A bandwidth estimation method based on data perturbation cross-spectral density phase cumulative distribution

Abstract

The application discloses a bandwidth estimation method based on data perturbation cross-spectral density phase cumulative distribution, which comprises the following steps: obtaining a time-domain signal to be analyzed and performing DC removal processing; introducing perturbation to the signal and calculating cross-spectral density; performing phase normalization processing and extracting enhanced cross-spectral density phase information; calculating a cumulative distribution function according to the amplitude of the cross-spectral density phase; identifying two inflection points in the cumulative distribution function to determine the cutoff frequency of the signal; and calculating the bandwidth of the signal according to the identified inflection point position and the corresponding frequency. The method aims to provide a novel means to accurately evaluate the bandwidth of a signal by analyzing the data perturbation cross-spectral density phase of the signal, thereby improving the bandwidth estimation accuracy in a complex signal and a low signal-to-noise ratio environment.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and in particular to bandwidth estimation techniques for wireless communication, audio signals, time-frequency signals and other types of signals. Specifically, it relates to a bandwidth estimation method based on the phase accumulation distribution of data perturbation cross-spectral density. Background Technology

[0002] In signal processing, bandwidth is a crucial parameter describing the frequency range of a signal, typically defined as the frequency range within which signal information can be effectively transmitted. The signal's spectrum describes its performance in the frequency domain, and accurate bandwidth estimation is essential for optimizing signal transmission, improving signal processing performance, and designing filters.

[0003] Traditional bandwidth estimation methods primarily rely on directly analyzing the spectral characteristics of a signal. These methods typically calculate the Fourier transform of the signal to determine the bandwidth. However, this approach has limitations. When faced with noise and limited data, direct spectral analysis cannot adequately account for the impact of noise on the signal's phase and amplitude, potentially leading to inaccurate bandwidth estimations. Especially with complex signals or in the presence of high noise, the reliability of spectral amplitude information decreases, significantly reducing the accuracy of traditional methods.

[0004] Therefore, a new method is urgently needed to improve the accuracy and reliability of bandwidth estimation. Summary of the Invention

[0005] The purpose of this invention is to provide a bandwidth estimation method based on the phase accumulation distribution of data perturbation cross-spectral density. Addressing the various shortcomings of current mainstream UAV takeoff radio monitoring and direction finding equipment, this device adopts a Watson-Watt direction finding system, utilizing a zero-IF architecture software radio chip as the core RF frequency conversion device, and integrating an FPGA and ARM into a single SOC (System-on-a-Chip) for data processing. This solution is lightweight, compact, and suitable for installation on micro-UAVs, while also possessing good direction finding accuracy and strong signal monitoring and identification capabilities.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A bandwidth estimation method based on the phase accumulation distribution of data perturbation cross-spectral density, the method comprising the following steps:

[0008] The time-domain signal to be analyzed is acquired and DC-free processed.

[0009] A perturbation is introduced into the signal, and the cross-spectral density is calculated;

[0010] Phase normalization is performed to extract the enhanced cross-spectral density phase information;

[0011] Calculate the cumulative distribution function based on the amplitude of the cross-spectral density phase;

[0012] Identify the two inflection points in the cumulative distribution function to determine the cutoff frequency of the signal;

[0013] The bandwidth of the signal is calculated based on the identified inflection point location and the corresponding frequency.

[0014] In some embodiments, the signal that introduces the perturbation is calculated using the following formula:

[0015]

[0016] Where σ is the perturbation amplitude, It is a random phase that follows a Gaussian distribution.

[0017] In some embodiments, the cross-spectral density is calculated using the following formula:

[0018] S xy (f)=F{x(n)}·F * {x′(n)}

[0019] Where F{x(n)} is the FFT transform result of signal x(n), F * {x′(n)} is the conjugate of the FFT transform result of signal x′(n).

[0020] In some embodiments, the phase normalization is calculated using the following formula:

[0021]

[0022] Extracting phase information from cross-spectral density:

[0023] φ(f)=atan2(Im(S xy (f)), Re(S) xy (f))).

[0024] In some embodiments, the cumulative distribution function is calculated using the following formula:

[0025]

[0026] The cumulative distribution function F(f) represents the cumulative phase amplitude at frequency f.

[0027] In some embodiments, identifying the two inflection points in the cumulative distribution function includes: identifying the first point F(i) of the cumulative distribution function. start ) and the last point F(i end Using these points as endpoints, we iterate through the cumulative distribution function to calculate F(i) and the slope at each point.L (i) and Slope H (i) Slope within the effective frequency band L (i) and Slope H (i) The position corresponding to the minimum value of each is the inflection point.

