阅读说明：本技术 一种基于短时傅里叶变换的脉内频率编码信号参数测量方法 (Intra-pulse frequency coding signal parameter measuring method based on short-time Fourier transform ) 是由 刘国满 高梅国 王帅勋 李永健 于 2019-09-06 设计创作，主要内容包括：本发明公开了一种基于短时傅里叶变换的脉内频率编码信号参数测量方法,属于雷达信号侦察技术领域,能够在复杂环境下,对存在脉内起伏、环境中有强干扰、接收信号弱条件下的脉内频率编码信号进行参数测量。具体为：对待检信号做短时傅里叶变换STFT,做二维形态学滤波平滑噪声基底,做二维过门限检测,即计算自适应门限值和大信号门限,取自适应门限值与大信号门限中较大值作为当前检测门限,对STFT的变换结果进行过门限检测。在二维过门限检测结果中检测子码。根据检测得到的子码的起止位置在待检信号的原始数据中截取每个子码对应的数据,并做傅里叶变换FFT计算子码频率,并根据子码频率进一步计算待检信号的其他参数。(The invention discloses a method for measuring parameters of an intra-pulse frequency coding signal based on short-time Fourier transform, belongs to the technical field of radar signal reconnaissance, and can be used for measuring the parameters of the intra-pulse frequency coding signal under the conditions of intra-pulse fluctuation, strong interference in the environment and weak received signal in a complex environment. The method specifically comprises the following steps: and performing short-time Fourier transform (STFT) on a signal to be detected, performing two-dimensional morphological filtering smoothing noise base, performing two-dimensional threshold crossing detection, namely calculating a self-adaptive threshold value and a large signal threshold, taking the larger value of the self-adaptive threshold value and the large signal threshold as a current detection threshold, and performing threshold crossing detection on a transformation result of the STFT. And detecting the subcodes in the two-dimensional threshold-crossing detection result. And intercepting data corresponding to each subcode from the original data of the signal to be detected according to the start-stop position of the subcode obtained by detection, performing Fourier transform (FFT) to calculate the frequency of the subcode, and further calculating other parameters of the signal to be detected according to the frequency of the subcode.)

1. A method for measuring intra-pulse frequency coding signal parameters based on short-time Fourier transform is characterized by comprising the following steps:

performing short-time Fourier transform (STFT) on a signal to be detected, calculating the length of one sub-code according to the result of the STFT, and setting the calculated length of the sub-code as the window length of subsequent STFT processing;

performing two-dimensional morphological filtering on the result of the STFT to smooth a noise substrate;

performing two-dimensional threshold-crossing detection on the STFT conversion result after the noise substrate is smoothed; the two-dimensional threshold crossing detection is as follows: taking a constant false alarm detection threshold as an adaptive threshold value, taking the maximum amplitude value of the signal to be detected multiplied by a preset attenuation coefficient as a large signal threshold, comparing the adaptive threshold value with the large signal threshold, taking the larger value of the adaptive threshold value and the large signal threshold as a current detection threshold, and performing threshold-crossing detection on the STFT conversion result after the noise substrate is smoothed;

detecting a sub-code in a two-dimensional threshold-crossing detection result;

and intercepting data corresponding to each subcode in the original data of the signal to be detected according to the start-stop position of the subcode obtained by detection, performing Fourier transform (FFT) to calculate the frequency of the subcode, and further calculating other parameters of the signal to be detected according to the frequency of the subcode.

2. The measurement method according to claim 1, wherein the constant false alarm detection threshold is used as an adaptive threshold value, and specifically comprises:

the calculated adaptive threshold value is

In the above formula, the first and second carbon atoms are,

3. The measurement method of claim 1, wherein the two-dimensional threshold crossing detection result is a two-dimensional result graph;

the detection of the subcode in the two-dimensional threshold-crossing detection result specifically comprises the following steps:

the maximum value of each column in the two-dimensional result graph is reserved, and the shape of each subcode on the two-dimensional time-frequency graph is converted into a line, namely the two-dimensional linear time-frequency graph is obtained;

and searching and determining the number and the starting and stopping positions of the subcodes on the two-dimensional linear time-frequency graph.

