JPH0743402A - Method and device for obtaining frequency of time change signal - Google Patents

Abstract

PURPOSE: To enable accurate frequency measurement by dividing an input signal, converting the signals obtained into sampled and coded signals, and using discrete Fourier transform(DFT) technique on them. CONSTITUTION: An input signal is first divided by a divider into a plurality of synchronous signals, which are added to L sampler/decoder devices 200. The sampler/decoder devices 200 sample the synchronous signals at different frequencies, and perform analog-to-digital conversion to convert the plurality of synchronous signals into coded signals. Next, a processing element 210 performs DFT on the individual coded signals, and accesses a decoding or memory storage device in which, in respective storage positions, the values of DFT corresponding to the binary expression of the addresses of the storage positions are stored. Then a logic circuit 220 combines the results of DFT on the individual signals to measure the frequency of the input signal.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a digital signal processing apparatus, and more particularly to a method and apparatus for obtaining the frequency and phase of a continuous signal or a burst signal in real time by utilizing a discrete Fourier transform. It is a thing.

[0002]

BACKGROUND OF THE INVENTION Reliable detection and processing of time-varying electronic signals to measure their frequency and phase has numerous practical applications. In the special case, the signal has a frequency that remains relatively constant over the time the signal is identified. However, in general, the frequency of a signal changes over time. In such cases, it is desirable to monitor both the frequency of the signal and the rate of change of the signal frequency.
Therefore, in the general case, an instantaneous frequency measurement is desired.

The signal to be processed may be continuous or may reach the detector as a short burst signal. For example, in the case of radar, both continuous and pulsed signals are used. In the case of an optical vibrometer using an interferometer, the signal is often continuous, but the frequency changes in proportion to the change in the speed of the vibrating element. Well-known laser
When working with a Doppler vibrometer (LDV), the signals occur as short bursts with each signal having a single frequency.

In many applications, signals must be processed at extremely high speeds. A signal processing means capable of processing signals at a speed close to real time is advantageous. Moreover, the signal can be buried in a relatively high level of background noise. As a result, the S / N ratio (SNR) is low (0 dB or less). The signal processing means must therefore be able to detect and measure the signal under these difficult conditions.

Many techniques have been developed for frequency measurement. Some of these techniques make frequency measurements almost instantaneously and the processing time is only limited by the duration of the signal being analyzed and the very short time it takes for the information to be transferred to storage. is there. These techniques are mainly used for analog integrators for frequency / voltage conversion or phase-locked loops (PL) for frequency demodulation.
L) is an analog technique. Another technique is based on counting the number of zero crossings in a signal within a given time period.

Although prior art analog methods provide simple methods for frequency measurement, they suffer from serious deficiencies. The performance of these techniques degrades rapidly as the signal-to-noise ratio drops below 20 dB. This is caused by the extra zero crossings caused by noise. Moreover, these methods do not provide a means for checking the validity of the measured frequency.

For applications requiring instantaneous frequency measurements with SNR as low as 0 dB or lower, digital signal processing techniques are commonly used. Several different digital signal processing algorithms have been developed for spectral analysis and frequency measurement. Most of these methods rely on variations of classical Fourier analysis. A general background description of prior art methods of digital signal processing using Fourier analysis was given in 1984 by McGraw-New York.
Published by Hill, Inc. "Probability, Random Varia" by Papoulis
bles, and Stochastic Prose
“Ssses” and November 1981, Proc. I
EEE, Vol. 69, No. 11, pp1388-1
419, published by S. M. Key and S.C. J. R.
Marple's "Spectral Analysis"
is, A Modern Perspective ”.

Although Fourier analysis provides optimal performance for both signal detection and frequency measurement, the classical Fourier transform technique suffers from some serious drawbacks.
First, only a few (although better than analog methods) of these techniques are capable of reliable frequency measurements with low SNR. Second, these techniques are computationally inadequate when high resolution is required, and as a result, most of the particular prior art implementations of this method are fairly complex and slow. These techniques are unsuitable for real-time signal processing, even when using state-of-the-art technology. On the other hand, in the case of a method that enables high speed processing, the number of data points used in the conversion is limited, so that high speed processing is performed at the expense of resolution and accuracy.

US patent application Ser. No. 07 / 833,338, filed February 2,1992, describes an alternative method and apparatus useful for detecting coherent time-varying signals using Fourier analysis. In an example of this method,
First, a high speed analog-to-digital converter (ADC) or other means is used to sample the input signal. The 1-bit sample value data is then sent to a serial input parallel output shift register or other suitable means.
The parallel output of the shift register is then sent to the decoding means. The decoding circuitry acts as an N-bit to M-bit mapping of the sampled signal.
(A memory medium such as ROM, RAM, or EPROM can be used for this purpose.) That is, a series of 1's and 0's from the sampled signal.
Is used to address a particular storage location. Within each storage location, the DFT is calculated and the DFT bin with maximum power is stored. This DFT bin is the sampling frequency f _s (an integer part of Nf / f, where N is DF
It corresponds to the integer part of the frequency of the signal which is dimensionless in terms of the number of T bins. The second number stored in each storage location should be that of the DFT with the largest power (other validation means could be stored). Information about the power signal can be used to validate the signal to determine if it corresponds to a coherent signal within the expected frequency range.