[0028] In some embodiments, calculating the signal bandwidth based on the identified inflection point positions and corresponding frequencies includes calculating the frequency values ​​f corresponding to the two inflection point positions of the cumulative distribution function. L and f H The signal bandwidth BW is calculated using the following formula:

[0029] BW = f H -f L .

[0030] In some embodiments, the time-domain signal is an audio signal or a communication signal.

[0031] The beneficial effects that the methods disclosed in this application may bring include, but are not limited to:

[0032] This invention offers enhanced noise immunity and estimation accuracy. Even in complex or low signal-to-noise ratio environments, particularly when signal spectral amplitude information is unreliable, it comprehensively considers the signal phase distribution, providing a more complete reflection of the signal's bandwidth characteristics. This method is widely applicable to the analysis and processing of audio signals, communication signals, and other composite signals, offering an effective solution for optimized signal bandwidth design and system performance improvement. Attached Figure Description

[0033] Figure 1 This is a flowchart of an embodiment of the present invention;

[0034] Figure 2 This is the power spectrum after DC removal processing when the time domain data is a 4G mobile communication signal superimposed with single-tone interference in an embodiment of the present invention.

[0035] Figure 3 This is a schematic diagram of the data perturbation cross-spectral density in an embodiment of the present invention;

[0036] Figure 4 This is a phase diagram of the cross-spectral density after phase enhancement in an embodiment of the present invention;

[0037] Figure 5 This is a schematic diagram of the phase accumulation distribution in an embodiment of the present invention;

[0038] Figure 6 slope L (i), slope H(i) and a schematic diagram of the minimum value within their respective effective frequency bands;

[0039] Figure 7 This diagram shows the start frequency, cutoff frequency, and bandwidth. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0041] Conversely, this application covers any substitutions, modifications, equivalent methods, and schemes made within the spirit and scope of this application as defined in the claims. Furthermore, to provide the public with a better understanding of this application, certain specific details are described in detail below. However, this application can be fully understood by those skilled in the art even without these detailed descriptions.

[0042] The following will provide a detailed description of a bandwidth estimation method based on the phase accumulation distribution of data perturbation cross-spectral density, which is involved in the embodiments of this application.

[0043] like Figure 1 As shown, this invention provides a bandwidth estimation method based on the phase accumulation distribution of data perturbation cross-spectral density.

[0044] By introducing a data perturbation mechanism, signal cross-spectral density analysis is performed, and phase accumulation distribution is calculated, overcoming the shortcomings of traditional methods and achieving accurate assessment of signal bandwidth. The specific method is as follows:

[0045] Step 1: Obtain the time-domain signal y(n) to be analyzed, and remove the DC component of the signal to obtain... in It is the mean of the signal;

[0046] Step 2: Calculate the perturbation cross-spectral density of the data:

[0047] ① Introduce perturbations: Add perturbations to the signal segment to obtain the signal.

[0048] Where σ is the perturbation amplitude. It is a random phase that follows a Gaussian distribution. A perturbation is introduced to enhance the signal's complexity, reflecting the true nature of the signal while ensuring that the calculated cross-spectral density is not constant.

[0049] ② Perform Fourier transforms on signals x(n) and x′(n) to calculate the cross-spectral density:

[0050] S xy(f)=F{x(n)}·F * {x′(n)}

[0051] Where F{x(n)} is the FFT transform result of signal x(n), F * {x′(n)} is the conjugate of the FFT transform result of signal x′(n).

[0052] Step 3: Phase Information Extraction

[0053] ① Phase enhancement: Phase information is improved through phase normalization.

[0054]

[0055] ② Extract phase information from cross-spectral density:

[0056] φ(f)=atan2(Im(S xy (f)), Re(S) xy (f)))

[0057] Step 4: Calculate the cumulative distribution function of the phase. The cumulative distribution function F(f) represents the cumulative phase amplitude at frequency f;

[0058] Step 5: Identify the inflection points. The phase cumulative distribution function F(f) has two distinct inflection points, corresponding to the low cutoff frequency f. L and high cutoff frequency f H The cumulative distribution function F(f) can be expressed as F(i), i = 1, 2, ..., L. Let the first point of the cumulative distribution be F(i). start ) and the last point F(i end ) respectively as endpoints

[0059] ① Traverse the cumulative distribution function points F(f) and calculate the slope of each point relative to its two endpoints:

[0060]

[0061]

[0062] ② Record the slope H (i), slope L (i) When the minimum value is obtained within the effective frequency band, i is the inflection point position, corresponding to the frequency f respectively. n f H f L .

[0063] Step 6: Based on the frequency f corresponding to the identified inflection point position. H f L Calculate the signal bandwidth BW = fH -f L This bandwidth reflects the effective range of energy distribution within the signal frequency range.