4. The measurement method according to any one of claims 3, wherein the searching and determining the number and start-stop positions of the sub-codes on the two-dimensional linear time-frequency diagram comprises the following steps:

detecting a non-zero point on the two-dimensional linear time-frequency diagram, wherein the current non-zero point is (i, j), if the points of the current non-zero point (i, j) in the front setting range in the time direction are all 0, the current non-zero point (i, j) is the initial position of the current sub-code, the current non-zero point (i, j) is taken as the initial point, and the first non-zero point obtained by detection in the rear setting range in the time direction is taken as the end position of the current sub-code, so that the start-stop position of the current sub-code is obtained;

and by analogy, detecting to obtain all the subcodes and the start-stop positions thereof.

5. The measurement method according to any one of claims 1 to 4, wherein the detecting the sub-code in the two-dimensional threshold crossing detection result further comprises filtering the noise sub-code, specifically:

calculating the length of the sub code according to the start and stop positions of the sub code;

and setting a noise sub-code length threshold value as a set proportion of the length of one sub-code calculated according to the STFT result, and filtering the sub-codes with the sub-code length smaller than the noise sub-code length threshold value.

6. The measurement method of claim 5, wherein the noise subcode filtering further comprises:

and detecting the initial positions of all the subcodes, and filtering the subcode with shorter length if the distance between the initial positions of the two subcodes is less than a set distance threshold.

7. The method of claim 1, 2, 3, 4 or 6, wherein detecting the sub-code in the two-dimensional threshold crossing detection result further comprises:

and arranging the length values of all the subcodes from small to large to obtain a subcode length sequence, selecting a set point in the subcode length sequence, and sequentially calculating the variance of the points with the preset number, and modifying the subcode length value corresponding to the set point into the mean value of the points with the preset number if the variance is mutated.

8. The method of claim 1, 2, 3, 4 or 6, wherein detecting the sub-code in the two-dimensional threshold crossing detection result further comprises:

taking the average value of all the sub-code lengths as the sub-code time width;

comparing the initial positions of every two adjacent subcodes, if the initial positions of two adjacent subcodes differ by N times of the subcode time width, missing N subcodes between the current two adjacent subcodes, and calculating the position of the missing subcode according to the positions of the current two adjacent subcodes and the subcode time width;

and completing the missing subcodes.

Technical Field

The invention relates to the technical field of radar signal reconnaissance, in particular to a method for measuring intra-pulse frequency coding signal parameters based on short-time Fourier transform.

Background

The use of large time-bandwidth signals is one of the most common methods to improve radar range, speed, and their joint resolution performance. The frequency coded signal is a large time-width bandwidth signal, and has good distance speed resolution performance and narrow instantaneous bandwidth. Compared with the linear frequency modulation signal, the frequency coding signal has stronger anti-interference and low interception performance.

Under ideal conditions, accurate parameter measurement results can be obtained through methods such as instantaneous frequency measurement, time-frequency analysis and the like, but under complex environments, the conditions of small signal-to-noise ratio, strong interference, distortion of signals, large fluctuation of bottom noise and the like make it very difficult to accurately measure parameters of frequency coding signals.

Disclosure of Invention

In view of this, the present invention provides a method for measuring parameters of an intra-pulse frequency coded signal based on short-time fourier transform, which can perform parameter measurement on the intra-pulse frequency coded signal under the conditions of intra-pulse fluctuation, strong interference in the environment, and weak received signal in a complex environment.

In order to achieve the purpose, the technical scheme of the invention comprises the following steps:

and performing short-time Fourier transform (STFT) on the signal to be detected, calculating the length of one sub-code according to the result of the STFT, and setting the calculated length of the sub-code as the window length of subsequent STFT processing.

Two-dimensional morphological filtering is performed on the result of the STFT to smooth the noise floor.

Performing two-dimensional threshold-crossing detection on the STFT conversion result after the noise substrate is smoothed; the two-dimensional threshold crossing detection is as follows: and taking a constant false alarm detection threshold as an adaptive threshold value, taking the maximum amplitude value of the signal to be detected multiplied by a preset attenuation coefficient as a large signal threshold, comparing the adaptive threshold value with the large signal threshold, taking the larger value of the adaptive threshold value and the large signal threshold as a current detection threshold, and carrying out threshold-crossing detection on the STFT conversion result after the noise substrate is smoothed.

And detecting the subcodes in the two-dimensional threshold-crossing detection result.

