A method for improving fractional fourier domain resolution based on dimensionless normalization factor design

Abstract

The application discloses a method for improving resolution of fractional Fourier domain based on design of dimension normalization factor, which comprises the following steps: firstly, performing fractional Fourier transform (FRFT) on a multi-component linear frequency modulation (LFM) signal to preliminarily estimate the frequency modulation coefficient of the multi-component LFM signal; secondly, designing a dimension normalization factor according to the frequency modulation coefficient to perform resampling and zero padding on the multi-component LFM signal; and finally, performing discrimination on the resampled and zero-padded signal through FRFT. The method can improve the resolution of the multi-component LFM signal in the fractional Fourier domain (including fractional order and fractional domain frequency) and obtain an optimized resolution effect.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of distinguishing multi-component linear frequency modulation signals in fractional Fourier domain, and particularly relates to a method for improving resolution in fractional Fourier domain based on design of dimension normalization factor. BACKGROUND

[0002] Signal detection is an important work of detection equipment such as sonar and radar. The sonar system or the radar system irradiates a certain form of sound wave or electromagnetic wave to the target, receives the echo signal generated after the irradiation, and then performs target signal detection through signal processing to estimate the target characteristic parameters. However, the signal is easily affected by the complex environment during the propagation process, such as a multi-path environment or a multi-target environment, resulting in that the received multi-component echo signal has strong coherence, and the signal aliasing phenomenon occurs in the time-frequency domain, which is not easy to distinguish and even causes signal missing detection, thereby affecting the estimation of the target characteristic parameters.

[0003] A linear frequency modulation (LFM) signal with good time-frequency resolution is often used as a transmitting signal of a sonar or a radar system. Compared with other time-frequency analysis methods, a fractional Fourier transform (FRFT) has a good energy focusing effect on the LFM signal, and is widely used in the detection of the LFM signal and the estimation of the parameters of the LFM signal. The focusing characteristics of the LFM signal in the fractional Fourier domain (including a fractional order p and a fractional domain frequency u) can be represented by coordinates (p, u). When the parameters of each component signal in the multi-component LFM signal are close, the optimal fractional order p of different component LFM signals and the u value corresponding to the peak value are close, which may cause the multi-component LFM signal to alias in the fractional domain, and it is difficult to distinguish different component LFM signals, and signal missing detection is likely to occur. Therefore, how to improve the resolution performance of the multi-component LFM signal in the fractional Fourier domain is one of the hot issues in signal detection technology. SUMMARY

[0004] The purpose of the application is to provide a method for improving the resolution in the fractional Fourier domain based on the design of the dimension normalization factor, which designs the dimension normalization factor of the fractional Fourier transform according to the frequency modulation coefficient of the multi-component LFM signal, realizes the resolution of the LFM signal in the fractional Fourier domain, and improves the resolution performance of the multi-component LFM signal.

[0005] To achieve the above purpose, the technical scheme adopted by the application is as follows:

[0006] A method for improving the resolution in the fractional Fourier domain based on the design of the dimension normalization factor, comprising the following steps:

[0007] Step 1, a multi-component LFM signal X c with a time length of T s seconds and a signal sampling frequency of f N×1= x1 + x2 + ... + x M The processing window is T. WL The fractional Fourier transform of seconds yields the result Y, where x... i Let X be the i-th linear frequency modulated signal component, 1≤i≤M, where M represents X. N×1 The number of linear frequency modulated signal components, X N×1 It is an N x 1 column vector. The number of sampling points. Indicates rounding down, window length T WL T is satisfied in seconds WL =T c

[0008] Step 2: Search for the maximum value in the fractional Fourier transform result Y, and obtain the frequency modulation coefficient from the fractional p corresponding to the maximum value. Hertz per second;

[0009] Step 3, based on Obtain the dimensionless normalization factor after design. And thus, the window length for fractional Fourier transform processing is selected. seconds and sampling frequency hertz;

[0010] Step 4: Calculate the window length based on the fractional Fourier transform. seconds and sampling frequency Hertz, for signal X N×1 Resampling and zero padding are performed to obtain

[0011] Step 5: Process the resampled and zero-padded multi-component linear frequency modulated signal. Fractional Fourier transform is performed to improve the resolution of multi-component linear frequency modulated signals in the fractional Fourier domain, which includes fractional order and fractional frequency domain.

