CN114003857A - Short-time linear regular transformation time-frequency analysis method based on variable sliding window - Google Patents
Short-time linear regular transformation time-frequency analysis method based on variable sliding window Download PDFInfo
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Abstract
The invention discloses a short-time linear regular transformation time-frequency analysis method based on a variable sliding window, which comprises the following steps: s1: acquiring non-stationary signal data; s2: segmenting an original signal according to the analysis task and the non-stationary signal characteristics, and performing discrete short-time linear regular transformation on the sub-segment signal by adopting different sliding window functions to obtain a sub-segment signal spectrum; s3: combining the spectral results of the sub-segment signals; s4: and outputting the time-frequency distribution graph of the time-frequency and frequency-frequency variation relation of the complete non-stationary signal obtained by combination in an oscilloscope. The invention selects different sliding window functions for each signal subsection based on the characteristics of non-stationary signals, and forms a short-time linear regular transformation time-frequency analysis method based on a variable sliding window. The method not only retains the advantages of short-time linear regular transformation, but also obtains a more accurate signal local time frequency distribution result based on variable window function analysis.
Description
Technical Field
The invention relates to the field of non-stationary signal time-frequency analysis, in particular to a short-time linear regular transformation time-frequency analysis method based on a variable sliding window.
Background
Most of signals generated in the complex industrial production process have non-stationary characteristics, for example, fault detection and diagnosis in a wind power grid-connected system face a large number of non-stationary signals. A single time domain analysis or frequency domain analysis of these non-stationary signals does not work well. The conventional Short-time Fourier transform (STFT) is one of the most effective methods for time-frequency joint analysis of non-stationary signals. In recent years, Short-time linear canonical transform (STLCT) is introduced into the field of signal processing as a generalized form of Short-time fourier transform.
However, when time-frequency analysis is performed using the STLCT signal, it is generally desirable to have a higher resolution in the time domain for signals that change more rapidly in frequency. For example, a higher temporal resolution facilitates observation of a fast-varying portion of its frequency (e.g., a spike signal). I.e. the time width desired to be observed is small, but under the influence of the uncertainty principle of the STLCT domain, the resolution of the frequency domain of the signal will necessarily decrease, and therefore, this is a problem faced by high frequency signals. Sometimes, the high-frequency signal is only a signal in a certain local time period in the whole signal, and the other time periods are low-frequency signals. For low frequency signals in these time periods, a higher frequency domain resolution is desired, but likewise the time resolution is reduced accordingly. Therefore, when the global window function type and the width are selected, the area of the time-frequency plane cell formed by the time width and the bandwidth (i.e. the time-frequency plane resolution) is constant in the whole STLCT time-frequency plane.
The disadvantages are as follows: the current STLCT adopts a global window function to analyze a non-stationary signal, and the problem that the local change characteristic of the non-stationary signal is difficult to accurately obtain exists.
Therefore, a time-frequency analysis method capable of accurately analyzing local frequency characteristics of non-stationary signals is needed.
Disclosure of Invention
In view of the above, the technical problem to be solved by the present invention is to provide a method capable of accurately reflecting the local frequency variation trend of a signal while retaining the advantages of the conventional short-time linear canonical transformation. The method divides the original non-stationary signal into a plurality of sections according to the analysis requirement, and performs the spectrum analysis based on the short-time linear regular transformation on each section by using a proper window function.
The purpose of the invention is realized as follows:
the invention provides a short-time linear regular transformation time-frequency analysis method based on a variable sliding window, which comprises the following steps:
s1: acquiring non-stationary signal data;
s2: segmenting an original signal according to the analysis task and the non-stationary signal characteristics, and performing discrete short-time linear regular transformation on the sub-segment signal by adopting different sliding window functions to obtain a sub-segment signal spectrum;
s3: carrying out transformation in the step S2 on each subsection of the original signal, and combining the frequency spectrum results of the subsegment signals;
s4: and outputting the time-frequency analysis graph of the time-frequency and frequency-spectrum change relation of the complete non-stationary signal obtained by combination in an oscilloscope.
Further, in the step S2, the original signal is segmented according to the analysis task and the non-stationary signal characteristics, and different sliding window functions are used to perform discrete short-time linear regular transformation on the sub-segment signal, so as to obtain a sub-segment signal spectrum, which specifically includes the following steps:
s21: according to the obtained non-stationary signal characteristics and analysis task, the non-stationary signal is divided into several subsections in a self-defined way on the time domain, different window functions are selected for each subsection, for example, the first subsection signal is analyzed by using a rectangular window function, generally speaking, the expression of the rectangular window function is
S22: the first sub-segment signal is multiplied by a rectangular window function, and then a Discrete Linear Canonical Transform (DLCT) is applied thereto, based on the multiplication result, aThe general expression is
Wherein a, b, c and d are free parameters satisfying ad-bc as 1, t is time, w is frequency, and j is imaginary unit. After selecting free parameters in the transformation formula, performing discrete short-time linear regular transformation under a rectangular window on the first subsegment signal to obtain a spectrogram of the first subsegment, and obtaining the result that
Further, in the step S3, the original signal is transformed in the step S2 for each sub-segment, and the spectrum results of the sub-segment signals are combined, specifically including the following steps:
s31: according to the original signal characteristics and the analysis task, a window function different from that of the first subsegment is used for the second subsegment signal, such as Hanning window function analysis; in general, expressions of Hanning Window functions
N.ltoreq.1 is the spectrogram of the second sub-segment obtained by applying the method of step S22.
S32: based on the slicing result of the original signal in the step S2, the above steps S21 and S22 (the type of window function may be changed according to the requirement of spectrum analysis) are repeated until the analysis is finished.
