locked to the VSGs. Moreover, since the calibration receiver 710 is only making unlocked power measurements, the calibration receiver 710 may be replaced by a power meter, thereby simplifying the hardware requirements of the calibration circuitry.

[00106] In a third approach, respective calibration tones from the VSG 704a and the VSG 704b may be at different frequencies but with some known relationship. In this case the VSG 704a and the VSG 704b may each generate a respective calibration tone at the same time in a synchronized manner, and the magnitude and phase differences may be simultaneously sampled. For example, Figure 3c illustrates calibration tone 312a, which may be generated by the VSG 704a, and calibration tone 312b, which may be generated by the VSG 704b. Similarly, calibration tones 314a and 314b may be generated by the VSG 704b and the VSG 704c, respectively. The complex calibration constant may be computed by taking into consideration the known relationship between the calibration tones. For example, a calibration constant may be determined for one or more of the VSGs 704a and 704b, based on the known relationship between the calibration tones 312a and 312b.

[00107] The calibration constants for each of the VSGs should be determined, or re-determined, each time the phases of the VSGs change relative to each other. For example, the relative phases of the VSGs may change if the relative phases of the LOs of the VSGs change. This may occur, e.g., if the LO frequencies of one or more VSGs change and the one or more VSGs are relocked. In some VSGs, the phase of the LO can be made to be deterministic. If this is the case, then a calibration constant may be determined once and stored for each frequency of the VSG. The stored calibration constant may then be recalled at some future time without the need for recalibration.

Exemplary Embodiments

[00108] Some embodiments may include a method for processing a digital signal using a plurality of parallel processing paths. The method may comprise: providing to each of the parallel processing paths a respective component signal comprising a copy of at least a respective frequency band of the digital signal, each respective frequency band having a respective center frequency and having a respective region of overlap with at least one other respective frequency band. The combination of the respective frequency bands may comprise an aggregate frequency band having an aggregate center frequency, wherein the respective center frequency of each respective frequency band has a respective frequency offset from the aggregate center frequency. At least a portion of each of the parallel processing paths may be phase-locked and time- synchronized with respect to the other parallel processing paths.

[00109] The method may further comprise, at each of the parallel processing paths, processing the respective component signal, wherein said processing comprises: frequency-shifting at least the respective frequency band of the respective component signal such that the respective center frequency is shifted to baseband; filtering at least the respective frequency band of the respective component signal, wherein said filtering of the respective component signals is configured to cause a sum of the component signals to have a unity frequency response within each region of overlap; adjusting at least one of gain and phase of at least the respective frequency band of the respective component signal, wherein said adjusting at least one of gain and phase of the respective component signals is configured to cause the sum of the component signals to have a continuous frequency response over the aggregate frequency band; and converting at least the respective frequency band of the respective component signal to a respective analog signal using a respective vector signal generator associated with the respective parallel processing path.

[00110] The method may further comprise combining the respective analog signals to obtain a composite signal.

[00111] In some embodiments of the preceding method, said converting the respective component signal comprises sampling at least a portion of the signal corresponding to the respective frequency band.

[00112] In some embodiments of the preceding method, said converting the respective component signal is configured to cause the aggregate center frequency to be located at a desired carrier frequency, and each respective center frequency to be offset from the desired carrier frequency by the respective frequency offset.

[00113] In some embodiments of the preceding method, said processing further comprises decimating at least the respective frequency band of the respective component signal to a rate that is less than or equal to a maximum sample rate of the respective vector signal generator. Said filtering may be performed by a digital filter after said decimating and before said adjusting at least one of gain and phase. For example, the digital filter may be a half-band filter.

[00114] Some embodiments may include an apparatus for processing a digital signal. The apparatus may comprise: a processing element comprising a plurality of parallel processing paths, wherein the digital signal processor is configured to provide to each of the parallel processing paths a respective component signal comprising a copy of at least a respective frequency band of the digital signal, each respective frequency band having a respective center frequency and having a respective region of overlap with at least one other respective frequency band, wherein the combination of the respective frequency bands comprises an aggregate frequency band having an aggregate center frequency, wherein the respective center frequency of each respective frequency band has a respective frequency offset from the aggregate center frequency, and wherein each of the parallel processing paths is configured to: frequency- shift at least the respective frequency band of the respective component signal such that the respective center frequency is shifted to baseband; filter at least the respective frequency band of the respective component signal, wherein said filtering of the respective component signals is configured to cause a sum of the component signals to have a unity frequency response within each region of overlap; and adjust gain and phase of at least the respective frequency band of the respective component signal, wherein said adjusting gain and phase of the respective component signals is configured to cause the sum of the component signals to have a continuous frequency response over the aggregate frequency band.

