**APPARATUS AND METHOD FOR THE ANALYSIS OF SIGNAL FREQUENCIES**

Alsop, Stephen (The Gables, Worksop Road South Anston Sheffield S25 5ET, GB)

Alsop, Stephen (The Gables, Worksop Road South Anston Sheffield S25 5ET, GB)

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**G01R23/16***; (IPC1-7): G01H1/14; G01M7/00; G01N29/00; G01R23/16; H03H17/02*

**H03H17/02**US6208944B1 | ||||

US4866441A | ||||

US6026418A |

1. | An apparatus for analysing a signal, the apparatus comprising signal receiving means, signal sampling means and data processing means, wherein the sampling means has at least two sampling components, each of said sampling components being adapted to sample the signal at a different sampling rate, and wherein the data processing means is adapted to apply frequency analysis techniques to the data derived from said at least two sampling components. |

2. | The apparatus of Claim 1, further comprising a display means. |

3. | The apparatus of either Claim 1 or Claim 2, wherein each of said sampling components comprises an analogue to digital signal converter, a data storage means and a control means. |

4. | The apparatus of Claim 3, wherein each of said sampling components further comprises a clock that determines the sampling rate of said sampling components. |

5. | The apparatus of either Claim 3 or Claim 4, wherein said data processing means controls the sampling, storing and communication of data from said sampling components via said control means. |

6. | The apparatus of any preceding claim, wherein said at least two sampling components sample the signal at first and second sampling rates, respectively, wherein said second sampling rate is nR1 Hz, where R1 is much less than n and where n is the first sampling rate. |

7. | The apparatus of any of Claims 1 to 6, wherein the sampling means has three sampling components having first, second and third sampling rates, respectively, wherein said second sampling rate is nR1 Hz and said third sampling rate is n+R2 Hz, where R1 and R2 are much less than n and where n is the first sampling rate. |

8. | The apparatus of any preceding claim, wherein said signal receiving means comprises at least one sensor or signal source. |

9. | A method of analysing the frequencies of a signal, said method comprising the steps of: receiving the signal via a signal receiving means; sampling the signal using at least two sampling components, the sampling components being adapted to sample the signal at different sampling rates; communicating the sampling data from said sampling components to a data processing means; applying a frequency analysis technique to the sampling data via said data processing means; and comparing the resultant frequencies of said frequency analysis step via said data processing means. |

10. | The method of Claim 9, wherein said at least two sampling components sample the signal at first and second sampling rates, respectively, wherein said second sampling rate is nR1 Hz, where R1 is much less than n and where n is the first sampling rate. |

11. | The method of Claim 9, wherein the signal is sampled using three sampling components having first, second and third sampling rates, respectively, wherein said second sampling rate is nR1 Hz and said third sampling rate is n+R2 Hz, where R1 and Ra are much less than n and where n is the first sampling rate. |

12. | The method of any of Claims 9 to 11, wherein the frequency analysis technique of the application step is chosen from the group comprising a Fast Fourier Transform, a Hartley Transform and a Chirp Transform. |

13. | The method of any of Claims 9 to 12 using an apparatus in accordance with any of Claims 1 to 8. |

The present invention relates to a method and apparatus for analysing and synthesising signal frequencies.

Known frequency analysis units generally contain built-in filters, which, as far as possible, block all component frequencies of a signal which exceed the maximum recoverable frequency of the analogue to digital (A/D) converter sampling unit which is used.

The maximum recoverable frequency is generally taken as up to half of the sampling rate of the A/D converter being used. More generally, in the area of frequency shift techniques, it is expressed that the maximum bandwidth that can be recovered is limited to half the sampled frequency. This consideration is as laid down in the universally stated Nyquist Criteria or as in Shannon's Sampling Theory. If the frequencies exceeding this limit are not blocked, aliased or"fold-over"signals would be produced, thereby giving erroneous information.

However, if an analogue signal to be monitored or analysed contains a frequency that occurs above the

Nyquist frequency of the A/D converter, then that frequency would be removed by filters and thus missed. The problem with this known arrangement is that it is necessary to know the highest frequency in advance, so that filters can be set accordingly.

