A Complex Plane Distribution Statistical Method for Separating Sinusoidal Signals and Random Noise

Abstract

The invention relates to the field of measurement and testing technology, and in particular to a complex plane distribution statistics method for separating a sinusoidal signal and random noise. The method can separate the sinusoidal signal and the random noise for signals under any signal-to-noise ratio conditions, and can obtain a pure target signal without noise interference without multiple measurements when the sampling rate is large enough. The invention has good application in data processing of measurement experiments such as mobile sound source level calibration, low signal-to-noise ratio measurement, and dynamic target intensity measurement, thereby improving measurement efficiency and reducing requirements on the noise level of experimental waters.

Description

Technical Field

[0001] The invention relates to the field of measurement and testing technology, and specifically to a complex plane distribution statistics method for separating sinusoidal signals and random noise. Background Art

[0002] Due to the randomness and irrelevance of noise in the time and frequency domains, the negative impact of background noise on the accuracy of measurement results cannot be completely eliminated. The only way to reduce the impact of background noise is to improve the signal-to-noise ratio of the measurement data by building a low background noise test domain, increasing the number of sensors, and increasing the magnitude of the measured quantity. However, many on-site in-situ measurements cannot be performed in a dedicated low-environmental noise test field; or the measurement of multiple sensors is affected by the directivity of the sound source, and the signals between sensors cannot form an effective reference; or the sound source level of the sound source itself is limited, making it difficult to improve the signal-to-noise ratio by increasing the effective signal.

[0003] When the signal-to-noise ratio of experimental data is destined to be unable to meet measurement requirements, a signal processing method based on low signal-to-noise ratio is needed to separate the sinusoidal target signal and the random noise signal.

[0004] At present, the commonly used means to separate sinusoidal target signals and random noise signals are to take the average of multiple measurements and to fit the measured signals using the least squares method. The condition for taking the average of multiple measurements is to measure stable signals continuously for multiple times. If the sensor position changes during the measurement process in waters with a lot of interference and changeable environmental conditions, it is impossible to use the multiple averaging method for measurement; the least squares method is used when the shape of the measured signal is relatively certain, and the length and arrival time of the signal need to be known in advance, otherwise the fitting result will be greatly different from the actual situation.

[0005] At present, all signal processing methods for reducing noise signal interference have certain requirements on the signal-to-noise ratio of the sampled signal within their scope of application, and the effect cannot be improved by improving the performance of the measuring instrument. Summary of the invention

[0006] In view of the shortcomings of the prior art, the object of the present invention is to provide a complex plane distribution statistics method for separating sinusoidal signals and random noise.

[0007] To achieve the above object, the present invention provides the following technical solution: a complex plane distribution statistics method for separating sinusoidal signals and random noise, the steps of which are:

[0008] (1) According to the sound source existing in the water area, the sound wave is excited, and the time domain function expression of the sound wave excited by the sound source is S(t), and the noise signal is measured by using a sensor;

[0009] (2) The sound wave reaches the sensor after time t0, the propagation loss is 1-α, and the sensor sampling rate is fs. At this time, the discrete signal collected by the sensor from time t = t0 is R[n], and the expression of R[n] is:

[0010] R[n]=α·S[n]+N[n] (1)

[0011] Where N[n] is the random noise signal measured by the sensor; n is the element number of the data array collected by the acquisition card;

[0012] (3) At this time, the discrete signal R[n] is transformed by FFT to obtain the spectrum array R of R[n] f [n],R f The expression for [n] is:

[0013] R f [n] = α·S f [n]+N f [n] (2)

[0014] Where S f [n] is the FFT array of S[n], N f [n] is the FFT array of N[n], both of which are complex arrays;

[0015] (4) If at this time α·S f [n] / N f [n]<<1, the target signal α·S cannot be obtained f The value of [n], therefore, needs to use complex plane distribution statistics;

[0016] (5) Assume that the sampling rate of the acquisition card is f s Much larger than S f [n] is the maximum frequency of the frequency component, and then R[n] is calculated according to formula (3):

[0017] R (x) [m] = R[(m+1)·x] (3)

[0018] Split into x arrays, split the original signal into 3 R (x) [m] array, then at this time,

[0019] R (x) [m]=α·S[(m+1)·x]+N[(m+1)·x] (4)

