RELATED DOCUMENTS This application is related to a document filed under the Document Disclosure Program, identified as Document # 274736.

BACKGROUND OF THE INVENTION The present invention relates to the field of digital signal processing. More specifically, one embodiment of the invention provides a means for converting a sampled representation of a time-continuous signal sampled by a first clock into a sampled representation of the time-continuous signal sampled by a second clock, where the first and second clocks are not synchronous with each other.

Fig. 1 shows one application, a communication system 10, in which the first and second clocks are typically not synchronized. Communication system 10 comprises a transmitter 12, a receiver 16, and an analog channel 14 connecting transmitter 12 to receiver 16. Transmitter 12 comprises an encoder 18, and possibly other modules not shown. Receiver 16 comprises a sigma-delta modulated (SDM) analog-to-digital converter (ADC) 20, a resampler 22, and a clock recovery means 24. Encoder 18 has an input for digital samples, an output for an analog signal, and a clock input coupled to a low frequency clock L, for timing the output of analog signal segments representing input digital samples. The analog output of transmitter 12 is an input to channel 14, which conveys the analog signal to the input of SDM ADC 20. SDM ADC 20 has a clock input driven by a high frequency clock H which iε used to trigger the digital sampling of the analog signal output by channel 14 at regular intervals. The output of SDM ADC 20 is coupled to resampler 22. The output of resampler 22 is the output of communication system 10, which is the digital sample stream which was input to transmitter 12, with some

delay and possibly some distortion. The output of resampler 22 is also an input to clock recovery means 24, which outputs a recovered clock L' to a second clock input of resampler 22. In alternate embodiments of communication system 10, clock L' is not recovered from the digital sample output, but is provided to resampler 22 via an external clock channel 21 from transmitter 12, or is supplied to receiver 16 by some other external clock source.

Communication system 10 is used to transfer digital samples from one point to another, over analog channel 14.

Digital data is converted to an analog signal in transmitter 12, sent over analog channel 14, digitized at receiver 16, and digitally manipulated to recover the digital data originally sent. Such digital-analog systems are used for modem communications, compact disk players, digital audio tape, mobile telephones, and the like.

Typically, the digital samples take on a value selected from a set of finite possible values, where the particular value is determined by digital data which is to be transferred. For example, in a specific embodiment of a modem communication system, digital data in the form of zeroes and ones (bits) is input to a transmitter at a rate of 9600 bits per second. The transmitter selects these bits four at a time, forming a "symbol", and generates a digital value ranging from 0 to 15. An encoder within the transmitter accepts these digital symbols and outputs a segment of an analog signal associated with the digital symbol for the duration of the clock cycle. As is well known in the art, to fully recover the digital symbol, the duration of the analog segment must be at least two clock cycles of clock L. In other words, encoder 18 will output a segment representing a symbol for at least the period of two clock cycles of clock L.

However, as far as the present system is concerned, the actual symbols are not important, since these can be determined from the samples of the analog signal, if the timing is correct. For example, if two samples are taken of each analog symbol segment representing a symbol, the particular symbol can usually be determined (noise may prevent

prefect recovery) . However, if receiver 16 does not know where the boundaries of the analog segments are, then it is possible that samples from adjoining symbols would be combined. Thus it is important to be sampling the analog channel signal synchronized with the incoming signals, usually at a rate comparable to the clock rate L (the low frequency clock) . However, this is not always possible or convenient, such as where the analog signal is sampled at a much higher rate, as is the case with SDM ADC's. In a typical digital receiver, the analog signal is first digitized, and then the signal is manipulated by a digital signal processor or digital filter circuits. One notable difference between an analog signal and a digital signal is that the analog signal is time-continuous and amplitude-continuous. Time-continuity means that the analog signal can be measured at any point in time, and it will have a value at that point in time, whereas amplitude-continuity means that the value at the measured point in time could have an infinite number of values within a finite range. By contrast, once digitized, the analog signal is represented by a digital signal, which is a series of digital samples. The digital samples can only take on a finite number of values, usually the value closest to the sampled analog signal, and the digital signal is not defined between digital samples in the series.

As the foregoing discussion points out, a receiver must accurately sample the analog signal, minimizing the error introduced by the fact that the digital signal is a finite approximation to the analog signal. To recover the data represented by the analog signal, it is not enough to recover the signal, since the boundaries of each analog signal segment must be found. In some systems, the analog segment (of the finite set of possibilities) can be determined from a single sampling of the analog signal, at a fixed point in the analog signal segment, usually the center. Of course, to know where the center of the segment is, the clock L which the encoder used to encode the digital samples into analog signal segments, must be recovered or provided to the receiver.

In some communication systems (as in the example of Fig. 1) , clock L is sent over a separate clock channel 21 from transmitter 12 to receiver 16, and in others it is provided by an external clock source (as would be the case in a digital mixer with asynchronous clocks) . However, since clock channel 21 uses communication capacity, in systems where communication capacity is at a premium, clock L is recovered from the analog signal itself. In a compact disk player, for example, channels are not at a premium, so clocking information can easily be provided on a clock channel. However, for telephone data transmissions, an additional clock channel would be costly. In the digital mixer example, of two asynchronously sampled signals to be mixed, one is resampled, using the other as the resampled clock. Many methods of sending analog data signals with recoverable clock information are known. Whether the clock is transferred separately or is recoverable from the analog signal, a problem remains in that the two clocks, the sampling clock H and the signal clock L are not synchronous. One obvious way to keep clock H and clock L in sync is to have clock H generated using a clock multiplier driven by clock L, in other words, phase-locking clock H to clock L. Since clock H is a higher frequency than clock L, the jitter of clock L is amplified at the frequency of clock H, and thus is one reason why phase-locking the clocks would be unacceptable. Lowering the frequency of clock H is not a viable solution, since clock H needs to be high so that SDM ADC 20 can oversample the analog signal to the appropriate resolution.

Fig. 2 is a block diagram of a typical resampling receiver 25, as would be used in communication system 10 (Fig. 1) . Receiver 25 comprises a SDM ADC 26, a resampler 28 coupled to the output of SDM ADC 26, and a clock recovery means 29 which adjusts the phase of the clock used to resample a signal. Clock recovery means 29 receives the digital data stream output by resampler 28 and provides a phase shift value or a recovered clock to an input of resampler 28. In alternate embodiments, the clock is generated by means other than recovery from the signal itself.

SDM ADC 26 comprises a noise shaper 30 for shaping the analog input to SDM ADC 26, an A/D 32 for converting the shaped analog input to one of N digital sample levels at each clock tick (a timing point such as a rising or falling edge) of an oversampling clock input to SDM ADC 26, and a low-pass filter (LPF) 34, which filters and decimates the digital sample stream. "Analog-to-digital converter" refers to the converter itself (such as A/D 32) , whereas "sigma-delta modulated analog-to-digital converter", or just SDM ADC, refers to the converter and the associated filtering conventionally associated with sigma-delta converters (such as SDM ADC 26) , to the extent that filtering is used. This difference is indicated in Fig. 2, by SDM ADC 26 and A/D 32.

Resampler 28 comprises an upsampler 36 coupled to an input of resampler 28, a LPF 38 coupled to the output of upsampler 36, and a sample selector 40 coupled to an output of LPF 38. In alternate embodiments, LPF 38 is replaced with an interpolator.

Receiver 25 transforms an analog, time-continuous signal into a stream of digital samples representing the value of the analog signal at clock ticks of a clock L', as follows.

The analog signal is applied to noise shaper 30, which outputs a noise-shaped analog signal to A/D 32, as is conventional for SDM ADC's. A/D 32 samples the input analog signal at a clock rate H which is much higher (oversampling) than the Nyquist rate for the input analog signal (twice the bandwidth) . The output of A/D 32 is fed back to noise shaper 30 through a digital-to-analog converter (D/A) 41. Noise shaper 30 shapes the analog signal to reduce the quantization error noise caused by A/D 32 sampling the amplitude-continuous input analog signal at only N levels (typically N=2 or 3) . The quantization noise is reduced by sampling the input signal at a high rate, moving the noise (using the noise shaper) to a higher frequency range than the signal bandwidth, and then low-pass filtering the signal to eliminate the high frequencies containing the noise.

LPF 34 filters away the high frequencies, and decimates the data sampling rate by a factor of D, to attain a

sampling rate comparable to twice the signal bandwidth. The decimation to a clock rate of H/D is done to simplify processing of the digital samples, as their number is reduced by a factor of D, and also to eliminate redundancy of digital samples representing a band-limited signal. The decimation does not result in loss of information, since the analog signal is band-limited to frequencies below (1/2 * H/D) . Using a sine filter comprising N integrators, a decimator, and N differentiators reduces hardware needs by a factor of roughly D/2, however such a filter introduces a fixed decimation phase, which is an undesired side effect when resampling to a different, and possibly varying, sampling phase.

Since the digital samples at clock rate H/D output by SDM ADC 26 do not coincide with the ticks of clock L (since H, or H/D, and L are independent of each other) , the signal must resynchronized to the original clock L. This is done in receiver 25 by resampling the signal with a new clock, L', which is phase-locked to the original clock L. Since the ticks of clock L and H/D are not necessarily coincident in time because of the interclock drift, the values of the analog signal at the ticks of clock L' are not available directly from the digital samples at clock rate H/D.

Resampler 28 provides these values at the clock L' ticks, by estimating the value of the time-continuous analog signal for the times of the clock L' ticks from the samples of the signal at the clock H/D ticks, which are available at the output of SDM ADC 26. Fig. 3, discussed below, illustrates the resampling process. A typical low frequency clock L for a modem is 9600 or 19200 hertz, and a typical high frequency clock H is 2.5 megahertz (or 2,457,600 hertz, with D=128 or 256), or higher if the receiver can process data at a high rate. Clock H is typically derived by a stable crystal oscillator. Although clock L might originally also derive from a stable oscillator, the clock L oscillator is free to drift relative to clock H, since the oscillators are independent. Furthermore, changes in the analog channel delay introduce apparent drifts of clock

L. Where the original clock L is recovered at receiver 25 from the analog signal, the recovered clock will cancel out any jitter caused by channel delay, but the jitter on clock L' will cause noise problems if clock H is tied to clock L' . Fig. 3(a) is a graph of the time-continuous analog signal applied to SDM ADC 26. Fig. 3(b) is a graph of the output of SDM ADC 26, which comprises digital values sampled at discrete times at a rate of H/D. Fig. 3(e) is a graph of digital values representing samples of the analog signal at times coincident with ticks of clock L'. Figs. 3(c)-(d) show on method of deriving the values at clock L' from the values at clock H/D.

Fig. 3(c) is a graph of the output of upsampler 36, where digital samples with zero values are interleaved between samples at clock rate H/D to increase the number of samples.

Fig. 3(d) is a graph of the output of LPF 38, overlaid with a graph of the original analog signal. Although the additional samples in Fig. 3(d) do not exactly sample the original analog signal, they are close because the analog signal is a band-limited signal limited to frequencies below

(1/2 * H/D). The digital samples in Fig. 3(e) are computed by interpolation of a number (in this case, 3) of the upsampled and low-pass filtered samples.

As shown in Fig. 2, when a SDM ADC and a resampler are combined, the digital signal is downsampled, filtered, upsampled, and re-filtered, all resulting in a loss of accuracy and consuming unnecessary signal processing resources. The input analog signal is first digitized at one clock rate, H, downsampled to another, H/D, upsampled to yet another, U*(H/D), and then resampled to a clock rate L' . From the above it is seen that an improved means for resampling sampled signals at an arbitrary phase is needed.

SUMMARY OF THE INVENTION An improved resychronizing sampler is provided by virtue of the present invention.

In one embodiment of a digital resampling system according to the present invention, a first digital signal is

converted to a second digital signal, where both signals represent the same analog signal sampled at two different clock rates which are not phase-locked together. The system includes a non-decimating filter, a phase indicator, a sample selector, a weight generator, a weighted averager, and an output clocker.

The non-decimating filter, clocked by the first clock, outputs filtered samples, one per clock cycle of the first clock, except that in some embodiments, the filter does not output filtered samples which the filter determines will not be used further down the signal path.

The phase indicator determines the relative phase position of the first and second clocks to determine the position of a tick (a rising or falling edge, or other identifiable point of a cycle) of the first clock with respect to a tick of the second clock, and outputs an integer phase signal representing an integer number identifying a clock cycle of the first clock in which a tick of the second clock occurs, and a fractional phase signal representing a fraction identifying a position of the tick of the second clock within the clock cycle of the first clock. The integer number might be a modulo count of the number of first clock ticks between a time origin point and the tick of the latest clock cycle of the second clock, where the modulo is a number close to the ratio of the first and second clock frequencies. In some embodiments, the integer phase output is an arbitrated clock.