And intercepting data corresponding to each subcode from the original data of the signal to be detected according to the start-stop position of the subcode obtained by detection, performing Fourier transform (FFT) to calculate the frequency of the subcode, and further calculating other parameters of the signal to be detected according to the frequency of the subcode.

Further, a constant false alarm detection threshold is used as a self-adaptive threshold value, and specifically: the calculated adaptive threshold value is

In the above formula, the first and second carbon atoms are,

to obtain the mean of the noise samples, k is the adjustment factor and δ is the offset compensation factor.

Further, the two-dimensional threshold-crossing detection result is a two-dimensional result graph; detecting the subcode in the two-dimensional threshold-crossing detection result, which specifically comprises the following steps: the maximum value of each column in the two-dimensional result graph is reserved, and the shape of each subcode on the two-dimensional time-frequency graph is converted into a line, namely the two-dimensional linear time-frequency graph is obtained; and searching and determining the number and the starting and stopping positions of the subcodes on the two-dimensional linear time-frequency graph.

Further, on the two-dimensional linear time-frequency diagram, the number and the start-stop positions of the sub-codes are searched and determined, and the following specific steps are adopted: detecting non-zero points on a two-dimensional linear time-frequency diagram, wherein the current non-zero points are (i, j), if the points of the current non-zero points (i, j) in the front setting range in the time direction are all 0, the current non-zero points (i, j) are the initial position of the current sub-code, the current non-zero points (i, j) are taken as the initial points, the first non-zero point obtained by detection in the rear setting range in the time direction is taken as the end position of the current sub-code, and therefore the start-stop position of the current sub-code is obtained; and by analogy, detecting to obtain all the subcodes and the start-stop positions thereof.

Further, detect the subcode in two-dimentional threshold detection result, later, still include the filtration of noise subcode, specifically be: calculating the length of the sub code according to the start and stop positions of the sub code; and setting a noise sub-code length threshold value as a set proportion for calculating the length of one sub-code according to the STFT result, and filtering the sub-codes of which the sub-code lengths are smaller than the noise sub-code length threshold value.

Further, the noise subcode filtering further comprises: and detecting the initial positions of all the subcodes, and filtering the subcode with shorter length if the distance between the initial positions of the two subcodes is less than a set distance threshold.

Further, detecting the sub-code in the two-dimensional threshold-crossing detection result, and then: and arranging the length values of all the subcodes from small to large to obtain a subcode length sequence, selecting a set point in the subcode length sequence, and sequentially calculating the variance of the points with the preset number, and modifying the subcode length value corresponding to the set point into the mean value of the points with the preset number if the variance is mutated.

Further, detecting the sub-code in the two-dimensional threshold-crossing detection result, and then: taking the average value of all the sub-code lengths as the sub-code time width; comparing the initial positions of every two adjacent subcodes, if the initial positions of two adjacent subcodes differ by N times of the subcode time width, missing N subcodes between the current two adjacent subcodes, and calculating the position of the missing subcode according to the positions of the current two adjacent subcodes and the subcode time width; and completing the missing subcodes.

Has the advantages that:

1. the subcodes are detected through the two-dimensional time-frequency graph, and a threshold crossing detection method and a noise floor smoothing method of the two-dimensional time-frequency graph are designed, so that the detection of intra-pulse frequency coding signals under the conditions of interference and large noise floor fluctuation can be better adapted;

2. an adjacent subcode segmentation and missing subcode completion method is designed, so that the detection of distorted signals can be better adapted;

drawings

Fig. 1 is a flowchart of a method for measuring intra-pulse frequency coding signal parameters based on short-time fourier transform according to an embodiment of the present invention;

FIG. 2 is a diagram illustrating the STFT result of the frequency-encoded signal according to an embodiment of the present invention;

fig. 3(a) is the original signal waveform before smoothing the noise floor, and fig. 3(b) is the noise floor after smoothing (right);

FIG. 4 is a schematic diagram of threshold generation for two-dimensional threshold crossing detection;

FIG. 5(a) is a result of edge detection in a noisy environment according to an embodiment of the present invention, and FIG. 5(b) is a result of edge detection in a non-noisy environment;

FIG. 6 is a diagram of a two-dimensional time-frequency analysis result of a frequency-coded signal, where FIG. 6(a) is before interception and FIG. 6(b) is after interception;

FIG. 7(a) is a diagram of a two-dimensional time-frequency analysis result graph of a frequency-coded signal before each row retains a maximum value; FIG. 7(b) is a diagram of a two-dimensional time-frequency analysis result graph of a frequency-coded signal after each row retains a maximum value;

fig. 8(a) is a graph showing variation in variance of the sub-code width, and fig. 8(b) is a graph showing variation in the sub-code width.