[0064] Example 2:

[0065] This example is based on complex time-domain signal data, combined with... Figure 1 As shown, a bandwidth estimation algorithm based on the phase accumulation distribution of data perturbation cross-spectral density includes the following steps:

[0066] 1. A 4G signal is transmitted through a signal source with a single-tone interference superimposed, and data is acquired at a sampling rate of 40MHz. The acquired time-domain signal is then de-DC processed and will serve as the basis for calculating the cross-spectral density in subsequent steps.

[0067] 2. Use data perturbation calculation methods to transform the time-domain signal to the frequency domain to obtain the cross-spectral density S of the signal. xy (f), specifically, the perturbation amplitude is 0.01, the FFT number is 8192, and the appendix... Figure 2 The power spectrum of the signal is shown in the figure. Figure 3 A schematic diagram of the perturbation cross-spectral density of the signal data is given.

[0068] 3. Calculate the phase φ(f) of the cross-spectral density after phase enhancement. Figure 4 The cross-spectral density phase diagram after phase enhancement is given.

[0069] 4. Integrate the amplitude of the cross-spectral density phase φ(f) and calculate the cumulative distribution function F(f). Figure 5 The diagram illustrates the cumulative phase distribution of the cross-spectral density. The cumulative distribution calculates the total phase amplitude within the frequency range by summing the cross-spectral density phase amplitudes. The cumulative distribution function allows for a more intuitive observation of the distribution characteristics of the cross-spectral density phase.

[0070] 5. Identify two obvious inflection points in the cumulative distribution function. Treat the first and last points of the cumulative distribution function as the two endpoints of a line segment. Then, iterate through the function points F(i) within the effective frequency band of the cumulative distribution and calculate the slope between each point and the two endpoints. L (i) Slope H (i) After the traversal is complete, process the Slope... L (i) and Slope H (i) Perform a minimum value search and retrieve the minimum slope. Lmax Slope HmaxThese correspond to the most significant inflection points, reflecting important changes in the cross-spectral density phase at those frequencies. The search range is within the effective frequency band; specifically, the effective bandwidth of the acquired signal is 0.78125 times the sampling rate, and the number of effective frequency band points is L × 0.78125 = 6400 points. (Appendix) Figure 6 The Slope is given in L (i) Slope H (i) and the display of their respective minimum values.

[0071] 6. Calculate the signal bandwidth, and denote the low cutoff frequency f. L High cutoff frequency f H for:

[0072] f L =f i , when Slope L (i) = Slope Lmin

[0073] f H =f i , when Slope H (i) = Slope Hmin

[0074] The signal bandwidth is achieved through BW = f H -f L Calculation, Appendix Figure 7 f is given in L f H And the display of signal bandwidth.

[0075] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A bandwidth estimation method based on the phase cumulative distribution of data perturbation cross-spectral density, characterized in that, The method includes the following steps: The time-domain signal to be analyzed is acquired and DC-free processed. A perturbation is introduced into the signal, and the cross-spectral density is calculated; Phase normalization is performed to extract the enhanced cross-spectral density phase information; Calculate the cumulative distribution function based on the amplitude of the cross-spectral density phase; Identify the two inflection points in the cumulative distribution function to determine the cutoff frequency of the signal; The bandwidth of the signal is calculated based on the identified inflection point location and the corresponding frequency; The signal that introduces the perturbation is calculated using the following formula: , ； Where σ is the perturbation amplitude, It is a random phase that follows a Gaussian distribution, obtained by removing the DC component of the signal. ,in The time-domain signal to be analyzed is... It is the mean of the signal; The cross-spectral density is calculated using the following formula: ； in, It is a signal The FFT transform result, It is a signal The conjugate of the FFT transform result.

2. The method according to claim 1, characterized in that, The phase normalization is calculated using the following formula: ； Extracting phase information from cross-spectral density: 。 3. The method according to claim 2, characterized in that, The cumulative distribution function is calculated using the following formula: ； Cumulative distribution function Indicates at a frequency of Accumulation of time phase amplitude.

4. The method according to claim 3, characterized in that, The identification of the two inflection points in the cumulative distribution function includes: by identifying the first point of the cumulative distribution function... And the last point Using each endpoint as an endpoint, traverse the cumulative distribution function and calculate respectively. The slope of the two points and Slope within the effective frequency band and The position corresponding to the point where each value reaches its minimum is the inflection point.

5. The method according to claim 1, characterized in that, The step of calculating the signal bandwidth based on the identified inflection point positions and corresponding frequencies includes calculating the frequency values ​​corresponding to the two inflection point positions of the cumulative distribution function. and The signal bandwidth λ is calculated using the following formula: 。 6. The method according to claim 1, characterized in that, The time-domain signals mentioned therein are audio signals and communication signals.

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