However, should a signal unexpectedly contain a frequency which occurs above the predicted maximum frequency, this frequency would be filtered out and so missed in the analysis.

One application of such signal analysis is in the vibration monitoring of machinery. Sensors can be placed at strategic locations on the machinery so as to monitor one or more signals, which are captured within a computer or dedicated spectrum analyser via one or more A/D converters. By monitoring the frequencies generated by the machinery during operation it is possible to establish whether components within the machinery are defective or malfunctioning. Naturally, a machine which has defective components will emit more vibration or noise signals than a machine with little or no defect within its components.

The captured signals are converted into computer data arrays by advanced frequency analysis techniques such as, for example, the Fast Fourier Transform (FFT), Hartley Transform or Chirp Transform. Thus, the frequency make up of the signals emitted by the machine can be analysed.

As previously discussed, the problem encountered when converting analogue signals to digital format is when the analogue signal contains frequencies which are too high to be contained within the previously explained bandwidth of the A/D converting system. Thus, the highest frequency which can be unambiguously retrieved cannot be greater than half of the sampling frequency of the A/D converter. In frequency shift techniques, the maximum bandwidth that can be unambiguously recovered is less than half of the capture frequency of the A/D converter.

If the sampling frequency of the A/D converter is too low, then the results provided by a frequency analysis technique, such as an FFT, will lead to a 'folding over'in accordance with Shannon's Sampling Theorem, giving erroneous results.

It is an aim of the present invention to obviate or mitigate one or more of the problems highlighted above.

According to a first aspect of the present invention, there is provided an apparatus for analysing a signal, the apparatus comprising signal receiving means, signal sampling means and data processing means, wherein the sampling means has at least two sampling components, each of said sampling components being adapted to sample the signal at a different sampling rate, and wherein the data processing means is adapted to apply frequency analysis techniques to the data derived from said at least two sampling components.

Preferably, said apparatus further comprises a display means.

Preferably, each of said sampling components comprises an analogue to digital signal converter, a data storage means and a control means. Preferably, each of said sampling components further comprises a clock that determines the sampling rate of said sampling components. Preferably, said data processing means controls the sampling, storing and communication of data from said sampling components via said control means.

Preferably, said at least two sampling components sample the signal at first and second sampling rates, respectively, wherein said second sampling rate is n-Ri Hz, where R1 is much less than n and where n is the first sampling rate.

Preferably, the sampling means has three sampling components having first, second and third sampling rates, respectively, wherein said second sampling rate is n-Rl Hz and said third sampling rate is n+R2 Hz, where Rland R2 are much less than n and where n is the first sampling rate.

In the preferred embodiment, R1 and R2 are chosen to be as small as possible as this factor contributes to increasing the maximum unambiguous recoverable frequency.

Preferably, said signal receiving means comprises at least one sensor or signal source.

According to a second aspect of the present invention, there is provided a method of analysing the frequencies of a signal, said method comprising the steps of: receiving the signal via a signal receiving means; sampling the signal using at least two sampling components, the sampling components being adapted to sample the signal at different sampling rates; communicating the sampling data from said sampling components to a data processing means; applying a frequency analysis technique to the sampling data via said data processing means; and comparing the resultant frequencies of said frequency analysis step via said data processing means.

Preferably, said at least two sampling components sample the signal at first and second sampling rates, respectively, wherein said second sampling rate is n-R1 Hz, where R1 is much less than n and where n is the first sampling rate.

Preferably, the signal is sampled using three sampling components having first, second and third sampling rates, respectively, wherein said second sampling rate is n-R1 Hz and said third sampling rate is n+R2 Hz, where R1 and R2 are much less than n and where n is the first sampling rate.

In the preferred embodiment, Ri and R2 are chosen to be as small as possible as this factor contributes to increasing the maximum unambiguous recoverable frequency.

Preferably, the frequency analysis technique of the application step is chosen from the group comprising a Fast Fourier Transform, a Hartley Transform and a Chirp Transform.