The invention has the advantages that: the invention analyzes the frequency spectrum information of the non-stationary signal based on the short-time linear regular transformation of the variable window. On the one hand, the short-time linear canonical transform is a more generalized short-time fourier transform, and has advantages in analyzing non-stationary signals such as multi-component signals and radar signals. On the other hand, the short-time linear canonical transform, like the classical short-time fourier transform, selects a global window function, i.e. a feature that is modifiable once the window function is selected. According to the method, the original signal is segmented according to the signal spectrum analysis requirement, and then the proper window function is selected according to different analysis tasks, so that the defect that the local spectrum characteristics of the signal cannot be accurately described due to the use of the global window function in the traditional method is overcome.
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In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the accompanying drawings, in which:
FIG. 1 is a flow chart of a short-time linear canonical transform time-frequency analysis method of a variable sliding window;
fig. 2 is a flow chart of a variable sliding window slicing signal.
Detailed description of the preferred embodiments
The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings; it should be understood that the preferred embodiments are illustrative of the invention only and are not limiting upon the scope of the invention.
Fig. 1 is a flow chart of a short-time linear regular transformation time-frequency analysis method of a variable sliding window, and fig. 2 is a flow chart of a variable sliding window slicing signal, as shown in the figure: the invention provides a short-time linear regular transformation time-frequency analysis method based on a variable sliding window, which comprises the following steps:
s1: acquiring non-stationary signal data;
s2: segmenting an original signal according to the analysis task and the non-stationary signal characteristics, and performing discrete short-time linear regular transformation on the sub-segment signal by adopting different sliding window functions to obtain a sub-segment signal spectrum;
s21: according to the obtained non-stationary signal characteristics and analysis task, the non-stationary signal is divided into several subsections in a self-defined way on the time domain, different window functions are selected for each subsection, for example, the first subsection signal is analyzed by using a rectangular window function, generally speaking, the expression of the rectangular window function is
S22: the first sub-segment signal is multiplied by a rectangular window function, and then a Discrete Linear Canonical Transform (DLCT) is applied thereto according to the multiplication result, and a general expression is
Wherein the ratio of a, b, c,d is a free parameter satisfying ad-bc as 1, t is time, w is frequency, and j is an imaginary unit. After selecting free parameters in the transformation formula, performing discrete short-time linear regular transformation under a rectangular window on the first subsegment signal to obtain a spectrogram of the first subsegment, and obtaining the result that
S3: carrying out transformation in the step S2 on each subsection of the original signal, and combining the frequency spectrum results of the subsegment signals;
s31: according to the original signal characteristics and the analysis task, a window function different from that of the first subsegment is used for the second subsegment signal, such as Hanning window function analysis; in general, expressions of Hanning Window functions
N.ltoreq.1 is the spectrogram of the second sub-segment obtained by applying the method of step S22.
S32: based on the slicing result of the original signal in step S2, the above steps S21 and S22 (the type of window function may be changed according to the requirement of spectrum analysis) are repeated until the analysis is finished.
S4: and outputting the time-frequency analysis graph of the time-frequency and frequency-spectrum change relation of the complete non-stationary signal obtained by combination in an oscilloscope.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and it is apparent that those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
Claims (3)
1. A short-time linear regular transformation time-frequency analysis method based on a variable sliding window is characterized in that: the method comprises the following steps:
s1: acquiring non-stationary signal data;
s2: segmenting an original signal according to the analysis task and the non-stationary signal characteristics, and performing discrete short-time linear regular transformation on the sub-segment signal by adopting different sliding window functions to obtain a sub-segment signal spectrum;
s3: carrying out transformation in the step S2 on each subsection of the original signal, and combining the frequency spectrum results of the subsegment signals;
s4: and outputting the time-frequency analysis graph of the time-frequency and frequency-spectrum change relation of the complete non-stationary signal obtained by combination in an oscilloscope.
2. The variable sliding window-based short-time linear canonical transform time-frequency analysis method according to claim 1, characterized in that: the original signal is segmented according to the analysis task and the non-stationary signal characteristics in the step S2, and the sub-segment signal is subjected to discrete short-time linear regular transformation by using different sliding window functions to obtain a sub-segment signal spectrum, which specifically includes the following steps:
s21: according to the obtained non-stationary signal characteristics and analysis task, the non-stationary signal is divided into several subsections in a self-defined way on the time domain, different window functions are selected for each subsection, for example, the first subsection signal is analyzed by using a rectangular window function, generally speaking, the expression of the rectangular window function is
S22: the first sub-segment signal is multiplied by a rectangular window function, and then a Discrete Linear Canonical Transform (DLCT) is applied thereto according to the multiplication result, and a general expression is
Wherein a, b, c and d are free parameters satisfying ad-bc as 1, t is time, w is frequency, and j is imaginary unit. After selecting free parameters in the transformation formula, performing discrete short-time linear regular transformation under a rectangular window on the first subsegment signal to obtain a spectrogram of the first subsegment, and obtaining the result that
3. The variable sliding window-based short-time linear canonical transform time-frequency analysis method according to claim 1, characterized in that: in step S3, the original signal is transformed in step S2 for each sub-segment, and the spectrum results of the sub-segment signals are combined, specifically including the following steps:
s31: according to the original signal characteristics and the analysis task, a window function different from that of the first subsegment is used for the second subsegment signal, such as Hanning window function analysis; in general, expressions of Hanning Window functions
The method of step S22 is then applied to obtain a spectrogram of the second sub-segment.
S32: based on the slicing result of the original signal in the step S2, the above steps S21 and S22 (the type of window function may be changed according to the requirement of spectrum analysis) are repeated until the analysis is finished.
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