CN112541156A

CN112541156A - Signal amplitude accurate estimation method

Info

Publication number: CN112541156A
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: 2021-03-23
Anticipated expiration: 2040-11-30
Also published as: CN112541156B

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 obtain the accurate signal amplitude. The invention provides a detection method convenient for realizing a computer program, which can calculate the amplitude of a single-frequency sinusoidal signal by using smaller sample data, has short time consumption and accurate result in the process and can be used for solving the practical problem in equipment engineering development. The invention has strong logic, easy realization of computer program, better universality and application in test equipment, can greatly improve the accuracy of the calculation result, and improves the estimation precision of the 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 greatly reduced, and correspondingly, the calculation time is 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 obtain the accurate signal amplitude.

Background

In the development of a certain equipment system, the signal amplitude of an output signal of a certain product needs to be accurately known, so that accurate calculation of signal amplitude data is very important.

There are many ways to obtain the signal amplitude. Although there are many signal amplitude acquisition methods, most of the acquired data has low accuracy or is difficult to realize due to factors such as cost and time consumption. At present, an accurate signal amplitude calculation method is an average analysis method adopting a great number of sample points, and large digital calculation time is required to be tolerated. However, at a high sampling rate, to obtain a signal amplitude with a high precision requirement, extremely large sample data and time consumption are required, which results in increased implementation difficulty. And the signal amplitude acquisition method which is short in calculation time consumption and accurate in result is found under the condition of smaller sample data, and therefore the method has practical value.

Disclosure of Invention

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

The technical scheme of the invention is as follows: a method for accurate estimation of signal amplitude comprising the steps of:

step 1: digitally sampling the analyzed single-frequency sinusoidal signal at a sampling rate of Fs to form a continuous digital signal sequence 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, and searching the maximum numerical value in the left half numerical value of the SPF, wherein the maximum numerical value is marked as (n, C), C is the maximum numerical value, and n is the serial number of the maximum numerical value. Taking 2 SPF elements around n, and sequentially marking as (n-2, A), (n-1, B), (n +1, D) and (n +2, E);

and step 3: and substituting the data into the formula (1) for calculation to obtain the amplitude Amp of the detected signal.

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

The further technical scheme of the invention is as follows: after sampling, a digital signal sequence is formed according to DFT requirements.

The further technical scheme of the invention is as follows: the requirements are as follows: the number of samples is denoted 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, easy realization of computer program, better universality and application in test equipment, can greatly improve the accuracy of a calculation result, and improves the estimation precision of signal frequency by more than 4 times compared with frequency resolution. Moreover, compared with the traditional FFT (fast Fourier transform) method, the number of required sample points is greatly reduced, and accordingly, the calculation time is reduced.

Drawings

FIG. 1: signal power spectrum value-taking map

FIG. 2: example 1 Signal diagram

FIG. 3: example 1 Signal Power Spectrum

FIG. 4: example 2 Signal diagram

FIG. 5: example 2 Signal Power Spectrum

Detailed Description

In the description of the present invention, it is to 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", and the like, indicate orientations and positional relationships based on those shown in the drawings, and are used only for convenience of description and simplicity of description, and do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be considered as limiting the present invention.

Referring to fig. 1-5, a single-frequency sinusoidal signal to be analyzed (known as the frequency of the signal is Fsig) is digitally sampled, forming a continuous sequence of digital signals, denoted 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.

Performing PSD (power spectral density) power spectrum analysis on the digital signal sequence, and recording the result as SPF:

and (5) searching the maximum value in the left half value of the SPF, and recording as (n, C), wherein C is the maximum value, and n is the serial number of the maximum value. Taking 2 SPF elements about n, 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 the 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 implementation mode is as follows:

step 1: the frequency of the known F (t) signal is: 56789Hz, f (t) is sampled at Fs 500000Hz, and a sequence X of points N8192 is obtained, as shown in fig. 2.

Step 2: and (5) carrying out power spectrum analysis on the X to obtain the power spectrum SPF of the X, as shown in figure 3. On the left half of fig. 3, a maximum of 123 can be found. Taking the left and right SPF elements at SPF number 123, which are sequentially denoted as (121, 0.0008), (122, 0.0040), (123, 0.2372), (124, 0.0028), (125, 0.0008);

and step 3: each data was substituted into equation (3) and calculated to give Amp of 0.9998.

Compared with the original signal amplitude of 1.0, the amplitude error is 0.0002.

Example 2:

let the 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 implementation mode is as follows:

step 1: the frequency of the known F (t) signal is: 4500Hz, f (t) is sampled according to Fs ═ 20000Hz, and a sequence X of 1024 points is obtained, wherein the signal sequence is shown in fig. 4;

step 2: and (5) 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, a maximum value 230 is found. Taking the left and right SPF elements at SPF serial number 230, and sequentially recording as (228, 0.0050), (229, 0.0143), (230, 0.1392), (231, 0.0597), (232, 0.0092);

and step 3: the data is substituted into equation (3) and calculated as: amp 0.9803.

Compared with the original signal amplitude of 1.0, the amplitude error is 0.0197.

Claims

1. A method for accurately estimating a signal amplitude, comprising the steps of:

2. The method as claimed in claim 1, wherein in step 1, the signal frequency of the single-frequency sinusoidal signal is known as Fsig.

3. A method for accurately estimating a signal amplitude as set forth in claim 1, wherein in step 1, after sampling, the digital signal sequence is formed according to DFT requirements.

4. A method of accurately estimating a signal amplitude as set forth in claim 3, wherein said requirement is: the number of samples is denoted as N, which is a positive integer power of 2.