CN112541157B

CN112541157B - Signal frequency accurate estimation method

Info

Publication number: CN112541157B
Application number: CN202011380638.4A
Authority: CN
Inventors: 赵益民; 孙开锋; 张涛; 寇小明
Original assignee: Xi'an Precision Machinery Research Institute
Current assignee: Xi'an Precision Machinery Research Institute
Priority date: 2020-11-30
Filing date: 2020-11-30
Publication date: 2024-03-22
Anticipated expiration: 2040-11-30
Also published as: CN112541157A

Abstract

The invention relates to a single-frequency sinusoidal signal frequency calculation method which is suitable for engineering analysis and performance evaluation needing to acquire accurate signal frequency. The invention provides a detection method which is convenient for realizing a computer program, can calculate the frequency of a single-frequency sinusoidal signal by using smaller sample data, has short time consumption in the process and accurate result, and can be used for solving the practical problem in equipment engineering development. The method has strong logic, is easy to realize computer programs, has better universality, can be applied to test equipment, can greatly improve the accuracy of calculation results, and improves the estimation accuracy of signal frequency by more than 4 times compared with the frequency resolution. Moreover, compared with the traditional FFT (fast Fourier transform) method, the number of required sample points is also greatly reduced, and the calculation time is correspondingly reduced.

Description

Signal frequency accurate estimation method

Technical Field

The invention relates to a single-frequency sinusoidal signal frequency calculation method which is suitable for engineering analysis and performance evaluation needing to acquire accurate signal frequency.

Background

In the development of a certain equipment system, the frequency of an output signal of a certain product needs to be accurately known, and the accuracy of the frequency represents the key technical characteristics of the product, so that it is important to accurately acquire frequency data.

In general, the method for acquiring the signal frequency includes:

a) Counting method: the signal frequency is converted by counting the number of positive and negative changes or peaks of the signal over a period of time. This method is simple, but is susceptible to large noise and is limited to integers only; to accurately obtain frequency data, a large amount of time is required to accumulate;

b) Filtering technology: the method is difficult to obtain an accurate frequency value and has large error;

c) Computational analysis techniques based on DFT (discrete fourier transform): and carrying out DFT spectrum change on the obtained signal digital sequence through acquisition, and obtaining a signal frequency value through the maximum value of the signal spectrum. To obtain accurate frequency values, a large amount of data (sample points) needs to be effectively acquired, i.e. limited to the frequency resolution.

Although there are various signal frequency acquisition methods, most of the acquired frequency data is not highly accurate or difficult to achieve due to cost, time consumption, and the like. At present, an accurate signal frequency calculation method is a DFT spectrum analysis method adopting a great number of sample points, however, at a high sampling rate, great sample data is required for obtaining an accurate signal frequency, and great digital calculation time consumption is required to be tolerated. It would be valuable to find a signal frequency acquisition method that is computationally inexpensive and results accurate with smaller sample data.

Disclosure of Invention

The invention solves the technical problems that: in order to overcome the defects of the prior art, the frequency of the single-frequency sinusoidal signal is rapidly and accurately calculated by using smaller sample data. The invention provides a detection method which is convenient for realizing a computer program, can calculate the frequency of a single-frequency sinusoidal signal by using smaller sample data, has short time consumption in the process and accurate result, and can be used for solving the practical problem in equipment engineering development.

The technical scheme of the invention is as follows: a signal frequency accurate estimation method comprises the following steps:

step 1: digitally sampling the analyzed single-frequency sinusoidal signal with a sampling rate of Fs; after sampling, a continuous digital signal sequence is formed, denoted as X: x= { x_i } (i=0, 1,2 … … N-1);

step 2: calculating Df, df=fs/N;

step 3: performing PSD power spectrum analysis on X to obtain power spectrum SPF of X, searching the maximum value in the left half value of the SPF, marking as (n, C), wherein C is the maximum value, and n is the serial number of the maximum value; taking about n and 2 SPF elements respectively, and sequentially marking the elements as (n-2, A), (n-1, B), (n+1, D) and (n+2, E);

step 4: and (3) carrying the data into a formula (1) for calculation, and obtaining the frequency F of the measured signal.

The invention further adopts the technical scheme that: in the step 1, a signal sequence is formed according to the sample number requirement of the DFT requirement.

The invention further adopts the technical scheme that: the requirements are as follows: the number of samples is noted as N, which is a positive integer power of 2.