The sample selector selects filtered samples from the filtered samples provided by the non-decimating filter based on the integer phase value. The sample selector selects M of the filtered samples per clock cycle of the second clock, the particular selections being those samples near the tick of the second clock. The weight generator generates M weights based on the fractional phase, and the weight averager weights the M filtered samples by the M weights, and outputs a sum or an average of the weighted samples. The output clocker synchronizes the output of these averaged samples, which are averaged once per cycle of the second clock, to the ticks of the second clock, if necessary.

In another embodiment of the present invention, the resampling system is used in a SDM ADC system, where the first clock is a high frequency sigma-delta sampling clock, and the second clock is a signal clock either recovered from the analog signal, provided by a clock channel, or an external clock source. In the SDM ADC system, the non-decimating filter is usually, but not necessarily, a low-pass filter.

In yet another embodiment of the present invention, the resampling system is used in a SDM digital-to-analog converter (DAC) system, where digital data clocked at a low frequency clock is selected into a group of M samples, also sampled at the low frequency clock. A phase detector detects the relative phase of the low frequency clock and a high frequency sampling clock. Since the clocks are independent, they will drift relative to each other, and the relative phase will not be constant. The phase detector outputs an integer phase signal or an arbitrated clock (which identifies the high frequency clock tick nearest or following a tick of the low frequency clock) , and a fractional phase signal or value. The fractional phase clock indicates where the low frequency tick falls within the clock cycle of the identified clock H cycle.

The fractional phase value is applied to a weighting means, which weights the samples in the group of M samples, and an input placer places one of the M weighted samples on a high frequency output line each clock cycle of the high frequency clock. The high frequency signal is then output to a SDM DAC which is operating with the high frequency clock. Thus, the low frequency digital signal is resampled to the high frequency clock before being input to a digital-to-analog converter (D/A) , and the resampling takes into account the relative drift of the high and low frequency clocks. In an alternate embodiment, the group of M samples are filtered by a finite impulse response (FIR) filter, the input placer averages the M filtered samples supplied to it, and applies that one averaged value to its output for each clock H (high frequency clock) tick in a clock L clock cycle.

If a low-pass or other filter is used after the input placer and before the SDM DAC, a filter which can accept

input samples at each tick of the high frequency clock is used. However, another filter which accepts inputs at M freely selectable, consecutive high frequency clock ticks could also be used. The selectabililty ensures that each sample which is used later is input to the filter, but only those samples which are known in advance to be needed are input.

A further understanding of the nature and advantages of the inventions herein may be realized by reference to the remaining portions of the specification and the attached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 is a block diagram of a communication system; Fig. 2 is a block diagram of a known method of sampling an analog signal and resampling and synchronizing the sampled signal to a clock recovered from the analog signal;

Figs. 3(a)-(e) are graphs illustrating a resampling operation; Fig. 4 is a block diagram of a embodiment of a sampling and resampling system according to the present invention, including a SDM ADC, a low-pass filter, and a resampler;

Fig. 5 is a block diagram of one embodiment of a SDM ADC used an the system of Fig. 4;

Fig. 6 is a block diagram of one embodiment of a low-pass filter used in the system of Fig. 4;

Fig. 7 is a block diagram of an alternate embodiment of a low-pass filter used in the system of Fig. 4; Fig. 8 is a block diagram of an embodiment of a resampler used in the system of Fig. 4;

Fig. 9 is a block diagram of an SDM DAC system where data clocked at a low rate is output clocked at a higher, unrelated rate; Fig. 10 is a block diagram of a non-decimating low-pass filter as used in the SDM DAC system shown in Fig. 9; Fig. 11 is a block diagram of an SDM DAC as used in the SDM DAC system shown in Fig. 9;

Fig. 12 is a block diagram of an alternate embodiment of a low-pass filter used in the SDM DAC system shown in Fig. 9;

Fig. 13 is a block diagram of a digital-to-digital resampling system according to the present invention; and

Fig. 14 is a block diagram of a digital-to-digital resampling system using an intermediate high-frequency clock.

DESCRIPTION OF THE PREFERRED EMBODIMENTS Fig. 4 is a block diagram of an sigma-delta modulating (SDM) , resampling ADC system 42 which converts an analog signal comprising analog signal segments clocked at a clock rate L into a digital signal clocked at a clock rate L', where clock L ¹ is phase locked to clock L, and the digital signal comprises digital samples representing samples of the analog signal segments.

ADC system 42 comprises a SDM ADC 44, a non-decimating low-pass filter (LPF) 46, a resampler 48, and a clock recovery means 50. In alternate embodiments, clock recovery means 50 is not used, and clock L' is provided by an external clock signal. The input to ADC system 42 is an analog signal, and where the external clock is used, a clock L' provided on clock channel 51, or otherwise, indicates the division of the analog signal into analog signal segments. The output of SDM ADC 44 is a digital signal with a clock rate H, which is input to LPF 46. The output of LPF 46 is a digital signal with a clock rate H (in contrast to the typical decimating low-pass filter, which has a lower output rate), which is an input to resampler 48. The output of resampler 48 is the output of ADC system 42. If clock recovery means 50 is used, its input is the output of resampler 48, and the output of clock recovery means 50 is clock L ¹ , which is input to a resampling clock input of resampler 48. On the other hand, if clock channel 51 is used, it is input to the resampling clock input of resampler 48. In some embodiments, clock L' is not a physical signal, but is a series of numbers indicating the timing of the cycles of clock L' . As is well known in the art of clocks, a physical clock

signal can be reconstructed from a series of cycle timing indicators, and a physical clock can be deconstructed into a series of cycle timing indicators. Clock H can also be deconstructed into numbers. For example, where the digital signal of interest is a signal sampled at clock rate H, clock H can be provided by a simple counter which counts the number of samples which have past a particular point in a signal processor.

In alternate embodiments, a design for ADC system 42 allows for a partially decimating LPF 46, in which case the output of LPF 46 is a digital signal with an intermediate clock rate I. This can be implemented as a decimating filter stage followed by a non-decimating filter.