Preferably, the method uses an apparatus in accordance with the first aspect of the present invention.

A preferred embodiment of the present invention will now be described, by way of example only, with reference to the accompanying drawings, in which: Figure 1 shows diagrammatically an example of how an alias frequency can occur; Figure 2 shows a graph illustrating the alias frequency of Figure 1; Figure 3 shows in diagrammatical form how multiple frequencies can create an alias frequency with the example of Figure 1; Figure 4 shows a block diagram of an asynchronous data logger component of the present invention;

Figure 5 shows a block diagram illustrating the steps of the analysis program of the present invention; and Figures 6 (a) and 6 (b) and 7 (a)- (c) show diagrammatically the frequency determination step of the present invention.

Before describing a preferred embodiment of the invention, an example of the problem of aliasing or fold-over'will be shown, with reference to Figure 1. If an analogue to digital (A/D) signal converter is sampling data at a sampling rate of, for example, 2 KHz, Nyquist's Criteria states that the maximum frequency that can be unambiguously detected is up to half of that sampling rate. In this example that value would be 1 KHz, as represented by Nyquist Frequency N in Figure 1. Therefore, if a signal is incoming at, for example, 0.8 KHz it can be sampled and analysed without problem. However, if a signal B at 1.2 KHz is present, because it is greater than the Nyquist frequency N (1 KHz) by 0.2 KHz, the signal will fold-over and appear as an aliased or perceived signal C of 0.8 KHz in the analysis. The incoming signal B at 1.2 KHz would not only be undetected as a 1.2 KHz signal but would also appear as an alias or perceived frequency L of 0.8 KHz if anti-aliasing filters did not provide adequate filtering.

As can be seen in Figure 2, because the incoming signal B has a higher frequency than the sampling rate D of the analogue to digital converter, the samples will not detect the true waveform. Sample points A produce an inaccurate waveform because the frequency of the signal B is higher than the Nyquist frequency N. Instead, they will create a lower frequency waveform C, known as the aliased signal.

Figure 3 shows in diagrammatical form how multiple fold-over or aliasing can occur. This example is based upon that shown in Figure 1, but with the multiple fold-over frequency ranges shown in the form of a sawtooth diagram comprised of frequency ranges NY1-NY6. Where the ranges meet are fold-over points FO1-FO5. The diagram shows that not only can the 1.2 KHz signal appear folded over as in Figure 1, but also a large number of other frequencies can also fold over and only. appear within the primary 0- 1 KHz range. For example, as already described with reference to Figure 1, the Nyquist range for this example is 0-1 KHz as the sampling frequency is 2 KHz. The Nyquist range is shown as the range NY1 in Figure 3, and the fold over point FOi is therefore at 1 KHz. The line NY2 represents the frequency range 1-2 KHz which is the fold over of the 0-1 KHz range represented by line NY1, the frequency range NY2 itself folding over at fold over point F02 (2 KHz). Thereafter, each 1 KHz range as represented by lines NY3-NY6 folds over at a respective fold over point FO3-FO5. For clarity, ranges NY1, NY3, and NY5 are referred to herein as positive slopes,

while ranges NY2, NY4, and NY6 are referred to as negative slopes.

In the particular example of Figure 3, reference line P illustrates how higher frequencies in the ranges NY2-NY6 would still show during analysis as an alias frequency of 0.8 KHz, as shown in Figure 1.

As 0.8 KHz is 0.2 KHz below the Nyquist frequency of 1 KHz, any frequency that is either 0.2 KHz above or below the frequency at the fold over points F03 and F05 (in this example 3 KHz and 5 KHz, respectively) would show up during analysis as 0.8 KHz. Thus, for example, an incoming frequency of 2.8 KHz lies within the NY3 frequency range but will show as 0.8 KHz in the NY1 range due to the aforementioned limitations of current analysis techniques.