While the above approach works quite well for a limited number of samples in the signal, this method
It has the drawback of being limited to sampling N discrete points. As a result, the frequency of the input signal cannot be measured within a precision higher than 1 / N of the sampling frequency. For example, 16 samples allow frequency estimation corresponding to a 16-point DFT, and the frequency of the signal can be decomposed to 1/16 of the sampling frequency. (This requires 2 ¹⁶ storage sizes, or 64K of storage. Larger number of sampling points will require larger storage, which is easy to use at the moment. In many cases this is not enough. The limited number of sampling points renders the method unusable for many practical applications. Therefore, it is desirable to have a method and apparatus that can measure the frequency of a signal with arbitrary accuracy.

The frequency resolution also depends on the sampling frequency. As the sampling frequency decreases, the frequency measurement resolution increases proportionally. Unfortunately, when the sampling frequency drops by more than twice the signal bandwidth, uncertainty arises due to aliasing. Aliasing is the folding of information from one band of frequency to another. This occurs as a result of sampling the signal below the Nyquist rate (twice the highest frequency of the input signal). Due to this apparent uncertainty, aliasing has been severely prevented in the prior art. On the other hand, the bandwidth of the signal over the time required to identify the signal is much lower than the highest frequency to be measured. Thus, the signal can be sampled at a rate well below twice the highest frequency without compromising the information associated with its spectrum. This also allows a much higher spectral signal analysis. (The resolution of spectral analysis is inversely proportional to the sampling frequency.)

[0012]

SUMMARY OF THE INVENTION It is an object of the present invention to overcome the problems associated with uncertainty in measuring signal frequency.

[0013]

By providing a method and apparatus for accurately measuring the frequency and phase of a time varying signal according to the present invention, the limitations of the prior art are overcome. According to the invention, the frequency of the signal can be measured with arbitrary accuracy, the measurement accuracy is exponentially high, while the number of components of the device (and thus its complexity and cost) is only linear. Does not increase.

A method for measuring the frequency of a time-varying electronic signal comprises: (a) supplying an unknown time-varying electronic signal as an input signal, and (b) dividing the input signal into a plurality of simultaneous signals. , (C) converting each of the simultaneous signals into a coded signal by sampling each of the simultaneous signals at a different frequency and performing analog-to-digital conversion, and (d) the coded signal. To a decoding or memory storage device in which a discrete Fourier transform is performed on each of the encoded signals, and the DFT value corresponding to the binary representation of the address of the storage position is stored in each storage position. Or (e) combining the results of the individual discrete Fourier transforms in some way so that the frequency of the input signal is measured. Constructed.

[0015]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT This specification describes an apparatus and method for accurately detecting and measuring the frequency and phase of a time-varying signal in near real time. In the following description, specific structures, specific arrangements, and details of components are set forth in order to provide a thorough understanding of the present invention. However, it will be apparent to one skilled in the art that the present invention may be practiced without those specific details. In other instances, well-known components, structures, and electronic processing means have not been described in order not to unnecessarily obscure the present invention. As mentioned above, the continuous Fourier analysis method provides a theoretically optimal means for frequency measurement. In practical digital applications, high speed analog
Since the unknown signal is sampled using a digital converter (ADC), the discrete Fourier transform (DFT) is used instead of the continuous method.
Is used. The discrete Fourier transform (DFT) is a mathematical approximation of the continuous Fourier transform method. The mathematical representation of DFT is well known to those skilled in the art and is for reference only.

[0016]

[Equation 1]

Is given as Here, F (n) is the value of the Fourier transform at the frequency (n / N) f _s , and N is the number of discrete samples x (k) obtained on the signal. (Note that in the general case F (n) is complex.) As N increases to infinity, the accuracy of the DFT approaches that of the continuous Fourier transform.

In the DFT method, the unknown input signal is
It is compared with N sine waves with discrete frequencies from f _s / 2 to f _s / 2. Where f _s is the sampling frequency.
When the sampled signal frequency and the sinusoidal frequency are very close, the product sum F (n) is large, indicating a close match. Then, the sine wave frequency is taken as the signal frequency.
Noise contributes to the power product over a wide range of frequencies when it is present, but does not show a single strong peak (ie, has a dominant frequency) unless the noise is coherent. If the signal-to-noise ratio is not too low, then the power in the frequency bin is well above the noise frequency,
The signal frequency can be easily identified. FIG. 3 is a graph of the power spectrum for the discrete Fourier transform of N = 16 points. Each bin in this graph represents an integer value of the frequency decomposed into 1 / N. The phase of the unknown input signal can be calculated using the following equation.

[0019]

[Equation 2]

Although the DFT gives a good approximation of the continuous Fourier transform, this process is not accurate by nature. Although smaller than using discrete samples, there will be a measurable error. The performance of DFT has been extensively analyzed. Considering N discrete samples, the frequency variance Var
(F) is given by the following equation.

[0021]

[Equation 3]

Where f _s is the sampling frequency. As can be seen from equation 3, the frequency measurement error is directly proportional to the square of f _s . Therefore, the frequency resolution can be significantly improved only by sampling at a lower sampling rate. On the other hand, for band-limited signals whose bandwidth is w,
The signal must be sampled at a rate higher than the Nyquist rate (ie 2w) to avoid aliasing problems.

