CN108828312A - A method of reducing Frequency Estimation calculation amount - Google Patents

Abstract

The present invention relates to a kind of methods for reducing Frequency Estimation calculation amount, i.e., reach the method quickly accurately calculated by data accumulation when carrying out Frequency Estimation to big data quantity signal to which calculation amount be greatly lowered, comprise the concrete steps that：The Fast Fourier Transform (FFT) for carrying out less points to initial data first obtains the rough estimate evaluation of frequency, phase term corresponding in initial data is repaid with obtained value complement, then data add up according to certain multiple by treated, carry out Frequency Estimation again later.This method is simple, is easy to hardware realization, can significantly promote Frequency Estimation speed and precision with it is almost consistent to original signal estimated result.

Description

A Method to Reduce Calculation Amount of Frequency Estimation

technical field

The invention relates to the field of signal processing, in particular to the field of signal frequency estimation.

Background technique

Frequency estimation of noisy sinusoidal signals is a classic topic in signal processing. The frequency estimation of the sinusoidal signal is mainly to obtain the frequency estimation value of the signal through time domain transformation or spectrum analysis. With the development of science and technology, the frequency estimation of sinusoidal signals is widely used in radar, sonar, speech, image analysis, biomedicine and communication and other fields, which has important research significance and application value.

The common method of frequency estimation is the frequency domain signal processing algorithm based on fast Fourier transform, among which the more representative algorithms are: Modified Rife (MRife) algorithm, James Tsui (J-T) algorithm, Newton iterative algorithm and so on. These algorithms generally need to calculate additional complex phase items and iterative processing in the calculation process, but in practical engineering applications, real-time frequency estimation of signals is often required, and the amount of signal data is usually large. In this case, the algorithm The amount of calculation will be greatly increased, seriously affecting the real-time realization of engineering applications.

In view of this, the inventors made in-depth ideas on many problems existing in frequency estimation, and then proposed a method for reducing the calculation amount of frequency estimation.

Contents of the invention

The purpose of the present invention is to provide a method for reducing the calculation amount of frequency estimation, which can reduce the calculation amount while ensuring the accuracy of frequency estimation.

In order to achieve the above object, the technical scheme adopted in the present invention is:

A method for reducing the calculation amount of frequency estimation, comprising the following steps:

Step 1. Perform fast Fourier transform on the received discrete signal x(n)=A exp(j(2πf ₀ T _s n+θ ₀ ))+ω(n) whose length is N points, and obtain N-point discrete signal of Among them, A, f ₀ , T _s , θ ₀ , ω(n) represent the signal amplitude, signal frequency, sampling time interval, signal initial phase and noise respectively;

Step 2. Find the position k _max corresponding to the maximum spectral line in X(k), construct the corresponding time-domain phase compensation item φ(n,k _max )=exp(-j2πnk _max /N), and use the constructed time-domain The phase compensation item performs phase compensation on the original signal x(n) to obtain the compensated signal x'(n)=x(n) φ(n,k _max );

Step 3. Accumulate the compensated signal x′(n) at every P point to obtain where m=0,1...,M-1;

Step 4. Using a frequency estimation algorithm to perform frequency estimation on the processed data to obtain the estimated frequency of the processed signal

Step 5. Compare the frequency corresponding to the phase compensation term φ(n,k _max ) obtained in step 2 with the estimated frequency of the processed signal Adding to get the estimated frequency of the original signal

In the step 3, the points of y(m) are M=N/P, P is a divisor of N, and P is a positive integer greater than 1.

After adopting the above scheme, the method is simple and easy to implement in hardware, and can greatly increase the speed of frequency estimation and the accuracy is almost the same as the estimation result of the original signal, thus ensuring the real-time realization of frequency estimation in practical application engineering.

Description of drawings

Fig. 1 is the implementation flowchart of the present invention;

Fig. 2 is the comparison diagram of the amount of computation of the original frequency estimation method and the frequency estimation method after the present invention;

Fig. 3 is a comparison diagram of the calculation result performance of the original flat rate estimation method and the frequency estimation method of the present invention.

Detailed ways

In order to elaborate the content of the present invention, the present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

As shown in FIG. 1 , the present invention discloses a method for reducing the calculation amount of frequency estimation, that is, a method for achieving fast and accurate calculation by greatly reducing the calculation amount through data accumulation when performing frequency estimation on a signal with a large amount of data. The present invention first performs a fast Fourier transform with fewer points on the original data to obtain a rough estimate of the frequency, uses the obtained value to compensate the corresponding phase item in the original data, and then accumulates the processed data according to a certain multiple, and then Then perform frequency estimation. Specifically include the following steps:

Step 1. Perform fast Fourier transform on the received discrete signal x(n)=A exp(j(2πf ₀ T _s n+θ ₀ ))+ω(n) whose length is N points, and obtain N-point discrete signal of Among them, A, f ₀ , T _s , θ ₀ , and ω(n) represent signal amplitude, signal frequency, sampling time interval, signal initial phase and noise, respectively.