Until now, it has been customary to use filters on the incoming signals to avoid-, within the limitations of filter technology-the fold over or aliasing effect. However, this can inadvertently filter out unexpected but important higher frequencies. In order to overcome the problem of fold-over without using filters, successive sampled data of the signal to be examined can be obtained by varying the sampling rate of the A/D converter.

This method of serially sampling the data can effectively sample at a higher sampling rate thus increasing the Nyquist Frequency, but this requires the signal to be stationary in terms of frequency components. The preferred embodiment of the present invention uses a multiple Asynchronous Data Logging

(ADL) system, which can be seen in block diagram form in Figure 4. In this example, the ADL has three independent 16-bit sampling channels, which sample the same signal over the same overall time sequence but at slightly different sampling rates, as they are each clocked independently at different rates. The three samples may then be analysed and mathematically recombined to overcome aliasing problems. Although the preferred embodiment of the ADL uses three channels, the ADL may have any number of channels greater than or equal to two, as will be described below.

With the preferred embodiment of the ADL shown in Figure 4, the signal to be analysed is passed from a signal source or sensor 1 to each of the three channels I-III via a buffer 2, with no filtering.

Each of the channels I-III comprises an analogue to digital (A/D) signal converter 3, a sampling clock 4 to set the sampling rate of the converter 3, a memory 5 or other suitable data storage means for storing sampled data and an individual channel control microcontroller 6, which serves as a control means and has overall control of the sampling, storing and communication of data in its particular channel. The overall control of the ADL is provided by a master microcontroller 7, which serves as a further control means and communicates with the individual microcontrollers 6, a data processing means such as a PC (not shown), and a display means, such as a PC monitor (not shown) which is used to

receive and subsequently analyse the data from the ADL, as will be described below.

The preferred data processing means contains control and download programs for the ADL. In summary, the set-up program is run first and communicates with the ADL to set up the rate of the sampling clock 4 of each of the channels I-III, indicating the required number of samples and when to start. Each of the clocks 4 in this particular example can provide sampling frequencies from 1,562.5 Hz up to 62,500 Hz. The control program determines when the sampling of the A/D converters 3 starts and stops.

Once the data has been logged in the ADL, the download program transfers the data to the data processing means for analysis.

In use, the ADL is connected to one or more sensors or signal sources 1. The set-up program can be run internally or by way of an external device, such as a PC, and initially detects the active channels of the ADL. The user then inputs each channel's chosen sampling times into the set-up, which are then conveyed to the individual channels of the ADL.

Sampling times are input into the set-up program such that the sampling frequencies of each channel are very close. For the embodiment shown here with three channels I-III the centre channel II will sample at n Hz, and the channels I and III will sample at n-R1 Hz and n+R2 Hz, respectively, where Ri and R2 are much less than n. Thus, as an example, channel I will sample at 1,999 Hz, channel II at

2,000 Hz and channel III at 2,001 Hz. In this instance, therefore, n is 2,000 Hz and R1 and R2 are each 1 Hz. However, it will be understood that Ri and R2 need not be the same value.

The control program then instructs the ADL to commence sampling, with the sampling being carried out until either (i) a stop instruction is given, (ii) the memory 5 of the channel is full or (iii) a pre-set number of samples have been taken. After the sampling has been completed, the download program transfers the stored data from the ADL to the data processing means for analysis.

Figure 5 shows in block diagram form the steps of the analysis program in the data processing means once the sample data is loaded into data arrays 8 corresponding to the number of sampling channels in the ADL. The resultant samples are then analysed by performing a frequency analysis technique, such as a Fast Fourier Transform (FFT), Hartley Transform, Chirp Transform or similar analysis technique, so as to locate the frequency components within the samples. In this example, the data arrays 8 are analysed through FFT engines 9 to produce resultant frequencies 10 in the Nyquist range. Some of the located frequencies 10 may be aliased frequencies.

To test whether these are true or aliased frequencies, the signals within each of the 3 channels are compared by comparison step 11 so as to isolate the aliased frequencies. The frequency spectra of the different channels are then combined

with each other to produce definitive and unambiguous results without anti-aliasing filters at results step 12. The waveforms produced by the samples from each channel can be shown for visual display on a display means (not shown), in a similar manner to that of an oscilloscope.