Next, the method used in the present invention will be described. Reference is first made to FIG. 1 where a simplified block diagram of a preferred embodiment of the process used in the method used for detecting the frequency and phase of a time varying signal is shown. First, the input signal to be measured is provided. In step 10, the input signal is split into a plurality of simultaneous signals 15. The simultaneous signals are S ₁ , S ₂ ,. ． ． It is named S _L. The number of simultaneous signals can vary.
FIG. 1 generally shows that there are L simultaneous signals.

In step 20, each simultaneous signal 15 is sampled and converted into an encoded data stream 25. Each simultaneous signal 15 is sampled at a different frequency, resulting in a different encoded data stream 25. Simultaneous signals are sampled at N different points. N corresponds to the value of N in equation 1. The encoded data signal is represented by E ₁ , E ₂ ,. ． ． Shown as E _L.

In step 30, each encoded data stream signal is processed to determine its frequency. The preferred embodiment uses the Discrete Fourier Transform (DFT). However, it will be apparent to those skilled in the art that other frequency measurement methods can be used. In step 40, each D
The FT results are combined in a novel way to yield a very accurate measurement of the frequency of the input signal.

Next, each process used in the method of the present invention will be described in detail. Referring again to FIG. 1, in step 10, the input signal is split into multiple simultaneous signals. In the preferred embodiment, the input signal is divided into eight simultaneous signals, so L = 8. The preferred embodiment uses eight simultaneous signals because that number has been found to yield a final frequency measurement that is accurate enough for most practical applications. However, it will be apparent to one skilled in the art that the value selected for L can be different and that more or less simultaneous signals can be used.

The simultaneous signal 15 is then sampled in step 20 at various frequencies. The sampling frequency of the signal in the _first stage S ₁ is denoted by f ₁ . In the preferred embodiment, each of the remaining frequencies is sampled at a frequency that is half the sampling frequency in the previous stage. That is, S ₂ is f
is sampled at _s / 2, _{S 3} is sampled at f _s / _{4, S} 4 are sampled at f _s / 8, and so on. This technique is easy to implement and is well known to those skilled in the art. Each simultaneous signal is sampled at the same number of points N. However, at each stage, the signal is reduced to 2 times the time of the previous stage due to the decrease in sampling frequency.
Sampled in double time. Therefore, the sampling resolution is twice the resolution of the previous stage. This is shown in FIG.

Sampling of the simultaneous signals in step 20 is done by a digitizer in the preferred embodiment. The digitizer produces a logic one output when the signal level is greater than zero and a logic zero output when the signal level is less than zero. This produces a coded stream of 1-bit data for each simultaneous signal. In the preferred embodiment, a 16-bit transform is used, where N = 16. The 16-bit encoded signal E _{i of} each encoded signal is used in step 30 to compute the DFT.

Another sampling method can be used to encode the simultaneous signals. For example, another embodiment using 4-bit sampling can be used. Also, instead of looking for zero-crossing locations, the encoder / sampler can use techniques to look for signal maxima and minima.

In step 30, the data from the simultaneous signals are processed using the discrete Fourier transform. In the present invention, the method used to calculate the DFT minimizes the amount of mathematical calculation required to produce the final frequency measurement.

N bits from the encoded data signal
A data point is stored and used as an address to read the data from the mass storage device. The storage device has 2 ^N storage locations, the addresses of which are 0 to 2 ^N -1.
Are represented by an N-bit binary representation of the numbers up to. (Recall that in the preferred embodiment, N = 16.) Each memory location or cell contains the value of the DFT for the particular pattern of 1s and 0s that make up each memory address. The memory location may also include a DFT power (or other validation means) to ensure that the DFT corresponds to a coherent signal.

Therefore, the DFT for each encoded data can be calculated quickly by simply addressing the storage device. This method allows for accurate frequency determination, while minimizing the number of components required, thus minimizing the overall cost of the system,
The system configuration can be very simple.

It will be apparent to those skilled in the art that although the present invention uses a DFT to calculate the frequency of each encoded data stream, other transform or frequency measurement methods can be used. The present invention only uses the DFT because it has been found to be the most reliable and most efficient method for frequency determination. Finally, step 4
At 0, the individual DFT results are combined in a novel way to yield a value for the frequency of the unknown input signal.
Another preferred embodiment of this method is described below.

Reference is now made to FIG. 2 in which a general block diagram of a circuit implementing the method of the present invention is shown. In this embodiment, the input signal is first divided by a divider (not shown in FIG. 2) and added to the L sampler / encoder devices 200. This corresponds to step 10 in the method. The function of each sampler / encoder device 200 is to generate a continuous or sampled data set at the frequency given by g _i (f). This corresponds to step 20 in the method. In FIG. 2, the sampler / encoder device 200 is
Since it can be realized simply by sampling the input signal of frequency f, g _i (f) can be written as follows. g _i (f) = (f) (modf ₁ ) (4)

The processing element 210 is then used to measure the frequency of this signal. The processing element measures the frequency of the output of each sampler / encoder device 200. As mentioned above, DFT is used as an efficient method for measuring the frequency of arithmetic devices, but another similar frequency measurement method can be used with similar results.