[0012] Furthermore, in step 2, the maximum value is found by iterating through the fractional Fourier transform result Y, and the fractional order corresponding to this maximum value is p. The frequency modulation coefficient was calculated. Hertz / second, where is the dimension normalization factor for the fractional Fourier transform.

[0013] Furthermore, in step 3, based on Obtain the dimensionless normalization factor after design. Selecting the window length for fractional Fourier transform processing seconds and sampling frequency Hertz satisfied it Simultaneously satisfy and

[0014] Further, in step 4, the sampling frequency Hz is used to X N×1 Resampling, obtaining the multi-component linear frequency modulation signal X' N′×1 , and the window length seconds is used to X' N′×1 Zero padding, obtaining where X' N′×1 is an N' row 1 column column vector, is row 1 column column vector, [·] T Indicates transposition.

[0015] Further, in step 5, the signal is calculated The approximate fractional order corresponding to the peak in the fractional Fourier domain is determined to determine the signal The range of the fractional order of the fractional Fourier transform of the signal is in the range [p l , p h ], and the fractional Fourier transform is performed on , thereby improving the resolution of the multi-component linear frequency modulation signal in the fractional Fourier domain Delta <= 0.5.

[0016] Beneficial effects: the method for improving the resolution in the fractional Fourier domain provided by the application is designed based on the dimensionless normalization factor. According to the frequency modulation coefficient of the multi-component linear frequency modulation signal, the dimensionless normalization factor of the fractional Fourier transform is designed, the resolution of the linear frequency modulation signal in the fractional Fourier domain is realized, the resolution performance of the multi-component linear frequency modulation signal is improved, and it is of great significance to detect the multi-component linear frequency modulation signal by FRFT. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 The method flowchart described in the application;

[0018] Figure 2 The result graph of the fractional Fourier transform of the multi-component linear frequency modulation signal without the designed dimensionless normalization factor;

[0019] Figure 3 The result graph of the fractional Fourier transform of the multi-component linear frequency modulation signal after designing the dimensionless normalization factor described in the application. DETAILED DESCRIPTION

[0020] To better understand the purpose, structure, and function of this invention, the following description, in conjunction with the accompanying drawings, provides a more detailed account of a method for improving the resolution of the fractional Fourier domain based on a dimensional normalization factor design.

[0021] Step 1: Set the multi-component linear frequency modulation signal X N×1 The signal = x1 + x2 has two components, x1 and x2, corresponding to the initial frequency f of the signal. l1 and f l2 Both are 500 Hz, and the signal pulse width is T. c1 and T c2 Both are 1 second, with frequency modulation coefficients k1 and k2 of 1000 Hz / s and 1002 Hz / s respectively, signal delays τ1 and τ2 are both 0 seconds, and signal sampling rate f s At 5000 Hz, the multi-component linear frequency modulated signal X N×1 The time length is T c The time is 1 second, and the window length for fractional Fourier transform processing is T. WL For 1 second, the multi-component frequency modulated signal X N×1 Perform a fractional Fourier transform to obtain the result Y, which is... Figure 2 As shown, signal X N×1 It is an N x 1 column vector.

[0022] Step 2: Search for the maximum value in the fractional Fourier transform result Y. The fractional order corresponding to this maximum value is p = 1.12579. Then... Obtain the frequency modulation coefficients corresponding to the multi-component linear frequency modulation signal Approximately 1001 Hz / second, of which is the dimension normalization factor for the fractional Fourier transform.

[0023] Step 3, based on Obtain the dimensionless normalization factor after design. And thus, the window length for fractional Fourier transform processing is selected. seconds and sampling frequency Hertz satisfied it Simultaneously satisfy and Due to the frequency modulation coefficient of the multi-component linear frequency modulated signal Approximately 1001 Hz / second, therefore it can be taken as... Approximately 5 seconds.

[0024] Step 4: Calculate the window length based on the fractional Fourier transform. seconds and sampling frequency Hertz, for signal X N×1 Resampling and zero padding are performed to obtain First, the sampling frequency Hertz, for signal X N×1 Resampling and zero padding are performed to obtain Since the sampling frequency remains unchanged, the resampled multi-component linear frequency modulated signal is X′. N′×1 =X N×1 Then, based on the window length seconds to X′ N′×1 Zero-padding yields a multi-component linear frequency modulated signal. Where X′ N′×1 Let N' be a column vector with 1 column and 1 row. for A column vector with row 1 and column 1.