To illustrate the method used by the analysis program, Figures 6 (a) and 6 (b) and 7 (a)- (c) show sawtooth diagrams similar to that of Figure 3.

Figures 6 (a) and 6 (b) illustrate the analysis program for use with an ADL having two sampling channels. Channels I and II have sampling rates of 1,999 and 2,000 Hz, respectively, where the Nyquist frequencies will be 999.5 Hz and 1000 Hz.

Therefore, for the reasons explained with reference to Figure 3, an incoming frequency of 4.6 KHz will appear in channel I (Figure 6 (a)) as a perceived or aliased signal of 602 Hz. Within the sawtooth diagram of channel II (Figure 6 (b)) the same frequency can be seen to appear as a perceived or aliased signal of 600 Hz. The analysis program of the data processing means can unambiguously recover the actual frequency by applying a simple equation to calculate the actual frequency, Fact : Fact= abs ( (F1-F2) Q-F1) where Q = S1/ (S1-S2) abs = absolute value

F1 and F2 are the perceived frequencies obtained from channels I and II, in this case 602 and 600 Hz respectively.

S1 and S2 are the relevant sampling frequencies for channels I and II, in this case 1,999 and 2,000 Hz respectively.

This gives the true and unambiguous Fact as 4,600 Hz by using only the 1,999 and 2,000 Hz sampling frequencies of channels I and II. However, utilising only the two sampling frequencies would limit the application in cases where the fold-over frequency folds over the fold-over point FO onto a higher frequency range, or Nyquist slope. Where the frequency folds over the fold-over point FO, the difference between the perceived frequencies established by sampling channels I and II will be artificially smaller.

Figures 7 (a)- (c) show an example with an incoming frequency of 4,998 Hz. This would appear as 999 Hz in the 1,999 Hz sampling channel I of Figure 7 (a) and as 998 Hz in the 2,000 Hz sampling channel II of Figure 6 (b). Here, Figure 7 (a) shows a movement up the frequency range from the 4,997.5 Hz fold-over point by 0.5 Hz on the 1,999 Hz channel I, so as to give a perceived or aliased frequency of 999 Hz (Nyquist Frequency of 999.5 Hz less 0.5 Hz). In the 2,000 Hz channel II case of Figure 7 (b), the

frequency moves down the frequency range from the 5000 Hz fold-over point by 2.0 Hz, so as to give a perceived or aliased frequency of 998 Hz (Nyquist Frequency of 1000 Hz less 2 Hz).

This potential movement around the fold-over points F can be a source of error. However, this problem is completely eliminated by the inclusion of a third input sampling frequency, shown here as the 2001 Hz sampling channel III in Figure 7 (c), which shows a fold over in frequency by 4.5 Hz to give a perceived or aliased frequency of 996 Hz (Nyquist Frequency of 1000.5 Hz less 4.5 Hz). By calculating Fact between channels I and II and channels II and III and then selecting the numerically larger of the two Fact values, a true and unambiguous correct sampled frequency is presented by the analysis program.

This technique provides the maximum unambiguous capture frequency, Fmax, attainable from the equation: Fmax = where F is the maximum sampling frequency of the channel II A/D converter of the ADL compatible with obtaining three distinct sampling frequencies at R frequencies . apart where R is the smallest incremental frequency of the ADL.

where the channel II is the middle sampling rate of the three A/D converters in the ADL.

As an example, when using three separate A/D channels, if the maximum sampling frequency of the centre channel sampling A/D converter was 100 KHz and the smallest incremental frequency was 1.0 Hz, this would give a possible frequency capture approaching 5 GHz.

Applying the above formula to existing A/D converters which can give sampling rates in excess of'l MHz and with an incremental frequency of 0.5 Hz would achieve recoverable frequencies approaching 1 THz.