Fig. 5 is a block diagram of one possible example of SDM ADC 44, a second-order sigma-delta converter of one given type. A forward signal path of SDM ADC 44 comprises, in order, adders 52, 54, an integrator 56, an amplifier 58, an adder 60, an integrator 62, and N-level analog-to-digital sampler (A/D) 64. All components in the forward path input analog signals (time and amplitude continuous) , and all, except A/D 64, output analog signals. The output of A/D 64 is a digital signal comprising digital samples each representing one of the N levels, output once per clock cycle of clock H. The feedback path of SDM ADC 44 comprises digital-to-analog converter (D/A) 66, and amplifiers 68, 70, and 72. D/A 66 is coupled to the digital output of A/D 64, and converts its output back to analog. Amplifiers 68 and 70 receive their input from the output of D/A 66; the output of amplifier 68 is an input to adder 54 and the output of amplifier 70 is an input to adder 60. Amplifier 72 has an input coupled to the output of integrator 62, and the output of amplifier 72 in an input to adder 52. The amplification factors of amplifiers 58, 68, 70, 72 are C ₀ , C _χ , C ₂ , C ₃ , respectively. Depending on the particular design, these numbers can be greater than one, equal to one (in which case, the amplifier can be eliminated) , less than one, or even zero. In one application, cf a modem, the values might be C ₀ = 1/2, C _α = -1/2, C ₂ = -1/2, and C ₃ = 0.

In operation, an analog signal input to SDM ADC 44 is output as digital N-level samples at a clock rate of H. The number of levels, N, is often chosen to be a power of two, and N=2 provides a 1-bit output. A 1-bit sampling eliminates the problem of having a multitude of voltage levels with which to compare the input signal, but 1-bit sampling causes considerable quantization noise. This quantization noise is moved (shaped) into higher frequency bands by the analog components of SDM ADC 44, as is well known in the art of sigma-delta converters.

Fig. 6 is a block diagram of LPF 46, which filters out the high frequency components of the digital signal output by SDM ADC 44, which consists mostly of quantization noise. Significantly, the number of samples output by LPF 46 is the same as the number of samples input.

LPF 46 has a forward path comprising several signal manipulating elements which are, in order, adder 80, adder 82, unit delay 84, which outputs its input one clock cycle later, multiplier 86, adder 88, unit delay 90, multiplier 93, and adder 91. The adders are used to add either feedback signals (adders 80, 82, 88) or feedforward signals (adder 91) to the forward path signal. Several feedback paths are also present. A multiplier 92 applies the output of unit delay 90 to one input of adder 80 after multiplying the output by C ₀ ; a multiplier 94 applies the output of unit delay 84 to one input of adder 82 after multiplying the output by C _x ; a multiplier 96 applies the output of unit delay 90 to one input of adder 88 after multiplying the output by C ₂ . A feedforward path from the output of unit delay 84 is applied to an input of adder 91 after being multiplied by a multiplier 95, which multiplies the output by C ₅ . Multiplier 86 and multiplier 93, on the forward path, multiply the forward signal by C ₃ , and C ₄ , respectively. LPF 46 thus forms a second-order infinite impulse response (IIR) filter. Depending on the particular design, C ₀ , C _α , C ₂ , C ₃ ,

C ₄ and C ₅ can each be greater than one, equal to one (in which case, the amplifier can be eliminated) , less than one, or even zero. In the prior modem example, the values might be C ₀ =

-1/128, C- _L = 1, C ₂ = 1-1/128, C ₃ = 1/64, C ₄ = 1/128, and C ₅ = 0.

Although Fig. 6 shows a second-order IIR, a preferred filter would have at least one more order than the noise shaper of the SDM ADC. This requirement has to do with the elimination of noise in the eventual output of the filter. If a second-order SDM noise shaper is used, the noise is shaped to rise in higher frequencies at a rate of 12 db/octave. If a second-order filter is used, the filter roll-off is 12 db/octave, so the noise would be flat up to the high frequencies, and therefore, at least a third-order filter, with 18 db/octave roll-off, should be used. Such a filter is easily constructed by placing two LPFs such as LPF 46 in the signal path in series. The second filter can be reduced to a first-order filter (giving a total of three orders) by setting C ₀ = C ₂ = C ₃ = C ₄ = 0, eliminating unit delay 90 if that saves hardware or software, and setting C _λ = 1 - 1/128, and C ₅ = 1/128. Although one set of values is given, other values might be preferred for other applications. Furthermore, the values which are expressed as powers of two as much as possible, might not be ideal where more resolution in the values is possible.

Fig. 7 is a block diagram of an alternate embodiment of a low-pass filter 46*, which is used in some embodiments of ADC system 42. LPF 46' comprises an integrator path, a selector system 111, and a differentiator array. The integrator path comprises N integrators, of which integrators 102, 108, and 110 are shown. Each integrator is similar, however only integrator 102 is shown in detail. Integrator 102 comprises an adder 104 (which is a modulo adder) and unit delay 106. An input of integrator 102 is coupled to an input of adder 104, the output of adder 104 is coupled to the input of unit delay 106.

The output of unit delay 106 is the output of integrator 102, and the output of unit delay 106 is also fed back to a second input of adder 104. In this way, integrator 102 provides the classical integrator impulse response, z' fl-z ^-1 ) .

Unit delay 106 is clocked by clock H which, as Fig. 4 shows, is synchronous with the samples of the digital signal input to LPF 46'. Each of the other N-l integrators also have unit delays clocked by clock H. The output of integrator N 110 is provided to selector system 111. Selector system 111 inputs integrated samples from integrator 110 at clock rate H, and outputs a number M of consecutive samples from integrator 110. The particular set of consecutive samples are determined by the arbitrated clock provided by resampler 34 (described along with Fig. 8). LPF 46' also comprises M differentiator stages. Stage 1 116 receives a first input from selector system 111, and outputs a differentiated signal of the input. Also shown are stage 2 128 and stage M 130, coupled to separate outputs of selector system 111. The details of one stage, stage 1 116 are shown. A stage comprises N differentiators clocked by clock L'. A differentiator, such as differentiator 1 118 comprises a unit delay 120 clocked by clock L', and a subtractor 122 (which is a modulo subtractor) , which outputs the difference between the output of unit delay 120 and the input of unit delay 120, the providing a filter with the impulse transfer function (1-z" ¹ ) .

LPF 46' is an Nth order sine filter, but one which effectively does not decimate its output. In a typical sine filter, the output is decimated at a fixed phase, and the elements in the signal path beyond the filter must adjust to having this fixed sampling phase. In the system of Fig. 2, the adjustment is the addition of upsampler 36. Thus, a filter like LPF 46' with H/L differentiator stages can output as many values as are input, by setting M=H/L. However, in practice, M=2 or 3 is often sufficient, and by timing the selection of samples so that only samples that are going to be used are processed, much hardware or software can be saved.

There are a number of ways of implementing selector system 111, one of which is shown in Fig. 7. Therein, selector system 111 comprises an M-stage delay line 112 and a latch 114, with delay line 112 clocked at clock rate H, and latch 114 clocked at clock rate L. Because the M values sent

to the differentiator stages are timed against the tick of clock L, which will likely vary with respect to the input clock H, only M differentiator stages are needed to cover all the phases used in the resampling process. In some embodiments of LPF 46', selector system 111 comprises a counter and a demultiplexer, where the counter counts clock H ticks starting from each clock L tick, and the demultiplexer passes the first sample of M samples to the first of M output lines, then demultiplexes the next M-l input samples onto the remaining M-l output lines, and then ignores the next values until the next clock L tick. In other embodiments, the clocks of the first stages of each differentiator stage is timed to latch the correct input sample. Although for illustration, N and M are at least three in Fig. 7, values lower than three are possible, depending on design requirements. For example, the higher H is, the lower M can be. Also, the innermost integrator and differentiator could be replaced by a hold circuit as is well known in the art of digital sine filter design. Also, other means could be provided to lead the clock L ticks to center the clock tick with respect to the contents of the M-stage delay line, if necessary.

Depending on design requirements, either LPF 46 or LPF 46* could be used. LPF 46 is more efficient in terms of hardware used (or computing power used, if implemented in software) , and provides all samples. On the other hand, LPF 46' does not introduce group delay into the digital signal, and does provide the M samples out of H/L which are actually used. LPF 46 can be made even more efficient with the proper selection of multiplier coefficients. If the coefficients (as an above example uses) are powers of two, the multipliers can be replaced with bit shifters.

Fig. 8 is a block diagram of resampler 48. Resampler 48 receives input from either LPF 46 (see Figs. 4, 6) or LPF 46' (see Figs. 4, 7), and outputs the desired signal, a digital representation of the analog signal originally input to ADC system 42, but one which is sampled at

clock rate L'. In some embodiments where a clocking signal is provided, clock L' is the same as clock L.

Resampler 48 comprises a sample selector 138, a phase detector 144, a weight generator 146, a weighted averager 139, and an output latch 152. Sample selector 138 comprises an M-stage delay line 140 and a latch 142. Weighted averager 139 comprises a multiplier 148 and a summer 150.

Delay line 140 is clocked by clock H, receives an input sample from LPF 46 once per clock H cycle, and stores the last M samples received. The M outputs of delay line 140 are input to latch 142, which latches them at the clock tick of the arbitrated clock L' . The arbitrated clock ticks in coordination (such as following them by a suitable delay) with clock ticks of clock H, but only those following clock L' ticks. Thus, the arbitrated clock can prevent the M values from being latched while they are changing in the M-stage delay, but the arbitrated clock doesn't have all the information about the position of ticks of clock L ¹ , only which clock H tick was closest. In this sense, the arbitrated clock is an indication of the integer phase only.

The M output lines are input lines for multiplier 148. Phase detector 144 has a low clock input, which is the resampling clock input of resampler 48 on which clock L' is received and a high clock input on which clock H is received, although in some embodiments, clock L' is represented by values in memory indicating the position of each cycle of clock L' rather than an physical clock signal in which the timing of each cycle of clock L' is determined by the arrival time of a clock L' tick at the resampling clock input of resampler 48. Phase detector 144 has an integer phase output, which clocks latch 142 (if LPF 46 is used) or in output to LPF 46' (if LPF 46' is used; see Fig. 7). Phase detector 144 also has a fractional phase output, which is an input to weight generator 146. The integer phase output can be an arbitrated clock as discussed above.

Weight generator 146 has M outputs for M weighting values, which are inputs to multiplier 148. Multiplier 148 has M outputs, which are inputs to summer 150, which has one

output. The one output of summer 150 is an input to output latch 152, which also has a clock input, clocked by clock L". The output of output latch 152 is also the output of resampler 48 as well as the output of ADC system 42. In alternate embodiments, where LPF 46' is used, the functionality of sample selector 138 is provided by sample selector 111 in LPF 46', and the output of LPF 46', which iε M digital signal lines, are inputs to multiplier 148. If LPF 46' iε used, the integer phase signal, which supplies the arbitrated clock to latch 142, is instead supplied to LPF 46'.

In effect, what resampler 48 does is select the M samples at clock rate H which are near a tick of clock L' , weight the M samples based on their distance from the tick of clock L', take an average of the weighted samples, and output that averaged value as the value of the signal at the tick of clock L'. Whether an average or a sum of the M weighted εampleε is taken is not important, since M is a constant value, and resampler 48 is a digital εystem, so a division by M is a εimply added function. However, logically, referring to the output of reεampler 48 as averaged samples makes more sense.

Non-decimating filter LPF 46 and quasi-non-decimating filter LPF 46' provide M samples from the M ticks of clock H nearest to the tick of L' , which are then used to interpolate the value of the original signal at the tick of L' . In some designε, the resampler cannot handle data at the rate of clock H, so a decimating filter is included in the signal path to lower the sample rate from H to H'. Of course, with the lower clock rate of H*, the M samples will not be as cloεe to the tick of clock L' and therefore won't give aε good an approximation for the original signal. The decision to trade off accuracy for lower sample rates depends on the application, but in any case, the lower clock rate H' should preferably be high enough that upsampling is not required to capture M signal samples near the tick of clock L'. If greater accuracy is needed, M can be increased. With the two inputs to phase detector 144, it determines a phase offset, which is a real number (integer and

fraction) indicating the relative offset of ticks of clock H and clock L' . For example, if the rising edges of clocks H and L' are uεed aε tickε, the phase offset would indicate where the rising edge of clock L' was relative to the rising edge of clock H. Of course, since the clockε are independent, this phase offset value will likely change for each rising edge of clock L' . The unit of meaεurement of the phase offset is the number of clock cycles of clock H, and in embodiments where the L' ticks are repreεented by numberε, the numberε are in time unitε εynchronized to the time units used to measure clock H, in which case phase detection is the operation of subtracting two numbers. Logically, in other embodiments, the two outputs of phase detector 144 can be thought of as an integer clock, or arbitrated clock, as described above, and a fractional phase output signal.

Since a reference point is needed, when ADC system 42 begins operation, a rising edge of clock H will be designated the origin, and all meaεurementε of phaεe will be to that point. Because the actual origin is not all that important to the operation of ADC system 42, any cycle can be used, and the origin can be moved every D clock cycles, thus giving a phase offset which is a modulo D real number. This shifting of the origin keeps the phase offset from growing monotonically. Furthermore, if D is chosen to be the nearest integer to the ratio H/L', then the phase offset value will only change by the small difference between H/L' and D. Thus, the phase offset describes the position of a rising edge (or other tick) of clock L' with respect to the rising edges (or other ticks) of clock H, modulo D. Phase detector 144 separates the phase offset into an integer phase and the remaining fractional phase. These two valueε, which are updated at the L' clock rate, are output by phaεe detector 144 aε the integer phaεe εignal and the fractional phaεe εignal. The integer phaεe εignal, or value, iε uεed for εelecting M εampleε which are input to resampler 48 at the H clock rate. Because the integer phase value identifies the clock cycle of clock H in which a tick of clock L' fallε, the input sample (clocked by clock H) which is

nearest in time to the tick of clock L' can be identified. In one particular embodiment, M=3. Where M=3, sample selector 138 selects the clock H sample closest to the clock L' tick, and one sample on either side of the first selected sample. In another embodiment, M=4, and sample selector 138 selectε the two clock H εampleε moεt previouε in time to the clock L' tick and the two clock H samples following the tick. Even if the M sampleε following the clock L' tick are uεed, the signal can then later be shifted by an appropriate amount if necesεary.

For proper interpolation, the M εamples should be weighted differently depending on their distance from the clock L' tick. For example, where M=4, the two samples closeεt to the clock L' tick will be weighted more heavily than the two εampleε further out on each εide, and if the clock L' tick iε cloεer to one of the two inner εampleε, that cloεer εample should be given more weight than the other samples. In one example, M=2 and one of the weights given to one of the two sampleε iε proportional to the diεtance from the clock L' tick to the other εample, i.e., a claεεical linear interpolation of a value between two pointε. If M=3, a parabolic interpolation can be done.

Weighting generator 146 performε this procesε of generating weighting valueε for weighting the M εelected εamples. It generateε M weightε, one per each of the M selected samples, from the fractional phaεe value which indicateε the relative position of the clock L' tick and the M sampleε. Becauεe of sample selector 138, the possible poεitionε of the clock L' tick within the M εelected samples can only vary by one full cycle of clock H, because otherwise, different εamples would have been εelected (neglecting any conεtant phaεe εhift of clock L'). For example, if M=4, the tick of clock L' will fall εomewhere between the middle two εampleε. If M iε odd, such as M=3, the particular samples used depend on how sample εelector 138 is implemented. In one implementation, the center sample of the three selected sampleε is the sample occurring juεt before the clock L' tick,

whereas in other implementations, the center sample is the εample which iε the cloεeεt either before or after the tick.

Weighted averager 139 outputs a weighted average (or sum, as discuεεed above) of the M selected sampleε, each weighted by one of the M weightε. Multiplier 148, if built in digital hardware, might be a parallel multiplier which accepts the M selected samples, pairs each of the M selected εampleε with an asεociated weight, and outputε the product of each of the pairε. If implemented in a digital εignal proceεεor, multiplier 148 might be an array multiply routine. In combination with εummer 150, which sums the M outputs of multiplier 148, weighting averager 139 essentially produces a scalar dot product of two vectors, a vector of M selected sample values and a vector of weights. Although weighting averager 139 calculates an output for each tick of clock L' , an output latch 152 iε uεed to enεure that the timing of the output is synchronized to clock L' itεelf. Of course, if the values output by resampler 48 do not need to be synchronous (such as where clock L' iε an imaginary clock present only in software) , then output latch 152 is not needed. Also, if the componentε of resampler 48 always use the same amount of time to do calculations, then output latch 152 is not needed.

Fig. 9 is a block diagram of a εigma-delta modulated digital-to-analog (SDM DAC) εystem 152 where data clocked at a low rate (clock L) is output clocked at a higher, unrelated rate (clock H) to a SDM DAC. SDM DAC system 152 compriseε a finite impulse response (FIR) filter 153, a sample weighting means 158, a sample rate converter 163, a SDM DAC 164, an analog filter 166, and a phase detector 168.

FIR filter 153 comprises an input for receiving data at a clock rate L, a clocking input, and M outputs for filtered samples. Sample weighting means 158 comprises M inputs for M filtered sampleε, an input for a weighting phaεe value, and M outputε for M weighted samples. Sample rate converter 163 comprises M inputs for M weighted samples, an input for a placement phase, a clocking input, and a clocked output. SDM DAC 164 compriseε an input for a digital signal,

a clock input timing the digital signal, and an analog signal output.

The data input of FIR filter 153 receives the data to be converted from digital to analog, and which represents sampleε of the εignal at tickε of clock L. The output of FIR filter 153 iε M filtered signals. The FIR filter shown in Fig. 9 compriseε Kth order FIR filterε, although some of the filters might be pass-through filterε (i.e., tranεfer function = 1 with matched delay) . Since M independent Kth order filterε would uεe K delay εtageε each, and the K delay εtageε of each filter would contain the same data, these can be combined into one delay line and M setε of K valueε.

The M outputε of FIR filter 153 are the M filtered εample inputε to εample weighting means 158, and the M weighted outputs of sample weighting means 158 are the M weighted signal inputs to sample rate converter 163. In some embodiments, sample rate converter 163 compriseε an input placer 160 coupled to receive the M weighted εignal inputε and an output which iε firεt filtered by a low-paεs filter 162, before being output. In either case, the output of sample rate converter 163 iε coupled to the digital εignal input of SDM DAC 164. The clock input of SDM DAC 164 iε clocked by clock H. The output of SDM DAC 164 iε an input to analog low-paεε filter 166, and the output of analog low-paεε filter iε the analog εignal output of the digital-to-analog εyεtem.

The operation of SDM DAC εyεtem 152 will now be deεcribed. The following discussion assumes that the clock L is not tied to clock H. Syεtem 152 will still work if they are phase locked, but it would not be aε uεeful. For example, if clock L and clock H are phaεe locked, FIR filter 153, sample weighting means 158 and sample rate converter 163 could be replaced with a simple counter to count the number of clock H cycles and output each input data value for a fixed number of clock H cycleε. The following diεcuεsion alεo aεεumeε that clock H is a higher frequency clock than clock L, as sigma-delta signal processing syεtemε operate at a higher clock rates than the signal which is being procesεed.

