CN111178325A - Signal extraction and processing method - Google Patents

Signal extraction and processing method Download PDF

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CN111178325A
CN111178325A CN202010028226.8A CN202010028226A CN111178325A CN 111178325 A CN111178325 A CN 111178325A CN 202010028226 A CN202010028226 A CN 202010028226A CN 111178325 A CN111178325 A CN 111178325A
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signal
norm
input signal
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张萍
韩叔桓
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Lanzhou University of Technology
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Abstract

The invention discloses a signal extraction and processing method, which relates to the technical field of signal extraction and processing, and specifically comprises the following steps: firstly, extracting upper and lower outlines of an input signal, averaging, carrying out Newton iteration to adjust norm to minimize the norm to obtain a variable-mode signal, then carrying out reduction operation on the variable-mode signal and the input signal for multiple times to obtain multiple groups of variable-mode signals, and carrying out Hilbert change on the multiple groups of variable-mode signals to obtain the amplitude and phase angle of all the variable-mode signals. The invention decomposes the signal to obtain the amplitude and the phase angle of the variable-mode signal, lays a solid foundation for the further processing of the subsequent signal, solves the defects of poor robustness, poor separation effect and easy error introduction of the traditional method, and can be widely applied to the existing filtering methods such as noise elimination, mode identification and the like.

Description

Signal extraction and processing method
Technical Field
The invention relates to the technical field of signal processing, in particular to a method for extracting and processing signals.
Background
With the continuous development of the digital signal processing field, the requirements of people on signal quality are continuously improved, in order to ensure the accurate extraction of signals in a complex environment and avoid the loss of important information, at present, various methods are adopted, but how to remove interference signals and clutter signals in original signals to enable the signals to meet the follow-up requirements is a troublesome problem. The modulation mode of the signal is to superpose a high-frequency target signal on a selected low-frequency carrier signal, and during signal transmission, clutter signals influencing the accurate extraction and processing of the signal are used. The traditional denoising method generally performs Fourier transform on signals, and the processing mode adopting the Fourier transform is more suitable for stable signals and has poor processing effect on non-stable signals. The processing of non-stationary signals is mainly to remove the existing clutter signals directly before demodulation, and requires either a high signal-to-noise ratio or a clean original signal. However, in the actual design, the algorithm is vague and difficult to understand, is not easy to implement, has poor effect, and is easy to lose important information, and aliasing signals are processed according to the method, because the aliasing signals are mutually overlapped on a time frequency domain and a frequency domain, the signals cannot be separated by the traditional time domain or frequency domain filtering method, so that the method for separating or extracting the aliasing signals has important theoretical significance and practical application value.
Disclosure of Invention
In order to solve the above problems, the present invention provides a method for extracting and processing signals.