The output 215 of the processing element 210 is then combined in a novel way to provide the final value f of the frequency of the input signal. Where f is a function g with G ₁
(F), g ₂ (f) ,. ． ． It can be written as g _L (f). This corresponds to step 40 of the method. That is, f = G [g ₁ (f), g ₂ (f) ,. ． ． g _L (f)] (5).

The gist of the present invention is that the set of functions g ₁ (f), g ₂ (f) ,. ． ． g _L
(F) and finding the function G. Two types of groups of those functions are described below. In the present invention, high resolution frequency measurements are made by using techniques similar to those used for calculating real radix r representations. Although the radix r representation is known to those skilled in the art, it has not previously been used in the field addressed by the present invention. Here, the general concept of the radix r expression will be described for background purposes. In the radix r representation, A is a real number with the value 0 ≦ A ≦ r ^M. The number A can be expressed as the following equation using the radix r expression.

[0038]

[Equation 4]

To calculate the count (a _i ) the number A is r ^M
First remove. Here, M is determined by the maximum number to be represented. This number is normalized by dividing A by r ^M to obtain A ₀ . Here, 0 ≦ A ₀ <1. Term (J +
The value of M) is an integer that determines the resolution by which the number A is represented, where M <J <∞. Furthermore, r
^{J + M} is the number of resolution steps in the number representation.

In the first stage, the count a ₀ is calculated by taking the integer part of the product rA ₀ . After calculating the a _0, subtract a ₀ from the product rA ₀ (i.e., take the fractional part of the number rA ₀₎ number R ₀ is calculated by. For the second iteration, the coefficient a ₁ is calculated by taking the integer part of the product rR ₀ . After the calculation of a _1, the number R ₁ is calculated by taking the fractional part of the number A ₁ . The same applies hereinafter. A ₀ is an irrational number, or the form is x / y (x and y are integers, y
If is a rational number of the form r ^z (z is not an integer) then this procedure continues indefinitely.

In order to show the conventional algorithm, the calculation of the radix-2 (binary) representation of the number A ₀ = 0.8 is shown below as an example. A ₀ = 0.8 rA ₀ = 1.6 a ₀ = 1 R ₀ = 0.6 A ₁ = rR ₀ = 1.2 a ₁ = 1 R ₁ = 0.2 A ₂ = rR ₁ = 0.4 a ₂ = 0 R ₂ = 0.4 A ₃ = rR ₂ = 0.8 a ₃ = 0 R ₃ = 0.8 A ₄ = rR ₃ = 1.6 a ₄ = 1 R ₄ = 0.6 A ₅ = RR ₄ = 1.2 a ₅ = 1 R ₅ = 0.2 A ₆ = rR ₅ = 0.4 a ₆ = 0 R ₆ = 0.8 Therefore, 0.1100110. ． ． Represents the binary (base 2) representation of the number 8.

From this example, the calculation of the real radix r representation is
It includes means for multiplying the remainder of each iteration by an integer r and means for calculating the integer part of this product. Furthermore, with each iteration, the precision in the representation of the number A is increased by the rate r. In the present invention, frequency measurements based on individual DFTs are made using techniques similar to those used for calculating the radix r representation. To demonstrate this application,
Think about if you want to measure the frequency range -f _s / 2~f _s / 2 over the frequency f. The sampling frequency is f _s
Is. The normalized frequency (signal frequency f with respect to this sampling frequency) is defined as f / f _s . The discrete frequency bins of the DFT represent the resolution given as f _s / N. DFT bins is an integral part of Nf / f _s.

Using the DFT, the integer part of the number representing the signal frequency f can be calculated by determining the DFT bin with the largest power. Other frequency measurement techniques that use sampled signals follow a similar pattern. Parameter Nf /
The iterative algorithm described above can be used to increase the accuracy of measuring f _{s and} thus the frequency. This iterative algorithm can be applied as follows.
Let f _si be the sampling frequency of iteration i. For this sampling frequency, the normalized frequency is given by f _i = f / f _si . When N samples for DFT is used, the integer part of Nf _i is the maximum should be in the DFT bins. For iteration (i + 1), the signal is f _si / r
(The r in is from radix r representation) factor r to Nf _i by sampling at a rate of can be multiplied by. The normalized frequency for that sampling frequency is rf _i .
Furthermore, for each iteration i, the integer part of the product rNf _i for this iteration is calculated by determining the DFT bin of the largest power.

In other words, for each iteration i + 1, the normalized frequency f _{i + 1} is the normalized frequency for iteration i multiplied by r (ie, f
_{i + 1} = rf _i ). Then, the maximum DF
By determining the T bottle, you can calculate the integer part of the Nf _i. As can be seen from the above description, these functions (obtained by sampling various frequencies) can be used to develop simple algorithms for making high resolution frequency measurements.

