CN112541156B

CN112541156B - Signal amplitude accurate estimation method

Info

Publication number: CN112541156B
Application number: CN202011380636.5A
Authority: CN
Inventors: 赵益民; 孙开锋; 张涛; 高智勇
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: 2024-02-02
Anticipated expiration: 2040-11-30
Also published as: CN112541156A

Abstract

The invention relates to a method for calculating the average amplitude of a single-frequency sinusoidal signal, which is suitable for engineering analysis and performance evaluation needing to acquire accurate signal amplitude. The invention provides a detection method which is convenient for realizing a computer program, can calculate the amplitude 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 amplitude accurate estimation method

Technical Field

The invention relates to a method for calculating the average amplitude of a single-frequency sinusoidal signal, which is suitable for engineering analysis and performance evaluation needing to acquire accurate signal amplitude.

Background

In development of a certain equipment system, it is necessary to precisely know the signal amplitude of the output signal of certain products, so it is important to precisely calculate the signal amplitude data.

There are many ways to obtain the signal amplitude. Although there are various signal amplitude acquisition methods, most of the acquired data is not highly accurate or difficult to achieve due to cost, time consumption, and the like. Currently, accurate signal amplitude calculation methods are average analysis methods that employ very large sample points and require a high tolerance for digital calculation time. However, at high sampling rates, extremely large sample data and time consuming are required to obtain the signal amplitude required for high accuracy, resulting in increased implementation difficulties. The signal amplitude acquisition method with short calculation time and accurate result is very practical value under the condition of seeking smaller sample data.

Disclosure of Invention

The invention solves the technical problems that: in order to overcome the defects of the prior art, the amplitude value 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 amplitude 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 amplitude accurate estimation method comprises the following steps:

step 1: digitally sampling the single frequency sinusoidal signal under analysis at a sampling rate Fs to form a continuous sequence of digital signals, denoted X: x= { x_i } (i=0, 1,2 … … N-1);

step 2: and carrying out PSD power spectrum analysis on the X to obtain the power spectrum SPF of the X, searching the maximum value in the left half value of the SPF, marking the maximum value 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 3: and (3) carrying out calculation by taking each data into a formula (1) to obtain the amplitude Amp of the measured signal.

The invention further adopts the technical scheme that: in said step 1, the signal frequency of the single frequency sinusoidal signal is known as Fsig.

The invention further adopts the technical scheme that: after sampling, a digital signal sequence is formed according to 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.

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 (fast Fourier transform) method, the number of required sample points is also greatly reduced, and the calculation time is correspondingly 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 being analyzed (known as Fsig) is digitally sampled, forming a continuous digital signal sequence, denoted as X, according to the sample count requirement (sample count N) of DFT (discrete fourier transform) requirements:

X＝{x _i }(i＝0，1，2.......N-1) (1)

wherein N is a positive integer power of 2; the sampling rate is noted 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, sequentially marking as (n-2, A), (n-1, B), (n+1, D) and (n+2, E), and calculating the amplitude Amp according to the following formula:

example 1:

let signal be F (t):

F(t)＝＝1.0·sin(56789，0·2π·t)+δ(t)

where δ (t) is gaussian noise with a standard deviation of 0.2. The specific embodiment is as follows:

step 1: the F (t) signal frequency is known as: 56789Hz, F (t) is sampled at fs=500000 Hz, and the sequence X of n=8192 points is obtained, as in fig. 2.

Step 2: 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 3: each data was taken to equation (3) and amp=0.9998 was calculated.

The amplitude error is 0.0002 compared with the original signal amplitude of 1.0.

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: the F (t) signal frequency is known as: 4500Hz, sampling F (t) according to fs=20000 Hz, obtaining a sequence X of n=1024 points, the signal sequence being as shown in fig. 4;

step 2: 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), (229,0.0143), (230,0.1392), (231,0.0597) and (232,0.0092);

step 3: each data is taken to equation (3) and calculated: amp= 0.9803.

The amplitude error is 0.0197 compared with the original signal amplitude of 1.0.

Claims

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

step 1: digitally sampling the single frequency sinusoidal signal under analysis at a sampling rate Fs to form a continuous sequence of digital signals, denoted X: x= { x_i } (i=0, 1,2 … … N-1); the signal frequency of the single frequency sinusoidal signal is known as Fsig; after sampling, forming a digital signal sequence according to DFT requirements, wherein the number of samples is recorded as N, and N is a positive integer power of 2;

step 2: 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 3: the data are carried into the formula (1) for calculation, the amplitude Amp of the measured signal can be obtained,