The specific technical scheme provided by the invention is as follows: a method of signal extraction and processing, comprising the steps of:
s1, obtaining an original signal x (t), and simultaneously setting a Z value, wherein the Z value is the number of the variable modulus signals to be obtained;
s2, inputting an original signal x (t) as an input signal u (t), and setting i = 1;
s3, extracting the upper and lower profiles of the input signal u (t) and averaging to obtain the characteristic signal of the input signal u (t)
Figure DEST_PATH_IMAGE001
；
S4, judging the characteristic signal
Figure 138851DEST_PATH_IMAGE001
Whether the difference between the number of the medium maximum value points and the number of the minimum value points is 1 or 0: if not, the characteristic signal is sent
Figure 284661DEST_PATH_IMAGE001
Return to execution of step S3 as an input signal;
if yes, the characteristic signal is sent
Figure 925858DEST_PATH_IMAGE001
Step S5 is executed as a maximum characteristic signal;
s5, setting a proportionality coefficient and aiming at the maximum characteristic signal
Figure 549738DEST_PATH_IMAGE001
Fitting the maximum value point and the minimum value point to obtain a signal
Figure 491149DEST_PATH_IMAGE002
Then make a request for
Figure 807861DEST_PATH_IMAGE002
With input signal u (t)
Figure DEST_PATH_IMAGE003
A norm; using Newton iteration to fine-tune the norm to minimize the norm
Figure 874037DEST_PATH_IMAGE002
As a variable mode signal
Figure 301607DEST_PATH_IMAGE004
；
S6, judging the mode-changing signal
Figure 35208DEST_PATH_IMAGE004
Is equal to Z: if yes, sequentially outputting all the variable modulus signals; if not, the mode-changing signal is adjusted
Figure 522821DEST_PATH_IMAGE004
Performing a subtraction operation with the input signal u (t) as a new input signal, returning to step S3, while letting i = i + 1;
s7, performing Hilbert transform on all the variable-mode signals output in the step S6, and then fusing to obtain the amplitude and phase angle of the variable-mode signals
Figure DEST_PATH_IMAGE005
2. Extraction of the signal according to claim 1And a processing method, wherein the step S3 extracts the upper and lower contours of the input signal u (t) and averages them to obtain a characteristic signal of the input signal u (t)
Figure 873031DEST_PATH_IMAGE001
The method comprises the following steps: collecting a maximum value point and a minimum value point of an input signal u (t), and recording the maximum value point as Xmax(1) To Xmax(n 1), the minimum value point is denoted as Xmin(1) To Xmin(n 2), n1 and n2 being the number of maximum and minimum points, respectively;
maximum value point X to be collectedmax(1) To Xmax(n 1) fitting to obtain the upper envelope x of the input signal u (t)1(t) collecting the minimum value point Xmin(1) To Xmin(n 2) fitting to obtain a lower envelope x of x (t)2(t) obtaining the upper envelope x by the formula (1)1(t) and the lower envelope x2(t) obtaining a characteristic signal from the mean value
Figure 862150DEST_PATH_IMAGE001
，
Figure 246995DEST_PATH_IMAGE006
（1）。
Further, the upper envelope x1(t) and the lower envelope x2(t) the fitting formula (1) is:
Figure DEST_PATH_IMAGE007
（2）。
further, the setting of the scaling factor is performed for the maximum characteristic signal
Figure 577614DEST_PATH_IMAGE001
Fitting the maximum value point and the minimum value point to obtain a fitted signal
Figure 680699DEST_PATH_IMAGE002
The method comprises the following steps:
s11, extracting maximum characteristic signal
Figure 450072DEST_PATH_IMAGE001
Is recorded as the maximum value point of
Figure 220582DEST_PATH_IMAGE008
To
Figure DEST_PATH_IMAGE009
Minimum value point is marked as
Figure 987681DEST_PATH_IMAGE010
To
Figure DEST_PATH_IMAGE011
，
Figure 515745DEST_PATH_IMAGE012
And
Figure DEST_PATH_IMAGE013
respectively representing the number of maximum points and minimum points;
s12, k1 to
Figure 292071DEST_PATH_IMAGE014
Each of the scale coefficients in the set of scale coefficients corresponds to a maximum point of the maximum characteristic signal
Figure 854771DEST_PATH_IMAGE008
To
Figure 855088DEST_PATH_IMAGE009
Or minimum point
Figure 667186DEST_PATH_IMAGE010
To
Figure 309520DEST_PATH_IMAGE011
Multiplying, fitting by equation (2) to obtain a signal
Figure 789043DEST_PATH_IMAGE002
Wherein k1 is set to
Figure 694682DEST_PATH_IMAGE014
The initial values of (a) are all 1;
accordingly, the formula (3) is used to obtain
Figure 728497DEST_PATH_IMAGE002
With input signal u (t)
Figure 643363DEST_PATH_IMAGE003
A norm;
Figure DEST_PATH_IMAGE015
（3）
wherein the content of the first and second substances,
Figure 180655DEST_PATH_IMAGE016
and ts is the norm, and the termination time of the current data acquisition.