[0025] Step 5, from Calculate signal The peak in the fractional Fourier domain corresponds to the approximate fractional order. To determine the signal Within the fractional order range of the fractional Fourier transform, where Obtain fractional order Taking Δ = 0.05, in [p l ,p h Within the scope The fractional Fourier transform, where This improves the resolution of multi-component linear frequency modulated signals in the fractional Fourier domain, enabling the resolution of multi-component linear frequency modulated signals.

[0026] Depend on Figure 2 and Figure 3 It can be seen that when the dimensional normalization factor of the fractional Fourier transform is not designed, the multi-component linear frequency modulated signal X N×1 The fractional Fourier transform result of x1 + x2 shows only one peak, indicating that components x1 and x2 are not distinguishable. When the dimensional normalization factor of the fractional Fourier transform is determined according to step 3... During the design process, the result of the fractional Fourier transform is: Figure 3 As shown, the fractional Fourier transform result has two spikes, realizing the multi-component linear frequency modulated signal X. N×1 The resolution of the two component signals in x1+x2 is improved. Therefore, by designing the dimensional normalization factor of the fractional Fourier transform using the method described in this invention, the resolution of the linear frequency modulated signal in the fractional Fourier domain can be improved.

[0027] It is to be understood that the present application is described by way of example only, and that modifications or alterations can be made to the features and embodiments described without departing from the spirit and scope of the application. In addition, modifications can be made to the features and embodiments described to accommodate specific situations and materials without departing from the spirit and scope of the application. Accordingly, the application is not limited to the specific embodiments disclosed herein, but rather, the scope of the application includes all embodiments falling within the scope of the claims.

Claims

1. A method for improving resolution in fractional Fourier domain based on design of dimensionless normalization factor, characterized in that, comprising the steps of: Step 1: For a time length of T c The second and the signal sampling frequency are f s Hertzian multi-component linear frequency modulated signal X N×1 =x1+x2+…+x M The processing window is T. WL The fractional Fourier transform of seconds yields the result Y, where x... i Let X be the i-th linear frequency modulated signal component, 1≤i≤M, where M represents X. N×1 The number of linear frequency modulated signal components, X N×1 It is an N x 1 column vector. The number of sampling points. Indicates rounding down, window length T WL T is satisfied in seconds WL =T c ; Step 2, search the maximum value in the fractional Fourier transform result Y, and get the frequency modulation coefficient p corresponding to the maximum value Hertz / second; Step 3, based on obtaining the designed dimensionless factor and thereby selecting the window length for the fractional Fourier transform processing seconds and the sampling frequency hertz; Step 4, window length according to fractional Fourier transform processing seconds and sampling frequency hertz, for the signal X N×1 resampling and zero padding to obtain Step 5, resampling and zero padding the multi-component chirp signal performing a fractional Fourier transform to improve resolution of the multi-component chirp signal in a fractional Fourier domain, wherein the fractional Fourier domain comprises a fractional order and a fractional domain frequency; In step 2, the frequency modulation coefficient is calculated as Hertz / second, wherein is a dimension normalization factor for the fractional Fourier transform;​ In step 3, according to obtaining the designed dimensionless factor selecting the window length of the fractional Fourier transform processing seconds and the sampling frequency hertz to satisfy satisfy and 2. The method for improving resolution in fractional Fourier domain based on design of a dimension normalizing factor according to claim 1, characterized in that: In step 4, the sampling frequency Hertz vs. X N×1 Resampling to get a multi-component chirp signal X' N′×1 with a window length seconds on X' N′×1 Zero-padding to get where X' N′×1 is a column vector of N' rows and 1 column, is a column vector of 1 row and 1 column, [·] T denotes transposition.

3. The method of claim 1, wherein the method is designed to improve resolution in fractional Fourier domain based on a dimension normalization factor. In step 5, the signal is determined by The calculation signal The approximate fractional order corresponding to the peak in the fractional Fourier domain To determine the signal In the range of the fractional order of the fractional Fourier transform, wherein In the range of [p l ,p h ] to the signal The fractional Fourier transform is performed, thereby improving the resolution of the multi-component linear frequency modulation signal in the fractional Fourier domain, wherein Δ≤0.5.

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