[00115] The apparatus may further comprise: a plurality of output ports, each configured to provide to a respective vector signal generator (VSG) an output of one of the plurality of parallel processing paths; a plurality of input ports, each of the input ports configured to receive from a respective VSG a respective analog signal comprising an analog version of the output of the respective one of the plurality of output ports; and a signal combiner configured to combine the respective analog signals to obtain a composite signal.

[00116] In some embodiments of the preceding apparatus, each of the parallel signal processing paths may be further configured to decimate at least the respective frequency band of the respective component signal to a rate that is less than or equal to a maximum sample rate of the respective vector signal generator. Said filtering may be performed by a digital filter after said decimating and before said adjusting gain and phase. The digital filter may be a half -band filter.

[00117] In some embodiments of the preceding apparatus, each respective analog signal received at one of the input ports may have been frequency-shifted relative to the respective output of the respective output port, such that the aggregate center frequency is located at a desired carrier frequency, and each respective center frequency is offset from the desired carrier frequency by the respective frequency offset.

[00118] Some embodiments may include a method for calibrating a signal processing system including at least a first vector signal generator (VSG) and a second VSG. The method may comprise: providing to a first signal processing path comprising the first VSG a first digital component signal. The first digital component signal may comprise a first frequency band within an aggregate frequency band of a digital input signal, the aggregate frequency band having an aggregate center frequency, and the first frequency band having a first center frequency at a first frequency offset from the aggregate center frequency. The method may further comprise providing to a second signal processing path comprising the second VSG a second digital component signal. The second digital component signal may comprise a second frequency band within the aggregate frequency band of the digital input signal, the second frequency band having a second center frequency at a second frequency offset from the aggregate center frequency, the second frequency band having a region of overlap with the first frequency band, the region of overlap containing a calibration tone, wherein the second VSG is phase-locked and time- synchronized with respect to the first VSG.

[00119] The method may further comprise: frequency shifting each of the first and second component signals, such that the first center frequency and the second center frequency are each shifted to baseband; converting the first and second digital component signals to first and second analog component signals, respectively, using the first VSG and the second VSG; computing a complex calibration constant based on a magnitude ratio and a phase difference, wherein the magnitude ratio is determined by a magnitude of the calibration tone as output by the first VSG and a magnitude of the calibration tone as output by the second VSG, and wherein the phase difference is determined by a phase of the calibration tone as output by the first VSG and a phase of the calibration tone as output by the second VSG; and storing the complex calibration constant in memory, wherein the complex calibration constant is useable to correct phase and gain mismatch between the first VSG and the second VSG.

[00120] In some embodiments of the preceding method, the method may further comprise filtering each of the first and second component signals, wherein said filtering is configured to cause a sum of the first and second analog component signals to have a unity frequency response within the region of overlap. Said filtering may be performed by one or more half-band filters after said frequency-shifting.

[00121] In some embodiments of the preceding method, said converting the first and second digital component signals may comprise shifting each of the first and second component signals, such that the aggregate center frequency is located at a desired carrier frequency, and each respective center frequency is offset from the desired carrier frequency by the respective frequency offset.

[00122] In some embodiments of the preceding method, the method may further comprise decimating the first digital component signal to a rate that is less than or equal to a maximum sample rate of the first VSG and decimating the second digital component signal to a rate that is less than or equal to a maximum sample rate of the second VSG.

[00123] In some embodiments of the preceding method, the first VSG may comprise a first local oscillator and the second VSG comprises a second local oscillator, wherein the phases of the first local oscillator and the second local oscillator are deterministic, such that the stored complex calibration constant is useable to correct phase and gain mismatch between the first VSG and the second VSG without recalibration, even after phase lock between the first VSG and the second VSG is lost and reacquired.

[00124] In some embodiments of the preceding method, said computing the complex calibration constant may comprise: disabling the output of the second VSG; measuring the magnitude and phase of the calibration tone as output by the first VSG while the output of the second VSG is disabled; disabling the output of the first VSG and enabling the output of the second VSG after said measuring; and measuring the magnitude and phase of the calibration tone as output by the second VSG while the output of the first VSG is disabled.

[00125] In some embodiments of the preceding method, said computing the complex calibration constant may comprise iteratively adjusting the magnitude and phase of the second VSG to cause deconstructive interference between the calibration tone as output by the first VSG and the calibration tone as output by the second VSG, such that the total power at the frequency of the calibration tone as output by the first VSG and the second VSG is minimized; and computing the complex calibration constant as the adjustment made to the magnitude and phase of the second VSG, rotated by 180 degrees.

[00126] Although the embodiments above have been described in considerable detail, numerous variations and modifications will become apparent to those skilled in the art once the above disclosure is fully appreciated. It is intended that the following claims be interpreted to embrace all such variations and modifications.