Further, the performing norm fine-tuning to minimize the norm in step S5 using newton iteration includes:
s13, iterating the norm through a formula (4) to obtain new proportionality coefficients k1 to
Figure 522775DEST_PATH_IMAGE014
Step S12 is executed to obtain a new one
Figure 309465DEST_PATH_IMAGE002
According to new
Figure 28022DEST_PATH_IMAGE002
Calculating the new value again according to equation (3)
Figure 950979DEST_PATH_IMAGE002
With input signal u (t)
Figure 464000DEST_PATH_IMAGE003
Norm, and repeatedly executing S13 until the norm is minimum after iteration u times;
Figure 737986DEST_PATH_IMAGE018
Figure 994655DEST_PATH_IMAGE020
Figure DEST_PATH_IMAGE021
（4）。
furthermore, the amplitude and phase angle of the modulus-varying signal
Figure 709802DEST_PATH_IMAGE022
Equation (5) for (t, w) is:
Figure DEST_PATH_IMAGE023
（5）
wherein m isiAnd (t) is a variable-mode signal, and t and w are respectively a time axis and a frequency axis of the current result.
The invention has the beneficial effects that:
the invention provides a signal extraction and processing method, which solves the defects that the traditional method is poor in robustness and easy to introduce errors, so that the detection result is closer to a true value, aliasing signals are decomposed efficiently, and the amplitude values and phase angles of all variable-mode signals of the original signals are obtained. The method has the advantages of simple algorithm and accurate separation, two broadband signal waveforms containing a plurality of frequency components can be separated by simple algorithm execution, and the separation of a plurality of signal components, namely the separation of multiple input and multiple output signals, can be completed by multiple times of algorithm execution.
In addition to the objects, features and advantages described above, other objects, features and advantages of the present invention are also provided. The present invention will be described in further detail below.
Description of the drawings:
fig. 1 is a flow chart of a signal extraction and processing method according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The signal extracting and processing method provided by any embodiment of the invention comprises the following steps:
s1, obtaining an original signal x (t), and simultaneously setting a Z value, wherein the Z value is the number of the variable modulus signals to be obtained;
a signal extracting and processing method according to any embodiment of the present invention, wherein the original signal x (t) may be any continuous mixed signal, for example, radar echo, bio-impedance signal;
the Z value may be set to any one of 1, 2, 3, 4, and 100.
S2, inputting an original signal x (t) as an input signal u (t), and setting i = 1;
s3, extracting the upper and lower profiles of the input signal u (t) and averaging to obtain the characteristic signal of the input signal u (t)
Figure 128145DEST_PATH_IMAGE001
；
In a signal extracting and processing method according to any embodiment of the present invention, the upper and lower contours of the input signal u (t) are extracted and averaged to obtain the characteristic signal of the input signal u (t)
Figure 889427DEST_PATH_IMAGE001
The method comprises the following steps: collecting a maximum value point and a minimum value point of an input signal u (t), and recording the maximum value point as Xmax(1) To Xmax(n 1), the minimum value point is denoted as Xmin(1) To Xmin(n 2), n1 and n2 being the number of maximum and minimum points, respectively;
maximum value point X to be collectedmax(1) To Xmax(n 1) fitting by equation (2) to obtain the upper envelope of the input signal u (t)Line x1(t) collecting the minimum value point Xmin(1) To Xmin(n 2) fitting by equation (2) to obtain the lower envelope x of x (t)2(t)；