Detailed Description

The invention is described in detail below by way of example with reference to the accompanying drawings.

The invention provides a method for measuring intra-pulse frequency coding signal parameters based on short-time Fourier transform, the specific flow is shown in figure 1, and the method comprises the following steps: :

step 1, performing short-time Fourier transform (STFT) of an initial window length on a signal to be detected, calculating the length of one sub-code according to the result of the STFT, and setting the calculated length of the sub-code as the window length of subsequent STFT processing.

In the embodiment of the invention, in order to balance time resolution and frequency resolution, the window length of short-time Fourier analysis is preferably designed to be the code element length, the window length is too short, the frequency domain resolution is deteriorated, the frequency in one sub-code is unchanged, too high time domain resolution is not needed, the window length is too long, the time domain resolution is deteriorated, and adjacent sub-codes may not be distinguished. However, since the length of the symbol in the actual signal is not fixed, an adaptive window length algorithm needs to be designed. The initial window length is set as the maximum subcode length, the maximum subcode length is assumed to be 2000 points, firstly, 2000 points of STFT are carried out on the signal, the length of one subcode is estimated according to the result of the STFT, and the window length is set as the window length of the subsequent STFT processing. The calculation method depends on the integrity of the first sub-code, and if the first sub-code is weak, fluctuation in the sub-code occurs or the first and second sub-codes are adhered due to close frequency, so that window length selection is wrong. Therefore, a default window length is set in the program, and when a problem occurs in the calculation window length, the default window length is selected. The calculated STFT is shown in fig. 2.

Step 2, performing two-dimensional morphological filtering on the result of the STFT to smooth a noise substrate;

due to the influence of a receiving system and a channel, a noise substrate of a received signal to be detected may have fluctuation, which is not beneficial to the detection of the signal, and therefore, two-dimensional morphological filtering is designed to smooth the noise substrate.

The morphological operation is an image processing method developed according to a mathematical morphology set theory method aiming at a binary image. The main content is to design a whole set of transformation (operation), concept and algorithm to describe the basic features of the image. The mathematical tools are different from a common frequency domain or spatial domain method, but a mathematical method for analyzing the conditions and the structures of the sets is based on set algebra, the science for quantitatively describing the geometric structures by using a set theory method is used, the purpose of morphology is mainly to obtain object topology and structure information, and the more essential morphology of an object is obtained more intuitively through certain operations of interaction of the object and structural elements, so the mathematical tools have obvious advantages in the aspect of image processing compared with other filters.

Generally, before time-frequency detection, binarization processing is performed on a time-frequency image, the operation object of binary morphology is a set, A is set as an image set, B is a structural element, and morphological operation is to operate A by B. Among them, the most basic binary morphological operations are erosion and dilation.

The set X is operated on by the structural element and is marked as

Namely, the corrosion of X is carried out by B, and then the expansion of the result is carried out by B:

and (3) performing closed operation on the set X by using the structural elements, and marking as X & B, namely firstly expanding the X by using B, and then corroding the result by using B:

the signal is subjected to an on operation to obtain a noise floor, and the difference operation with the original signal is performed to obtain a flat noise floor, as shown in fig. 3, where fig. 3(a) is an original signal waveform before the noise floor is smoothed, and fig. 3(b) is a flat noise floor.

As can be seen from the above figure, after the noise substrate is extracted through morphological filtering, the noise substrate can be stabilized, which is beneficial to the detection of signals. In the embodiment of the invention, morphological filtering is carried out on each column of the short-time Fourier analysis.

And 3, performing two-dimensional threshold-crossing detection on the STFT conversion result after the noise base is smoothed.

The two-dimensional threshold crossing detection is as follows: the constant false alarm detection threshold is used as the self-adaptive threshold value, and the calculated self-adaptive threshold value is

In the above formula, the first and second carbon atoms are,

to obtain the mean value of the noise samples, the embodiment of the invention may be a chi-squareThe mean of the distribution, k is the adjustment factor and δ is the offset compensation factor.