An example serves to elucidate this procedure. In FIG. 5, the actual frequency ratio is Nf / f _s = 5.123.
At, the DFT with N = 16 is calculated. In the preferred embodiment of the present invention, radix-2 is used because binary math is well known in the art and is easily implemented. Figure 5
In the example, the frequency is represented as DFT bin 5 with an unknown remainder of 0.123. In the next iteration, the sampling frequency is divided by 2 and the DFT is calculated.
Dividing by two is equivalent to multiplying the normalized frequency by two. The frequencies are represented as DFT bins with an unknown remainder of 0.245. In the next iteration, the sampling frequency is again divided by 2. The result is a frequency calculated by the DFT that must be 20.492. However, frequency ratios above 16 are aliased. Therefore, the aliased frequency is 4.492 (2
Represented as 0.492-16), it enters bin 4 with an unknown remainder of 0.492. The fact that aliasing has occurred can be determined by comparing the current frequency ratio value with previous results. This gives enough information to identify the points where aliasing occurs at each stage.

The algorithms show that the residue after each iteration is increased by a factor of 2, but remains indeterminate until more than one. Then this integer value is
It contributes to the number of DFT bins, which indicates that the remainder in the first iteration is known to be about 1/2 ⁱ . Since the number of iterations is known up to this point, the information about the remainder in the first iteration is better defined. This is equivalent to admitting that the resolution is doubled after each iteration. Another way to explain this is that in the first iteration, the frequency is ± 0.5 of the DFT frequency bin.
Is known to be within, and in the second iteration, the frequency is known to be within ± 0.25 (relative to the initial bandwidth) of the DFT frequency bin, and so on. Figure 6
Shows how the present invention increases the accuracy of frequency measurements at each iteration.

In practice, in order to calculate the integer part of the DFT bin (ratio Nf / f ⁱ ) when the power is maximum, there is an uncertainty of ± 1 in the number of DFT bins. is there. For example, when the actual ratio Nf / f ⁱ is equal to 1.5, should it be a the DFT bin 1 or 2 which is the maximum. Also, if the actual ratio is equal to 0.5, the DFT bin with the largest power can be 0 or 1. This ambiguity propagates throughout the measurement as the sampling frequency decreases. The present invention overcomes the ambiguity by slightly modifying the base radix r equation. Therefore, the preferred embodiment uses a radix r number representation modified as follows to represent the number A:

[0048]

[Equation 5]

Here, b _i is an integer such that −1 ≦ b _i <r. By this representation, the number A is represented by different sets of counts b _i (one between the number A and its radix-2 representation).
Note that there is a one-to-one correspondence, which is different from the case described above, ie different from the coefficients a _i ). For example, in the modified radix-2 representation, the number A
= 0.4 can be expressed by the following two expressions.

A ₀ = 0.4 rA ₀ = 0.8 b ₀ = 1 R ₀ = -0.2 A ₁ = rR ₀ = -0.4 b ₁ = 0 R ₁ = -0.4 A ₂ = rR ₁ = -0.8 b ₂ = -1 R ₂ = 0.2 A ₃ = rR ₂ = 0.4 b ₃ = 0 R ₃ = 0.4 A ₄ = rR ₃ = 0.8 b ₄ = 1 R ₄ = −0.2 and

A ₀ = 0.4 rA ₀ = 0.8 b ₀ = 0 R ₀ = 0.8 A ₁ = rR ₀ = 1.6 b ₁ = 1 R ₁ = 0.6 A ₂ = rR ₁ = 1.2 b ₂ = 1 R ₂ = 0.2 A ₃ = rR ₂ = 0.4 b ₃ = 0 R ₃ = 0.4 A ₄ = rR ₃ = 0.8 b ₄ = 0 R ₄ = 0. 8 A ₅ = rR ₄ = 1.6 b ₅ = 1 R ₅ = 0.6

Therefore, the number A is changed to (1, 0, -1, 0,
1, 0. ． ． ) Or (0, 1, 1, 0, 0,
1. ． ． ). It can easily be demonstrated that both expressions correspond to the same number A. Furthermore, many other representations can be provided for the same number A. These alternative representations can be used to resolve the uncertainties encountered in computing the DFT bin where the power is maximum. The uncertainty of ± 1 DFT bin at any stage modifies the representation of that number, but the final result after a sufficient number of stages provides the same resolution in the definition of the number.

Referring again to FIG. 1, in the preferred embodiment, the last frequency measurement in step 40 is expressed in Equation 7 above.
Is performed using. The coefficient b _i in equation 7 is the individual DF
It is simply the result of T. The individual DFTs are added together,
The final sum is taken as the frequency of the unknown input signal.

When calculating frequencies using the radix-r algorithm, the number of points used for the DFT is not necessarily limited to the 16 used in the preferred embodiment.
In fact, more points within the limits are preferred for DFT calculation. For example, the more points that are used, the more robust it is to noise. There is a practical limit to the number N of points that can be effectively used in the transformation. For example, as the number of sampling points increases, the configuration becomes more complicated, which increases the cost of the entire system. Further, even if the number of sampling points increases beyond a certain parameter, the accuracy of the frequency measurement result does not significantly increase.

Using N sample points for the DFT,
The coefficients b _i can be used using the following equation: b _i = (d _{i + 1} −rd _i ) modN where −N / 2 <αmodN ≦ N / 2, α = d _{i + 1} −
rd _i . The term d _i represents the maximum power DFT frequency bin in the i th process. For example, a bin uncertainty of ± 1 should have caused the DFT bin to be +1 at iteration i, i.e. 9 even though d _i = 1
Consider the case where it is set to 0. For i + 1 iterations, the DFT bin is 18. This is bin 2, (d
alias back to _{i + 1} = 2). When these values into equation _{8, b i = (2-20)} modN = -2 are obtained. This indicates that the DFT bin in the previous iteration was shifted by +1 due to measurement uncertainty.