When the input digital signal is received by filter 153, the signal is filtered into M filtered signals. In a simple embodiment, filter 153 acts only like a delay line, and the M filtered outputs comprise unfiltered samples delayed by up to M ticks of clock L. Where M=2, two input samples are passed to weighting means 158. In a more complex case, the M filtered values output by filter 153 are approximationε of the analog εignal at M adjacent tickε εeparated by the period of clock H. In the complex case, one of the M εignalε can be the input unfiltered except for a matching delay, and the other εignalε are filtered by an FIR uεing the K εtageε. A higher value of K reεultε in a better approximation of the analog εignal at adjacent clock ticks. In both caseε, M εignalε are applied to weighting meanε 158 per clock L tick, however the cases are treated differently in input placer 160 (see below) .

Phase detector 168 operates in a similar manner to phase detector 144, detecting the phase difference between tickε of clock L and clock H, and outputting an integer value (or an arbitrated clock) and a fractional value for each cycle of clock L, indicating the poεition of the clock L tick with reεpect to the clock H tickε. In εome embodimentε, the integer phaεe output indicates a count of the number of clock H cycles since the last clock L tick, whereaε in other embodimentε, a count of clock H cycleε is kept modulo εome number to keep the count in reasonable bounds, and the integer phaεe output indicateε the clock L tickε aε a function of the count of clock H cycles. As should be apparent from this discusεion, both methodε of indicating relative phaεe are equivalent. The fractional phaεe εignal (one fractional phaεe value per clock L cycle) iε uεed by εample weighting meanε 158 to weight the M filtered εignalε (again, one εample per output line per cycle of clock L) . Sample weighting meanε 158 operateε in a similar manner to weight generator 146 and multiplier 148 (see Fig. 8) . The weight values (M per clock L cycle) are then output to input placer 160.

In the simpler case mentioned above, input placer 160 outputε one of the M weighted valueε per clock cycle of

clock H. The first weighted value is output after the phase integer signal indicates the first clock H cycle after a clock L tick, followed by the second weighted value, etc. , up to the Mth weighted value. Input placer 160 then outputs zero values until the phase integer signal again indicates the first clock H cycle after a clock L tick. In other embodiments, input placer 160 outputs the Mth value on each clock cycle of clock H after the first M clock cycles of clock H, until the next tick of clock L. Of course, deciding what to output in between each of the M outputs, either a value or zero, is only necessary when more than M clock cycles of clock H occur in a clock cycle of clock L.

In the more complex case discuεsed above, input placer 160 averages itε M weighted input εignals, and places this one reεult on itε output for the duration of a clock L cycle. In applicationε requiring a conεtant output value for the duration of a clock L cycle, thiε more complex caεe iε preferred.

Fig. 10 iε a block diagram of LPF 162, which operateε in a manner εimilar to LPF 46, shown in Fig. 6, except posεibly with different coefficients. In the same way as LPF 46, additional stageε might be added to increaεe the order of LPF 162. However implemented, LPF 162 accepts each of the input samples from input placer 160. If input placer 160 and LPF 162 are combined, LPF 162 could be implemented similar to LPF 46', with M stages.

Fig. 11 is a block diagram of SDM DAC 164, which is a εecond-order sigma-delta digital-to-analog converter and compriseε an adder 182, two integratorε 183, 184, three feedback pathε 185, 187, 189, an N-level translator 186, and an N-level D/A 188. Integrator 183 comprises an adder 192, a unit delay 190, and a unit multiplier 194. Integrator 184 comprises an adder 198, a unit delay 196, and a unit multiplier 200. A forward signal path paεεeε an input εignal at a clock rate H, in order, to adder 82, integrator 183, integrator 184, N-level translator 186, and D/A 188. Within integrator 183, the input of integrator 183 is applied to

adder 192, which outputs the signal to unit delay 190, which outputs the signal to integrator 184. Within integrator 183, a feedback path is provided from unit delay 190 through unit multiplier 194 to another input of adder 192. In some embodiments, unit multiplier 194 is eliminated or replaced with a non-unity coefficient multiplier. Within integrator 184, the input of integrator 184 iε applied to adder 198, which outputε the εignal to unit delay 196, which outputε the εignal to translator 186. Within integrator 184, a feedback path is provided from unit delay 196 through unit multiplier 200 to another input of adder 198. In some embodiments, unit multiplier 200 iε eliminated or replaced with a non-unity coefficient multiplier.

Feedback path 185 feeds the signal at the output of translator 186 back to adder 192 through a multiplier 202; feedback path 187 feeds the signal at the output of translator 186 back to adder 198 through a multiplier 204; and feedback path 189 feeds the signal at the output of integrator 184 back to adder 182 through a multiplier 206. In operation, a digital signal at clock rate H is input to SDM DAC 164, is filtered by the digital elements, and a filtered signal at clock rate H is applied to N-level translator 186. Latch 186 outputs one digital value from N possible values, and an analog signal level represented by that digital value is output by D/A 188. For example. If tranεlator 186 were a two-level translator, it could output the most significant bit of the digital value output by integrator 184, and D/A 188 would output either a high or low voltage. In a three level translator, D/A 188 might output one of a positive voltage, zero volts, or a negative voltage.

Fig. 12 is a block diagram of an alternate embodiment of a sample rate converter 220, which could be used in place of sample rate converter 163 in SDM DAC system 152, shown in Fig. 9. Sample rate converter 220 acceptε M input valueε per clock L cycle, and outputs one output value per clock cycle of clock H. Sample rate converter 220 comprises M differentiator stageε 222, 224,..., 226, an input placer 250, and an integrator εtage 251. Each differentiator εtage iε

εimilarly configured, however only stage 1 222 is shown in detail. A differentiator stage comprises N differentiators 228, 230, ..., 232, clocked by clock L. Each differentiator comprises a unit delay and an adder. For example, differentiator 1 228 compriseε unit delay 234 and adder 236. The differentiator εtageε collectively output M εignalε clocked by clock L (one value per εignal per clock L cycle) . Theεe M εignals are applied to input placer 250 which outputs one of the M values (or zero, in some cases) each clock cycle of clock H, as does input placer 160 (see Fig. 9) . The output signal clocked by clock H is then applied to integrator stage 251. The particular one of the M values or zero to be output is determined by the integer phase signal input to input placer 250, as diεcuεεed in connection with input placer 160.

Integrator εtage 251 compriεeε N integrators, similarly configured. One such integrator, integrator 1 252, is shown in detail. Integrator 1 252 compriεeε adder 258 and unit delay 260 coupled aε a conventional integrator. Fig. 13 iε a block diagram of a digital-to-digital resampling syεtem 300 wherein a εignal εampled at a high frequency is resampled at a lower frequency where the two frequencies are independent of each other. Resampling syεtem 300 compriεes a non-decimating filter 302 (such as LPF 46 or LPF 46'), a sample selector 303, a weighting averager 307, a latch 312, a phase detector 322, and a weight generator 324.