[0020] (6) Since the noise signal is random, and S[(m+1)·x] and S[n] only differ in sampling rate, but have the same frequency components, and the FFT arrays of any set of S[(m+1)·x] are basically the same, formula (4) can be expressed as:

[0021] R f (x) [m] = α·S f [m]+N f [m]m <n max / x (5)

[0022] Where n max is the number of elements in the array R[n]. It can be seen that by splitting, for any fixed integer m, R f (x) [m] became R f [m] in terms of α·S f [m] is the center, N f [m] is a set of distribution rules;

[0023] (7) When x is large enough, the center of the distribution is determined by using the ensemble estimation distribution function, and we get α·S f The specific value of [m].

[0024] Compared with the prior art, the invention has the following beneficial effects: utilizing the temporal and spatial irrelevance of noise signals, a complex plane distribution statistics method for separating sinusoidal signals and random noise is proposed. Using this method, in theory, sinusoidal signals and random noise can be separated for signals under any signal-to-noise ratio, and when the sampling rate is large enough, a pure target signal without noise interference can be obtained without multiple measurements.

[0025] This method can be well applied in data processing of measurement experiments such as mobile sound source level calibration, low signal-to-noise ratio measurement, dynamic target intensity measurement, etc., to improve measurement efficiency and reduce the requirements for noise levels in experimental waters. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 This is the sampling diagram of the signal frequency 1kHz and the sampling rate 100kHz;

[0027] Figure 1 Middle: The sinusoidal signal Vp is 0.01V (top), the noise signal is randomly distributed in the range of -0.5 to 0.5 (middle), and the final signal measured by the sensor is the superposition of the two (bottom);

[0028] Figure 2 Signal complex plane spectrum diagram;

[0029] Figure 2 Middle: The complex plane spectrum of the target signal (left), the complex plane spectrum of the noise signal (middle), and the complex plane spectrum of the signal finally measured by the sensor (right);

[0030] Figure 3 Split array for original signal;

[0031] Figure 3 From top to bottom in the figure are the original signal, R (1) [m],R (2) [m] and R (3) [m] array;

[0032] Figure 4 is the distribution set of the collected signal at 1kHz;

[0033] Figure 5 It is a sampling distribution diagram fitted according to the distribution set of the collected signal at 1kHz. DETAILED DESCRIPTION

[0034] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0035] This patent application is based on the background of hydrophone complex sensitivity calibration technology, underwater target intensity measurement technology, and underwater sound source level measurement technology.

[0036] The present invention provides a technical solution: a complex plane distribution statistics method for separating sinusoidal signals and random noise, the complex plane distribution statistics method for separating sinusoidal signals and random noise, the steps of which are:

[0037] (1) According to the sound source existing in the water area, the sound wave is excited, and the time domain function expression of the sound wave excited by the sound source is S(t), and the noise signal is measured by using a sensor;

[0038] (2) The sound wave reaches the sensor after time t0, the propagation loss is 1-α, and the sensor sampling rate is fs. At this time, the discrete signal collected by the sensor from time t = t0 is R[n], and the expression of R[n] is:

[0039] R[n]=α·S[n]+N[n] (1)

[0040] Where N[n] is the random noise signal measured by the sensor; n is the element number of the data array collected by the acquisition card, that is, R[m] is the mth element in the data array collected by the sensor since time t=t0, as Figure 1 shown.

[0041] If we perform FFT transformation on the discrete signal R[n], we get the spectrum array R of R[n] f [n], we can get:

[0042] R f [n] = α·S f [n]+N f [n] (2)

[0043] Where S f [n] is the FFT array of S[n], N f [n] is the FFT array of N[n], both of which are complex arrays, such as Figure 2 shown.

[0044] If at this time α·S f [n] / N f [n]<<1, the target signal α·S cannot be obtained f The value of [n], therefore, needs to use complex plane distribution statistics.