Reference is now made to FIG. 7, where a simplified block diagram of a circuit employing the present invention for detecting the frequency of an input signal is shown. The input signal is supplied via the input line. From there, the input signal is split into L simultaneous components. Each co-ingredient is sent to a different stage (designated as stage 1, stage 2, etc.). In the preferred embodiment, there are a total of eight stages, as described above. Eight steps have been found to yield final frequency measurements that are accurate enough for many real-world applications. However, the number of steps can vary depending on the actual resolution desired for a particular application.

Each simultaneous signal is supplied to the decoder 102. The decoder 102 is a digitizer that produces a sampled 1-bit signal, as described above. Each simultaneous signal is sampled at a different frequency.

The sampling frequency for the first stage is number 1.
04, labeled f _s1 . Each signal in the subsequent stages is sampled by the constant divisor r in the previous stage. The divisor r is the same value as r used in the modified radix r number representation in FIG. In the preferred embodiment, the value of r is 2, and each stage is sampled at half the frequency of the previous stage. As described above, the frequency resolution is increased by a factor of 2 with each addition. The frequency resolution is then given by 1 / (N2 ^L ). Thus, the addition at each stage increases the frequency resolution exponentially and only linearly increases the hardware realization. This is a clear advantage as it allows high resolution frequency measurements to be made with much simpler hardware compared to conventional methods. This method has a great advantage that a high-resolution frequency measurement can be performed inexpensively and reliably using the Fourier analysis method.

In the preferred embodiment, 16 of the input signal
Samples are used. This is equivalent to a 16-point DFT,
That is, N = 16 in Expression 1. The output of each decoder 102 is then provided to a serial input-parallel output shift register 105. The output of the shift register is supplied to the decoding means 110. The decoding circuit operates as an N-bit to M-bit mapping. As above, R
Storage media such as OM, RAM and EPROM can be used for this task. In this case, the shift register output can be used as an address for the M2 ^N bit memory. Two numbers are stored in each memory cell. The first one gives the DFT bin where the power is largest (which corresponds to the integer part of the ratio Nf / f _i with an uncertainty of ± 1). This number corresponds to the DFT bin whose power is the largest. The second number stored in the memory cell gives the power of the DFT bin with the largest power (other means of checking the validity of the sampled signal can also be used for the i th stage. ).

The information about the signal power can be used to validate the signal for indication of the presence of the signal and validation of the frequency measurement. The two numbers for the various stages are then added to the decoding circuit 115. It is not necessary to have a different memory for the decoding circuit 110 at each stage. The reason is that the decoding circuit stores the same data regardless of the sampling frequency of the input signal. In other words, the output of the decoding circuit depends only on the output of the shift register 105. Thus, each shift register 105 can be used to address a single memory circuit, regardless of the number of stages in the device. This approach significantly reduces the total number of components and therefore the cost of the system.

The logic decoding circuit 115 includes the shift register 10
5. Receive the output from 5 and combine the results of the individual DFTs according to the manner shown above with respect to Equation 7. Individual b _i
The coefficients are added to produce the final value of the frequency of the input signal.

[0062] As understood from the above description, the processor in the preferred embodiment can provide a measurement of f _3/8 per second. When the sampling frequency is f ₃ = 80 MHz, the processor uses Fourier analysis to obtain 10 million per second for 16 real numbers or 8 subprime numbers used in the transform of the present invention. Supply the frequency measurement of. This is 32, 64, 128, 2
It can easily be extended to transforms with 56 or more sample points. This far exceeds the performance of current methods using current technology.

The method described above uses a fixed radix r representation. For this method, it is desirable to sample the signal at a rate that is more than twice the highest input frequency in the first stage. This approach allows proper frequency measurements to be taken over the maximum range of input frequencies. less than,
Another embodiment of the method of combining the outputs for the individual DFTs to produce the final frequency measurements is described. In this alternative embodiment, the highest input frequency of 2
All stages can be sampled at a much lower than doubled rate.

In this alternative embodiment, the final signal frequency is measured using fixed radix representation. In this method, the numerical representation coefficients are calculated using modular arithmetic. The calculation of numbers from its mixed radix representation can be done using the Chinese Remainder Theorem or mixed radix formulas.

In order to apply this alternative method to high resolution frequency measurements, the signal frequency f is set at various sampling frequencies f _s1 ,
f _s2 . ． ． It is sampled with f _sn . The sampling frequency is selected as follows. That is, let N _i (0 <i <n) represent the number of DFT frequency bins for the process i where the maximum power occurs. The sampling frequency for process i is f _si
And the decomposition process for _i is S _i = f _si / N _i
Given by. The sampling frequencies f _si , .., such that the ratio S _i / S _j (for 0 <i, j <N) is a rational number of the form X _i / X _j . ． ． f _sn is selected. Where X _i , X _j
Are both prime numbers (for 0 <i, j <N).