Whilst only.,,, a. selected two of the three sampled frequencies are used to unambiguously determine frequencies up to Flax, thé addition of further A/D sampling units operating at the same or different sampling frequencies, sampling at the same or different times in phase, or selectively varying the frequency of any channel, will give an increase in the frequency resolution and also enable better determination of aliased signals when more than one are at the same amplitude levels.

The preferred embodiment of the invention uses three separate but constant frequency sampling channels, where only two of the three channels are required

whilst both lie on the same slope and are therefore of the same polarity (negative or positive) on the sawtooth diagram. The third channel may be on an adjacent slope and, as such, will therefore be of a different polarity. An enhancement of the device can be obtained, by way of an example, by slightly varying the frequencies of the sampling channels during the capture process. With an increase in sampling frequencies the perceived aliased frequencies, if in fact they are aliased frequencies, will decrease for any component lying on a negative slope and correspondingly increase for any component lying on a positive slope. Using this method only two channels will be required to unambiguously retrieve the actual frequency component.

Using the preceding technique, an enhanced embodiment of the invention can be achieved in that, by predicting the polarity of the perceived frequencies the maximum frequency that can be unambiguously retrieved will be extended as in following equation: FEmax = Lowest Common Denominator of (S1, S2,'S3, etc) where FEmax is the enhanced maximum attainable frequency.

S1, S2, S3,... etc are the sampling frequencies on channels I, II and III, etc.

This premise is based on the fact that the cyclic repeatability of multiply sampling frequencies is the Lowest Common Denominator of those sampling frequencies and thus up to that value, ie FEmaX, there will be no repeated perceived or aliased frequencies, ie each pattern of perceived or aliased frequencies from a given Fact will be unique and will only repeat once Fact is greater than FEmax.

As an example, since the Lowest Common Denominator depends upon the combination of the prime numbers, a careful selection of sampling frequencies which correspond to prime numbers, such as 101 Hz, 103 Hz along with 105 Hz will give an unambiguous retrieval of frequencies greater than 1 MHz and will be considerably greater when there is an increase in the number of sampling channels.

This technique may be utilised, with the use of- appropriately specified components, in such applications as communications and radar. An additional area of this application is to bring multiple high bandwidth frequency signals into lower frequency spectra.

The preferred embodiments described herein have only considered the analysis of sampled frequencies, however this technique is equally capable of being used to synthesise signals to provide a means of communicating within high frequency bandwidths with low frequency generating equipment.

The present invention explains and demonstrates a method and apparatus for capturing and analyzing signals which have hitherto been greater in frequency than can currently be unambiguously captured and analysed, due to the universally stated law of sampling known as Shannon's Sampling Theorem'. The present invention overcomes this limitation, as defined by Shannon, by using two or more asynchronously clocked A/D converters and recombining the results using a formula developed for the purpose. As well as the aforementioned vibration analysis, the present invention has potential use across a wide area of industrial, commercial, consumer, and communication applications, such as: (a). bandwidth, such as radio and television channels to be released for other use; (b) control applications where interference. and signal distortion can be avoided and thereby reduce erroneous actions being initiated ; (c) medical applications where high frequency x-ray and other scanning techniques will be able to use lower and less expensive frequency generating and analyzing equipment; and (d) industrial and consumer product safety where the use of high frequency microwave type equipment can be isolated by generating the hazardous transparent reallocation of a large number of communication wavebands to operate within a smaller bandwidth, thus enabling existing large

areas of signals more remote from the specific application point.

Modifications and improvements can be incorporated without departing from the scope of the invention.

For example, faster sampling A/D converters can be used so as to increase the maximum captured frequencies as appropriate. Furthermore, although the ADL of the preferred embodiment is described as being a stand-alone unit, it may also be provided as an internal component of the data processing means upon which the analysis system is.. held.

It will be also be understood by those skilled in the art that the method as hereinbefore. described could be adapted so as to operate as a signal transmitter as well as a receiver. In this way, multiple incoming signals having varying frequencies could,., be. analysed and synthesised by the present, invention and then transmitted as a single frequency signal. The single frequency signal then could be received and analysed in the manner of the present invention by a second receiver elsewhere.

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