[0045] Assume that the sampling rate of the acquisition card is f s Much larger than S f [n] is the maximum frequency of the frequency component, and then R[n] is calculated according to formula (3)

[0046] R (x) [m] = R[(m+1)·x] (3)

[0047] Split into x arrays, such as Figure 3 As shown, the original signal is split into 3 R (x) [m] array. Then,

[0048] R (x) [m]=α·S[(m+1)·x]+N[(m+1)·x] (4)

[0049] Since the noise signal is random, and the only difference between S[(m+1)·x] and S[n] is the sampling rate, the frequency components are the same, and the FFT arrays of any set of S[(m+1)·x] are basically the same. Therefore, formula (4) can be expressed as:

[0050] R f (x) [m] = α·S f [m]+N f [m]m <n max / x (5)

[0051] Where n max is the number of elements in the array R[n]. It can be seen that by splitting, for any fixed integer m, R f (x) [m] became R f [m] in terms of α·S f [m] is the center, N f[m] is a set of distribution rules, such as Figure 4 The distribution of the acquired signal at 1kHz is shown.

[0052] When x is large enough, we can use the set estimation distribution function to determine the center of the distribution and get α·S f The specific value of [m], such as Figure 5 The sampling distribution diagram shown is fitted according to the distribution set of the collected signal at 1kHz. The point with the densest distribution of samples at 1kHz is (0.01, 0). It can be seen that the target signal is a sine function with a frequency of 1kHz and a single peak value of 0.01.

[0053] Through this technical solution, it consists in the following steps:

[0054] 101: The distribution of the random signal spectrum on the complex plane is random, while the spectrum of the sinusoidal signal on the complex plane is deterministic. When the two are superimposed, it can be seen that the random signal distribution on the complex plane is shifted, and the shift amount is the complex value of the spectrum of the sinusoidal signal;

[0055] 102: When the sampling rate is high enough, the collected original signal can be used to calculate R using formula (4) (x) [m] = α·S[(m+1)·x]+N[(m+1)·x], and then Fourier transform the new array obtained by decomposition, in which the sinusoidal signal part has the same performance;

[0056] 103: In the new array after disassembly, the Fourier transform result of the noise signal is random, but the law followed by the randomness is the same, and the complex distribution of the noise should be symmetrical about a certain point;

[0057] 104: The complex plane distribution function of noise cannot be replaced by the method of averaging multiple measurements, because the size of the average will be affected by extreme values. However, measuring the sinusoidal signal by calculating the maximum value of the distribution function will not be affected by extreme values ​​and the measurement has strong consistency.

[0058] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A complex plane distribution statistics method for separating sinusoidal signals and random noise, characterized in that: The steps are: (1) According to the sound source existing in the water area, the sound wave is excited, and the time domain function expression of the sound wave excited by the sound source is S(t), and the noise signal is measured by using a sensor; (2) The sound wave reaches the sensor after time t0, the propagation loss is 1-α, and the sensor sampling rate is fs. At this time, the discrete signal collected by the sensor from time t = t0 is R[n], and the expression of R[n] is: R[n]=α·S[n]+N[n] (1) Where N[n] is the random noise signal measured by the sensor; n is the element number of the data array collected by the acquisition card; (3) At this time, the discrete signal R[n] is transformed by FFT to obtain the spectrum array R of R[n] f [n],R f The expression for [n] is: R f [n]=α·S f [n]+N f [n] (2) Where S f [n] is the FFT array of S[n], N f [n] is the FFT array of N[n], both of which are complex arrays; (4) If at this time α·S f [n] / N f [n]<<1, the target signal α·S cannot be obtained f The value of [n], therefore, needs to use complex plane distribution statistics; (5) Assume that the sampling rate of the acquisition card is f s Much larger than S f [n] is the maximum frequency of the frequency component, and then R[n] is calculated according to formula (3): R (x) [m]=R[(m+1)·x] (3) Split into x arrays, split the original signal into 3 R (x) [m] array, then at this time, R (x) [m]=α·S[(m+1)·x]+N[(m+1)·x] (4) (6) Since the noise signal is random, and S[(m+1)·x] and S[n] only differ in sampling rate, but have the same frequency components, and the FFT arrays of any set of S[(m+1)·x] are basically the same, formula (4) can be expressed as: R f (x) [m]=α·S f [m]+N f [m]m<n max / x (5) Where n max is the number of elements in the array R[n]. It can be seen that by splitting, for any fixed integer m, R f (x) [m] became R f [m] in terms of α·S f [m] is the center, N f [m] is a set of distribution rules; (7) When x is large enough, the center of the distribution is determined by using the set estimation distribution function. The sinusoidal signal is measured by calculating the maximum value of the distribution function to obtain α·S f The specific value of [m].

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