For example, N ₁ = N ₂ = 16 and f _s1 = 16
/ 13MHz and f _s2 = 16 / 15MHz,
S ₁ = 13, S ₂ = 15, and the ratio S ₁ / S ₂ = 13/15 is X
_{This corresponds to 1} = 13 and X ₂ = 15. Here, 13 and 15 are both prime numbers. For a signal whose frequency is f, the DFT output of process i is given by: d _i = int [f / S _i ] modN _i = int [N _i f / f _3i ] modN _i where d _i is the DFT frequency bin with the largest power (for process i).

For example, if f = 3.4 MHz, N
₁ = N ₂ = 16, f _S1 = 16/13 MHz and f _S2
= 16/15 MHz, d ₁ = int [(3.4 / 16) (13) (16)] m
od13 = 5 d ₂ = int [(3.4 / 16) (15) (16)] m
od15 = 6. To recover the frequency f from the value of d _i , each d
multiplied First, the ratio X _i / N _{i i.} Then the frequency is calculated using the Chinese Remainder Theorem or the mixed radix formula.

As explained above for the preferred embodiment, there may be a ± 1 ambiguity in the determination of the maximum power DFT bin. Unlike the case of fixed radix r representations, the reward of this ambiguity is to give completely false results. To eliminate this ambiguity, for any two frequencies f1 and f2 (within the range of measuring the frequency), if | d _i1 −d _i2 | ≦ 10 <i <n, the frequency f ₁ , F ₂ must satisfy | f ₁ −f ₂ | <S _i . Here, d _i1 and d _i2 are DFT expressions for f ₁ and f ₂ , respectively. This alternative embodiment can be easily implemented by proper selection and programming of the logic decoding circuit (element 220 in FIG. 2, element 115 in FIG. 7). Implementation of this alternative embodiment will be apparent to those skilled in the art.

The present invention also includes means for measuring the phase of the input signal. FIG. 8 shows a possible configuration for real-time phase measurement implementation. This configuration can be realized using analog components, digital components, or hybrid components.

In one possible implementation, the frequencies measured using the instantaneous frequency measuring circuit 152 are used to generate sine and cosine waves at a frequency equal to the input signal frequency 150. Look-up tables, decoding circuits, or specialized analog circuits can be used for this purpose. Multiplier 1 for the generated sine wave and cosine wave
The input signal is multiplied by 55. This multiplication can be done with an analog multiplier when the two signals (ie, the generated sine or cosine wave and the input signal) are in analog form, or when the two signals are in digital form. Can be performed using a digital multiplier, or can be performed using a multiplying digital-to-analog converter when one signal is in analog form and the second signal is in digital form. Therefore, the output of the multiplier is given by: _{sin (ω 0 t + φ)} sinω 0 t = 0.5cosφ- 0.5cos (2ω + φ) (9) sin (ω 0 t + φ) cosω 0 t = 0.5sinφ- 0.5sin (2ω + φ) (10)

Then, using the integrator 150, Equation 9 and Equation 1
Eliminate the second term of 0. An analog integrator can be used if an analog multiplier is used, or a digital accumulator can be used if a digital multiplier is used. Therefore, the output of the accumulator is 0.5co
Given sφ and 0.5 sinφ, the phase can be calculated.

The phase difference between the two signals can then be obtained by calculating the phase (relative to a common reference) of each signal and determining the phase difference between the two signals. Since the above method uses Fourier analysis for frequency measurement, this technique can reliably measure frequency even when the S / N ratio is 0 db. Furthermore, this method also provides an efficient means for signal detection. This allows the invention to process burst signals as well as continuous signals. Further validation means may be provided when comparing the frequency measured at each stage with the frequency measured at the previous stage.

When the present invention is used to process burst signals, a time domain burst detector can be included to avoid false detections and to process coherent background signals. This avoids triggering the detector with a coherent background signal. A time domain burst detector combined with a frequency domain detector can be considered as part of another embodiment of the invention. The time domain burst detector utilizes a threshold level setting that any signal voltage must exceed to enable the burst detector circuit. This method requires that the high-pass filtered signal exceed positive and negative voltage levels, and first rectify the signal voltage and then square that signal voltage to trigger the circuit. Several methods are possible for this, including one that utilizes signal power to:

[Brief description of drawings]

1 is a flow chart depicting a preferred embodiment of the method of the present invention.

FIG. 2 is a schematic block diagram showing the structure of a preferred embodiment of the present invention.

FIG. 3 is a schematic diagram of a power spectrum for an N = 16 point discrete Fourier transform, where each bin in the figure represents an integer value of the frequency resolved to 1 / N.

FIG. 4 is a schematic diagram showing how dividing the sampling frequency by r improves frequency resolution.

FIG. 5 is a diagram illustrating how the resolution of frequency measurement is increased in the subsequent stage by using the method of the present invention.

FIG. 6 is a diagram showing how the ± 1 bin uncertainty at each stage decreases as it propagates through each stage and the frequency is aliased.

FIG. 7 is a schematic block diagram of a circuit for detecting the frequency of an input signal using the present invention.

FIG. 8 is a diagram showing a possible configuration for a circuit for simultaneously measuring the phase of a signal in real time.

[Explanation of symbols]

200 sampler / encoder, 210 processing elements, 22
0 logic circuit.