Step 2. Find the position k _max corresponding to the maximum spectral line in X(k), construct the corresponding time-domain phase compensation item φ(n,k _max )=exp(-j2πnk _max /N), and use the constructed time-domain The phase compensation term performs phase compensation on the original signal x(n) to obtain a compensated signal: x′(n)=x(n)·φ(n,k _max ).

Step 3. Accumulate the compensated signal x′(n) at every P point to obtain where m=0,1...,M-1. At this time, the number of points in y(m) becomes M=N/P, which is reduced by P times compared to the original number of points in x(n). P is a divisor of N, and P is a positive integer greater than 1.

Step 4. Using a frequency estimation algorithm to perform frequency estimation on the processed data to obtain the estimated frequency of the processed signal

Step 5. Compare the frequency corresponding to the phase compensation term φ(n,k _max ) obtained in step 2 with the estimated frequency of the processed signal Adding to get the estimated frequency of the original signal

Using the above method can reduce the amount of calculation on the basis of ensuring the accuracy of frequency estimation, thereby ensuring the real-time realization of frequency estimation in practical application projects. In order to prove the technical effect of the present invention, an example will be exemplified below through simulation.

Use matlab to generate a signal with an initial frequency of 20MHz, add additive Gaussian white noise to the generated signal, the signal-to-noise ratio of the signal varies from -10dB to 20dB, and the change interval is 0.1dB, the number of signal points N is 8192 points, the signal after compensation Accumulate every 16 points, that is, take P=16. Under each signal-to-noise ratio condition, 1000 Monte Carlo simulations are performed, and each simulation uses the J-T algorithm and the MRife algorithm respectively. The J-T algorithm and the MRife algorithm after this method are used to estimate the frequency of the same signal, and Calculate the root mean square error (Root Mean Square Error, RMSE), verify and compare the performance of this method.

Table 1 is a comparison of the calculation amount between the original frequency estimation method and the frequency estimation method of the present invention, wherein the J-T algorithm uses three iterations, the MRife algorithm uses one correction, and P takes 16. From the calculation formula in the table, it can be concluded that the number of complex multiplications and the number of complex additions of the J-T algorithm are 102400 times, and the number of complex number additions is 139264 times; after adopting this method, the number of complex number multiplications is reduced by 38400 times, and the number of complex number additions is reduced by 22528 times. The number of complex multiplications and complex additions of the MRife algorithm is 69632 times, and the number of complex additions is 117419 times; after using this method, the number of complex multiplications is reduced by 7680 times, and the number of complex additions is reduced by 2048 times, and the calculation amount of the two algorithms is greatly reduced. And it should be noted that: the J-T algorithm also needs to additionally calculate the complex exponential term in each iteration, the calculation amount of this part is related to the number of signal points and its time-consuming accounts for a large proportion of the total time-consuming, and the method of the present invention can greatly Reducing the number of signal points will greatly reduce the number of complex exponential terms that require additional calculations. Therefore, the method of the present invention has a more significant effect on the J-T algorithm and similar frequency estimation algorithms that require additional calculation of complex exponential terms.

Fig. 3 has provided 4 methods (J-T algorithm, the J-T algorithm after adopting the method of the present invention, MRife algorithm, the MRife algorithm after adopting the method of the present invention) to carry out the performance comparison of frequency estimation, what CRLB represents in the figure is the Cramerot lower bound , is the best estimation accuracy that can be obtained in unbiased estimation. It can be seen from the figure that the performance of the J-T algorithm is better than that of the MRife algorithm, and the performance of the algorithm after adopting the method of the present invention is basically the same as that of the original algorithm. It can be seen that the present invention greatly reduces the calculation amount of the algorithm without affecting the accuracy of the algorithm, and has great significance in engineering realization.

The above is only an embodiment of the present invention, and does not limit the technical scope of the present invention in any way. Therefore, any minor modifications, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention still belong to the present invention. within the scope of the technical program.

Claims (2)

1. a kind of method for reducing Frequency Estimation calculation amount, it is characterised in that：Include the following steps：

Step 1 is discrete signal x (n)=Aexp (j (2 π f of N point to the length received₀T_sn+θ₀))+ω (n) progress is quickly Fourier transformation obtains the N point discrete signal on frequency domainWherein A, f₀、T_s、θ₀、 ω (n) respectively represents signal amplitude, signal frequency, sampling time interval, signal first phase and noise；

Step 2 finds the corresponding position k of maximum spectral line in X (k)_max, construct corresponding time domain phase compensation term φ (n, k_max)=exp (- j2 π nk_max/ N), phase compensation is carried out to original signal x (n) with the time domain phase compensation term constructed and is obtained Compensated signal x ' (n)=x (n) φ (n, k_max)；

Step 3 adds up compensated signal x ' (n) every P point, obtainsWherein m=0, 1...,M-1；

Step 4, using frequency estimation algorithm, to treated, data carry out Frequency Estimation, the estimation frequency of signal after being handled

Step 5, by phase compensation term φ (n, k obtained in step 2_max) the estimation frequency of signal after corresponding frequency and processing Addition obtains the estimation frequency of original signal

2. a kind of method for reducing Frequency Estimation calculation amount according to claim 1, it is characterised in that：In the step 3, The points of y (m) are M=N/P, and P is the approximate number of N, and P is the positive integer greater than 1.