The invention further adopts the technical scheme that: in the step 3, the power spectrum analysis result is recorded as SPF:

effects of the invention

The invention has the technical effects that: the method has strong logic, is easy to realize computer programs, has better universality, can be applied to test equipment, can greatly improve the accuracy of calculation results, and improves the estimation accuracy of signal frequency by more than 4 times compared with the frequency resolution. Moreover, compared with the traditional FFT (Fourier transform) method, the number of required sample points is also greatly reduced, and accordingly, the calculation time is reduced.

Drawings

Fig. 1: signal power spectrum value diagram

Fig. 2: example 1 Signal diagram

Fig. 3: example 1 Signal Power spectrogram

Fig. 4: example 2 Signal diagram

Fig. 5: example 2 Signal Power spectrogram

Detailed Description

In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings are merely for convenience in describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be configured and operated in a specific orientation, and thus should not be construed as limiting the present invention.

Referring to fig. 1-5, the single frequency sinusoidal signal to be analyzed is digitally sampled, and a continuous digital signal sequence is formed according to the sample number requirement (the number of samples is denoted as N) of the DFT (discrete fourier transform) requirement, which is denoted as X:

X＝{x _i }(i＝0，1，2.......N-1) (1)

wherein N is a positive integer power of 2; let the sampling rate be Fs.

PSD (Power spectral Density) power spectral analysis was performed on the digital signal sequence, and the result was noted as SPF:

and searching the maximum value in the left half value of the SPF, and marking the maximum value as (n, C), wherein C is the maximum value, and n is the serial number where the maximum value is located. Taking about n and 2 SPF elements, respectively, and sequentially marking the elements as (n-2, A), (n-1, B), (n+1, D) and (n+2, E), as shown in figure 1, calculating the frequency F of a detected signal according to the following formula:

where Df is the frequency resolution, df=fs/N.

Example 1:

let signal be F (t):

F(t)＝1.0·sin(1200·2π·t)+δ(t)

where δ (t) is gaussian noise with a standard deviation of 0.12.

The specific embodiment is as follows:

step one: f (t) is sampled according to fs=10000 Hz to obtain a sequence X of n=1024 points, as shown in fig. 2;

step two: df=fs/n≡9.77Hz;

step three: and (3) carrying out power spectrum analysis on the X to obtain the power spectrum SPF of the X, as shown in figure 3. In the left half of fig. 3, a maximum value of 123 is found. Taking about 2 SPF elements at the position of the serial number 123 of the SPF, and sequentially marking the SPF elements as (121,0.0008), (122,0.0040), (123,0.2372), (124,0.0028) and (125,0.0008);

step four: each data is taken to equation (3) and calculated: f is approximately 1201.12Hz.

The frequency estimation error is 1.12Hz compared to the original signal frequency of 1200 Hz.

Example 2:

let signal be F (t):

F(t)＝1.0·sin(4500·2π·t)+δ(t)

where δ (t) is gaussian noise with a standard deviation of 0.3. The specific embodiment is as follows:

step 1: f (t) is sampled according to fs=20000 Hz to obtain a sequence X of n=1024 points, and the signal sequence is shown in fig. 4;

step 2: df=fs/n≡19.53;

step 3: and (3) carrying out power spectrum analysis on the X to obtain the power spectrum SPF of the X, as shown in figure 5. In fig. 5, the maximum value is found to be 230. Taking the number 230 of the SPF and the number 2 of the SPF elements, and sequentially marking the SPF elements as (228,0.0050), (229,0.0110), (230,0.1458), (231,0.0690) and (232,0.0082);

step 4: each data is taken to equation (3) and calculated: f is approximately 4497.24Hz.

The frequency estimation error is-2.76 Hz compared to the original signal frequency 4500 Hz.

Claims

1. The accurate signal frequency estimation method is characterized by comprising the following steps:

step 1: digitally sampling the analyzed single-frequency sinusoidal signal with a sampling rate of Fs; after sampling, a continuous digital signal sequence is formed, denoted as X: x= { X _i -i=0, 1,2 … … N-1); n is a positive integer power of 2; setting the sampling rate as Fs;

step 2: calculating Df, df=fs/N;

2. The method of claim 1, wherein in step 1, the signal sequence is formed according to the number of sample points required by DFT.

3. A method for accurate signal frequency estimation according to claim 2, wherein said requirements are: the number of samples is noted as N, which is a positive integer power of 2.

4. The method of claim 1, wherein in the step 3, the result of the power spectrum analysis is recorded as SPF: