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Signal extension method and system based on time-frequency coefficient variance minimization
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A time-frequency coefficient, minimization technology, applied in the field of signal processing, can solve the problem of not involving the selection of continuation points, and achieve the effect of increasing the effective signal length, improving frequency resolution, and good stability
Active Publication Date: 2018-08-28
TSINGHUA UNIV
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The key to signal extension is to periodically extend the signal at an appropriate point, and the above methods do not involve the selection of extension points (especially when the signal is mixed with white noise, the selection of extension points will become more important), and makes the implementation of periodic extensions random
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Embodiment 1
[0039] In this example, with s 1 (t) is an example signal, signal s 1 (t) includes two frequencies of 100Hz and 200Hz, and its sampling frequency is 2KHz, then the signal s 1 (t) is expressed as:
[0040]
[0041] Among them, adding a white noise signal with an intensity of 0.1, the signal s 1 (t) Waveform diagram in the time domain such as image 3 shown.
[0042] Based on this, in this embodiment, the signal extension method based on the minimization of time-frequency coefficient variance includes the following steps:
[0043] Step 1: Set the search range to [1,M], M is 210, that is, the search range is [1,210].
[0044] Step 2: Set search position i=1.
[0045] Step 3: Select signal s 1 (N 1 ), (N 1 =1, 2, 3, ..., N, N is the number of signal sampling points), for s 1 (N 1 ) to perform Gabor transformation (other time-frequency transformations are also possible, such as continuous wavelet transformation), and record the number of Gabor transformation columns a...
Embodiment 2
[0053] In this example, with s 2 (t) is an example signal, signal s 2 (t) includes two frequencies of 400Hz and 401Hz, and its sampling frequency is 2KHz, then the signal s 2 (t) is expressed as:
[0054]
[0055] Based on this, in this embodiment, the signal extension method based on the minimization of time-frequency coefficient variance includes the following steps:
[0056] Step 10: Set the search range to [1,M], and M to 210, that is, the search range to [1,210].
[0057] Step 20: Set search position i=1.
[0058] Step 30: Take signal s 1 (N 1 ), (N 1 =1, 2, 3, ..., N, N is the number of signal sampling points), for s 1 (N 1 ) to perform Gabor transformation (other time-frequency transformations are also possible, such as continuous wavelet transformation), and record the number of Gabor transformation columns as L=64.
[0059] Step 40: Select signal s 2 (N 2 ), (N 2 =2, 3, 4, ..., N, N is the number of signal sampling points), for the signal s 2 (N 2 ) i...
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Abstract
The invention provides a signal extending method and system based on minimization of a time-frequency coefficient variance. The method comprises the following steps of: setting a search range to [1,M] and an initial search position i to 1; selecting a signal s(n1) to be extended in the search range, and performing time-frequency transformation, wherein a time-frequency transformation column number is L; selecting a signal s(n2) to be extended, and turning the s(n2) so as to obtain an extended signal sy; connecting the sy with the s2(n2) so as to perform signal extension, so that the extended signal sp is obtained; performing time-frequency transformation of the sp, and calculating the variance of the L-1th column of a time-frequency transformation coefficient; repeating the above steps till variances corresponding to various search positions in the search range are obtained; and comparing the variances corresponding to all the search positions, searching the search position corresponding the maximum variance, and taking extension corresponding to the search position as the final signal extension. By means of the signal extending method and system disclosed by the invention, the port effect can be effectively inhibited; and the signal frequency resolution is improved.
Description
technical field [0001] The invention relates to the technical field of one-dimensional signal processing, in particular to a signal extension method and system based on the minimization of time-frequency coefficient variance. Background technique [0002] In the process of one-dimensional signal processing and analysis, two types of problems are generally encountered, namely: the problem of endpoint effects and the problem of insufficient signal sampling time length and insufficient signal frequency resolution. To this end, related technologies have proposed a variety of signal continuation methods, such as direct continuation methods such as signal sequence dual continuation, signal sequence mirror continuation, signal sequence periodic continuation, and time series-based continuation and neural network-based prediction continuation methods Tuo and other methods. The key to signal extension is to periodically extend the signal at an appropriate point, and the above methods...
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