The input εignal at clock rate H is applied to filter 302, which outputs a filtered εignal at clock rate H. Filter 302 and εample selector 303 are clocked by clock H, and latch 312 is clocked by clock L. The output of non-decimating filter 302 is an input to sample selector 303. The M outputs of sample εelector 303 are inputs to weighting averager 307.

Sample selector 303 comprises an M-stage delay line 304 and a latch 306. Weighted averager 307 compriseε a multiplier 308 and a εummer 310. Delay line 304 is clocked by clock H, receives an input sample from filter 302 once per clock H cycle, and has M outputs. The M outputs of delay line 304 are input to latch 306, which has M output lines and is

clocked by the arbitrated clock. The M output lineε of latch 306 are input lineε for multiplier 308. Phaεe detector 322 haε a low clock input coupled to clock L and a high clock input on which clock H iε received, although in εome embodimentε, clock H iε a virtual clock tied to the input of valueε to filter 302.

Phaεe detector 322 haε an integer phaεe output (arbitrated clock) , which iε an input to latch 306, and a fractional phaεe output, which iε an input to weight generator 324. Weight generator 324 haε M outputε for M weighting valueε, which are inputε to multiplier 308. Multiplier 308 haε M outputs, which are inputs to summer 310, which has one output. The one output of εummer 310 iε an input to output latch 312, which alεo haε a clock input, clocked by clock L. The output of output latch 312 iε also the output of resampling syεtem 300.

Aε with εample εelector 138 (εee Fig. 8) , the functionality of εample εelector 303, in εome embodimentε, iε not provided by an M-element delay line and a latch, but by a module which outputε M εampleε εelected conεecutively from input samples at clock rate H, where the choice of the M samples is determined by an integer phase value (arbitrated clock) supplied to sample selector 303 by phase detector 322. Aε with reεampler 48, reεampling εyεtem 300 εelectε M samples of the signal input at the clock rate H which are near a tick of clock L, weight the M samples based on their distance from the tick of clock L, take an average of the weighted εampleε, and output that averaged value aε the value of the εignal at the clock L tick, and doeε εo without needing an upεampler.

Fig. 14 iε a block diagram of a digital-to-digital resampling syεtem 400 uεing an intermediate high-frequency clock. Reεampling system 400 comprises a Kth order FIR filter 404, a sample weighting means 408, input placer 410, non-decimating filter 414 (such as LPF 46 or LPF 46'), sample selector 418, weighting averager 420, latch 424, and phase detectors 428, 430. Resampling syεtem accepts an input signal at the input to filter 404 at a clock rate L _α and outputs a

resampled signal representing the same signal as the input signal, but sampled at clock L ₂ , using clock H, where clock H is of a higher frequency than clocks ^ and L ₂ , and where the three clocks are independent. Such a system is useful for mixing digital signals sampled with independent clocks.

Filter 404 outputs M signals (M sampleε per clock L _x cycle) to sample weighting means 408. Sample weighting meanε 408 inputε a fractional phaεe εignal (one value per clock L ₁ cycle) from phase detector 428, and outputs M weighted signalε (M εampleε per clock L _x cycle) to input placer 410. Input placer 410 receives an integer phaεe signal from phase detector 428, and clock H, and outputs one sample per clock cycle of clock H to non-decimating filter 414. Non-decimating filter 414 outputε one filtered value per clock cycle of clock H, to εample selector 418.

Sample selector is clocked by clock H, receives an integer phase signal (arbitrated clock) from phase detector 430, and outputs M selected sampleε per clock cycle of clock L ₂ . Sample εelector 418 can time the output of the M samples be receiving clock L ₂ directly, or by using the integer phase signal and the clock H to determine the ticks of clock L ₂ .

The M outputs of sample selector 418 are the M signal inputε to weighted averager 420, which alεo receiveε a fractional phase εignal from phaεe detector 430. The output signal of weighted averager 420 is one signal with εampleε at tickε of clock L ₂ . Thiε output iε input to latch 424, which, if uεed, ensures that the signal sampleε are output εynchronouεly with the tickε of clock L ₂ . The resampling of a signal clock L _x to a signal at clock L will now be described. The clock I.^ signal is input to filter 404, which is similar to filter 153 (see Fig. 9), outputs M εignals at the L _x clock rate. Phase detector 428 determines where a tick of clock ^ falls in time with reεpect to the tickε of clock H, and outputε two εignalε. The integer phaεe εignal (arbitrated clock) indicateε the clock H ticks between which the clock ^ tick falls, while the fractional

phase signal indicates where between those clock H tickε the clock L-L tick fallε.

The fractional phaεe εignal iε εupplied to εample weighting meanε 403, which weights each of the M signals with reεpect to their poεitionε relative to a clock H tick. The weighted valueε are then paεεed to input placer 410.

Input placer 410, referring to the supplied integer phase εignal, outputε one of the M input εignal εampleε per clock H cycle. The operation of input placer 410 is similar to that of input placer 160 (see Fig. 9) . Input placer 410 outputs the one sample per clock H to non-decimating filter 414, which filters the values and outputs a filtered signal, one sample per clock H cycle. Of courεe, internally non-decimating filter 414 could by decimating by εampling firεt at an even higher frequency.

The output of non-decimating filter 414 is input to sample selector 418, which outputs M of the clock rate H sampleε each clock cycle of clock L ₂ . The particular M εampleε εelected are determined by the integer phaεe (arbitrated clock) εignal, aε with εample selector 303 (see Fig. 13) . The M εamples are then weighted and averaged by weighted averager 420 into one εample per clock cycle of clock L ₂ . The weightε given to each of the M εampleε input to weighted averager 420 are determined by the fractional phase signal, as with weight generator 324 and weighted averager 307 (see Fig. 13) . Phase detector 430 indicates the integer and fractional portion of the phase difference between clock L ₂ and clock H. Finally, latch 424, if used, ensures that the clock rate L ₂ output of weighted averager 420 is synchronous with clock L ₂ .

The above description is illuεtrative and not reεtrictive. Many variationε of the invention will become apparent to those of skill in the art upon review of this discloεure. Merely by way of example, the invention could be practiced with digital hardware or in εoftware modules performing similar functions in a digital signal procesεor. The scope of the invention should, therefore, be determined not with reference to the above deεcription, but instead

should be determined with reference to the appended claimε along with their full εcope of equivalentε.