The maximum amplitude value of the signal to be detected is multiplied by a preset attenuation coefficient to serve as a large signal threshold (the attenuation coefficient in the embodiment of the invention can be set according to an empirical value), the adaptive threshold value and the large signal threshold are compared, the larger value of the adaptive threshold value and the large signal threshold is taken as a current detection threshold, and threshold-passing detection is carried out on the STFT conversion result after the noise substrate is smoothed. FIG. 4 is a schematic diagram of threshold generation for two-dimensional threshold crossing detection.

The principle of the step is as follows: after the STFT is calculated, it is necessary to extract subcode information from the result of the STFT and calculate signal parameters. The program first performs image segmentation on the obtained two-dimensional distribution map. As there is noise in the actual signal and the signal-to-noise ratio of the signal is low, the result obtained by using the edge detection algorithm contains a lot of noise, as shown in fig. 5, fig. 5(a) is the edge detection result in the noise environment, and fig. 5(b) is the edge detection result in the noise-free environment. Therefore, a segmentation method using threshold detection is required to efficiently extract a signal (frequency-coded signal) from the two-dimensional distribution map.

Therefore, in the embodiment of the invention, the two-dimensional threshold-crossing detection is carried out on the STFT conversion result after the noise base is smoothed, namely, the threshold-crossing point keeps the original value, and the point which does not cross the threshold is set as 0.

The two-dimensional threshold-crossing detection method is to perform threshold-crossing detection on signals on a time sequence, namely performing threshold-crossing detection on each column of the STFT result. Meanwhile, in order to reduce the subsequent computation amount, in the embodiment of the present invention, coordinates of four points of the leftmost point, the rightmost point, the topmost point, and the bottommost point in the threshold points are calculated, and a signal in a rectangular region surrounded by the four points is extracted for subsequent analysis, as shown in fig. 6, fig. 6 is a two-dimensional time-frequency analysis result diagram of the frequency coding signal, fig. 6(a) is before clipping, and fig. 6(b) is after clipping.

The detection effect of a single self-adaptive threshold is poor due to the influence of harmonic waves and the like on a time-frequency two-dimensional result graph of the STFT. Therefore, a detection method of the adaptive threshold + the large signal threshold is designed, and a threshold generation schematic diagram is shown in fig. 6.

However, after the large signal threshold is added at present, when the harmonic energy is higher, the large signal threshold is higher, so that the weak code element is not easy to detect when detecting the signal with fluctuating amplitude, and therefore, a module for detecting the weak code element is added subsequently.

The design of the adaptive threshold requires an estimation of the noise distribution model. Assuming that the noise is zero-mean gaussian noise, its power spectral density is uniformly distributed over the entire frequency interval (-infinity, + ∞).

In practice, the power spectral density of noise typically has a flat band-limited spectral density, since the receiver bandwidth cannot be infinite. In an actual sampling process, it is impossible to take an infinitely long signal, and the energy of the noise sampled in a finite time can be regarded as the sum of a series of random variables with zero mean and the same variance. Thus, each column of the short-time Fourier analysis results can be viewed as an energy distribution function of the signal within the window function, with the noise floor obeying a Chi-squared distribution. For each row of the short-time Fourier analysis, two adjacent points are not independent. The digital short-time fourier transform can be written as:

where x is the input signal and w is the N-point window. It can be seen that when m is fixed, i.e. for each column of the short-time fourier analysis, the position of the window function is fixed, the data of this column can be seen as the energy distribution function of the signal within the time window function. When w is fixed, i.e. for each row of the short-time fourier analysis, the values of two adjacent points are:

let x (n) w (n-mN) ═ s (n, m)

It can be seen that N-1 points of s (N, m +1) are the same as s (N, m), so that two adjacent points of each row of the STFT result are not independent from each other, and the probability density distribution model is complicated.

Therefore, in the embodiment of the invention, the two-dimensional threshold detection is selected to be performed on each column of the STFT to realize the detection of the target signal.

And 4, detecting the subcodes in the two-dimensional threshold-crossing detection result.