─────────────────────────────────────────────────── ─── Continuation of the front page (51) Int.Cl. ⁶ Identification number Internal reference number FI Technical indication location H03M 1/14 B (72) Inventor Carrid Ebrahim United States 94086 Sunnyvale del Rey, California Avenue・ 550

Claims (8)

[Claims] 1. A method comprising: (a) supplying an input signal; (b) dividing the input signal into a plurality of simultaneous signals; and (c) simultaneously sampling the simultaneous signals at different frequencies. Generating a plurality of coded signals, (d) mapping each of the coded signals to a known representation of the signal having a pre-computed value representing the frequency of the coded signal, (e) ) A method of determining the frequency of a time varying signal, comprising the step of calculating the frequency of the input signal using the known representation. 2. (a) supplying a time-varying electronic signal as an input signal, (b) dividing the input signal into L simultaneous signals, and (c) an analog using 1-bit sampling. -Converting each of the L simultaneous signals into a coded signal by performing a digital conversion; (d) performing a discrete Fourier transform (DFT) on each of the coded signals; e) A method for obtaining the frequency of the time-varying electronic signal, which comprises the step of obtaining the frequency of the time-varying electronic signal using the result of the discrete Fourier transform. 3. (a) supplying a time-varying electronic signal as an input signal, (b) dividing the input signal into a series of L simultaneous signals, and (c) for each of the simultaneous signals. , L by performing an analog-to-digital conversion utilizing 1-bit sampling, which is performed at half the sampling frequency of the preceding simultaneous signal and at a total of N different points. Converting each of the simultaneous signals into a coded signal; (d) storing each of the coded signals in a shift register; and (e) utilizing each of the coded signals, respectively, at least, including the value of the discrete Fourier transform corresponding to the binary representation of the storage address, and a memory address of 2 ^N, and accessing the memory means, When f) b _i is equal to the DFT bins with should the maximum from each stage i, the frequency F of the input signal (X) wherein [6] The A method for determining the frequency of a time-varying electronic signal, the method comprising the steps of: 4. A time varying signal is received as an input signal,
Input means for splitting the input signal into a plurality of different simultaneous signals; and at least one sampler coupled to the input means for sampling each of the simultaneous signals at different frequencies to generate a plurality of encoded signals. / Encoder means, at least one processing means for determining a respective frequency transformation of the coded signal, and a combination of the frequency transformations coupled to the processing means for determining the frequency of the time-varying signal A device for determining the frequency of a time-varying electronic signal, which is composed of logic circuit means. 5. A time-varying signal is received as an input signal,
Input means for dividing the input signal into L different simultaneous signals; and N connected at different frequencies, connected to the input means in parallel.
L samplers / encoder devices for sampling each of the simultaneous signals at a number of different points to generate L coded signals and coupled to each of the sampler / encoder devices. hand,
A processing element for performing a discrete Fourier transform on each of the encoded signals, and a radix of a number r, coupled to each of the processing elements, to obtain a measurement of the frequency of the time-varying signal.
A device for measuring the frequency of a time-varying electronic signal, comprising logic circuit means for combining said Fourier transforms based on a representation. 6. A time-varying signal is received as an input signal,
Input means for splitting the input signal into a plurality of different simultaneous signals; a 1-bit decoder coupled to each of the simultaneous signals for sampling the simultaneous signal at N different points at different frequencies; An N-bit serial input parallel output shift register coupled to each of the decoders and an N-bit pattern from said shift register coupled to each of said shift registers for receiving the output of said shift register Of at least one N-bit / M-bit decoding circuit that outputs a value corresponding to the discrete Fourier transform of each of the decoding circuits, each of the decoding circuits being coupled to a single logical decoding means, based on a radix-r representation. Combining the Discrete Fourier Transform to obtain a final measurement for the frequency of the input signal A device that measures the frequency of time-varying electronic signals. 7. A time varying signal is received as an input signal,
Input means for dividing the input signal into a plurality of different simultaneous signals; a 1-bit decoder coupled to each of the simultaneous signals for sampling the simultaneous signal at N different points at different frequencies; An N-bit serial input parallel output shift register coupled to each of the decoders and an N-bit pattern from said shift register coupled to each of said shift registers for receiving the output of said shift register Of N-bit to M-bit decoding circuits for outputting a value corresponding to the discrete Fourier transform of each of the decoding circuits, each of the decoding circuits being coupled to a single logical decoding means, relating to the frequency of the input signal. Combining the discrete Fourier transforms based on a mixed radix representation to obtain a final measurement, A device that measures the frequency of time-varying electronic signals. 8. A time varying signal is received as an input signal,
Input means for splitting the input signal into L different simultaneous signals; generating a sampled or continuous signal output having a frequency coupled to the input means, the frequency being a function of the frequency of the input signal And thereby coupled to each of the L sampler / encoder devices representing the frequency of the input signal as a vector of L components, and the sampler / encoder device,
A processing element for measuring the frequency of the output of the sampler / encoder device, and a combination of the processing elements coupled to each of the processing elements to combine the frequencies to obtain the input signal from the vector of the L components. An apparatus for measuring the frequency of a time-varying electronic signal, which comprises a logic circuit means for calculating the frequency.