In the embodiment of the invention, the two-dimensional threshold-crossing detection result is a two-dimensional result graph; detecting the sub-code in the two-dimensional threshold-crossing detection result, specifically:

the maximum value of each column in the two-dimensional result graph is reserved, and the shape of each subcode on the two-dimensional time-frequency graph is converted into a line, namely the two-dimensional linear time-frequency graph is obtained; as shown in fig. 7, fig. 7(a) is a schematic diagram of a two-dimensional time-frequency analysis result graph of a frequency-coded signal before each column retains a maximum value; fig. 7(b) is a schematic diagram of a two-dimensional time-frequency analysis result graph of the frequency-coded signal after each column retains a maximum value.

On the two-dimensional linear time-frequency diagram, the number and the start-stop positions of the sub-codes are searched and determined, and the following specific steps can be adopted:

on a two-dimensional linear time-frequency diagram, detecting a non-zero point, wherein the current non-zero point is (i, j), and if the current non-zero point (i, j) is 0 at all points in a front setting range in the time direction (for example, zero is detected in a range (i: i-2, j-2: j +2) except (i, j)), the current non-zero point (i, j) is the starting position of the current sub-code, the current non-zero point (i, j) is used as the starting point, and the first non-zero point detected in a rear setting range in the time direction is used as the ending position of the current sub-code (for example, the first non-zero point except (i, j) is detected in a range (i: i +2, j-2: j +2) so as to obtain the starting and stopping positions of the current sub-code, and by analogy, detecting all the sub-codes and the starting and stopping positions thereof.

In the embodiment of the invention, after the detection of the subcodes, the noise subcodes are filtered. The number of the sub-codes and the length of the sub-codes can be obtained through the calculation, under the conditions of low signal-to-noise ratio and fluctuation in a large pulse, noise can exceed a threshold, and compared with signals, the width of the detected noise sub-codes is much narrower than that of the signal sub-codes, so that the noise sub-codes can be filtered by setting a reasonable noise sub-code length threshold value, and most of the noise sub-codes can be removed. The design principle of the length threshold of the noise subcodes is to remove the noise subcodes as much as possible, and the mistakenly removed signal subcodes can be supplemented back through subsequent processing. When the width of one sub-code is calculated in the calculation of the STFT, noise can be filtered by taking one third of the width of one sub-code as a threshold value.

It can be seen that the noise points which pass the threshold can be effectively removed by eliminating the narrow subcodes. Because the threshold value cannot be accurately set, the noise sub-code removal result is generally not ideal, in order to further remove noise, the starting positions of all the sub-codes are detected, and if the distance between the starting positions of the two sub-codes is smaller than the set distance threshold value, one of the two sub-codes with shorter sub-code length is filtered, namely, the other sub-code with longer sub-code length is reserved.

By filtering noise twice, all noise points are basically removed from the detection result, all signal subcodes are reserved, and the average length of the word code is calculated according to the lengths of the signal subcodes and is used as the time width of the actual subcodes. When the average length of the subcodes is calculated, due to the fact that some adhered subcodes exist, the difference between the average length calculated by utilizing the lengths of all the subcodes and an actual value is large, the length values of all the subcodes are arranged from small to large to obtain a subcode length sequence, set points are selected from the subcode length sequence, the variances of the preset number of points are sequentially calculated, and if the variances suddenly change, the length values of the subcodes corresponding to the set points are modified into the mean value of the preset number of points. As shown in fig. 8, the experimental results demonstrate that the result of such calculation is closer to the length of the true subcode.

Fig. 8(a) shows a variation in variance of the sub-code width, and fig. 8(b) shows a variation in the sub-code width. Comparing the two figures, it can be seen that the variance of the subcode width changes abruptly after the 14 th point, and the variance calculation starts from the 5 th point, thus corresponding to the actual subcode length changing abruptly from the 18 th point.

Detecting the sub-codes in the two-dimensional threshold-crossing detection result, and then completing missing sub-codes:

taking the average value of all the sub-code lengths as the sub-code time width;

comparing the initial positions of every two adjacent subcodes, if the initial positions of two adjacent subcodes differ by N times of the subcode time width, missing N subcodes between the current two adjacent subcodes, and calculating the position of the missing subcode according to the positions of the current two adjacent subcodes and the subcode time width;

and completing the missing subcodes.

And 5, intercepting data corresponding to each subcode from the original data of the signal to be detected according to the start-stop position of the subcode obtained by detection, performing Fourier transform (FFT) to calculate the frequency of the subcode, and further calculating other parameters of the signal to be detected according to the frequency of the subcode.

In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.