Calculating the upper envelope line x by formula (1)1(t) and the lower envelope x2(t) obtaining a characteristic signal from the mean value
Figure 684208DEST_PATH_IMAGE001
，
Figure 316178DEST_PATH_IMAGE006
（1）。
Figure 171001DEST_PATH_IMAGE007
（2）。
S4, judging the characteristic signal
Figure 419580DEST_PATH_IMAGE001
Whether the difference between the number of the medium maximum value points and the number of the minimum value points is 1 or 0: if not, the characteristic signal is sent
Figure 752472DEST_PATH_IMAGE001
Return to execution of step S3 as an input signal;
if yes, the characteristic signal is sent
Figure 770107DEST_PATH_IMAGE001
Step S5 is executed as a maximum characteristic signal;
s5, setting a proportionality coefficient and aiming at the maximum characteristic signal
Figure 61411DEST_PATH_IMAGE001
Fitting the maximum value point and the minimum value point to obtain a signal
Figure 531706DEST_PATH_IMAGE002
Then make a request for
Figure 668290DEST_PATH_IMAGE002
With input signal u (t)
Figure 274852DEST_PATH_IMAGE003
A norm; using Newton iteration to fine-tune the norm to minimize the norm
Figure 737057DEST_PATH_IMAGE002
As a variable mode signal
Figure 960228DEST_PATH_IMAGE004
；
A signal extracting and processing method according to any of the embodiments of the present invention, wherein the scaling factor is set to k1 to
Figure 103764DEST_PATH_IMAGE014
To ensure the continuity of the signal, k1 is set to
Figure 95991DEST_PATH_IMAGE014
All are 1, and the maximum characteristic signal is obtained
Figure 729098DEST_PATH_IMAGE001
Is recorded as the maximum value point of
Figure 173986DEST_PATH_IMAGE008
To
Figure 449109DEST_PATH_IMAGE009
Minimum value point is marked as
Figure 30263DEST_PATH_IMAGE010
To
Figure 303113DEST_PATH_IMAGE011
，
Figure 235297DEST_PATH_IMAGE012
And
Figure 517373DEST_PATH_IMAGE013
each representing a maximum point and a minimum pointCounting;
k1 to
Figure 218613DEST_PATH_IMAGE014
Each of the scale coefficients in the set of scale coefficients corresponds to a maximum point of the maximum characteristic signal
Figure 927943DEST_PATH_IMAGE008
To
Figure 347423DEST_PATH_IMAGE009
Or minimum value
Figure 698770DEST_PATH_IMAGE010
To
Figure 520096DEST_PATH_IMAGE011
Multiplying, fitting by equation (2) to obtain a signal
Figure 931485DEST_PATH_IMAGE002
。
Exemplary, k1And
Figure 838261DEST_PATH_IMAGE008
multiplication, k2And
Figure 727720DEST_PATH_IMAGE024
multiplication,,,,,, kplus-1And
Figure DEST_PATH_IMAGE025
multiplication, kplusAnd
Figure 137973DEST_PATH_IMAGE011
multiplication.
A method of extracting and processing a signal according to any of the embodiments of the present invention, wherein the method comprises
Figure 454685DEST_PATH_IMAGE002
With input signal u (t)
Figure 114336DEST_PATH_IMAGE003
The norm is given by equation (3):
Figure 807486DEST_PATH_IMAGE015
（3）
wherein the content of the first and second substances,
Figure 868982DEST_PATH_IMAGE016
and ts is the norm, and the termination time of the current data acquisition.
In the method for extracting and processing a signal according to any embodiment of the present invention, a specific way of finely adjusting a norm by using newton iteration to minimize the norm is as follows:
the norm is iterated through equation (4) to obtain new scaling factors k1 to
Figure 622175DEST_PATH_IMAGE014
New k1 to
Figure 769122DEST_PATH_IMAGE014
Each of the scale coefficients is in one-to-one correspondence with
Figure 384DEST_PATH_IMAGE001
Maximum value point of
Figure 916387DEST_PATH_IMAGE008
To
Figure 840481DEST_PATH_IMAGE009
Or minimum value
Figure 474724DEST_PATH_IMAGE010
To
Figure 509676DEST_PATH_IMAGE011
Multiplying, fitting by equation (2) to obtain a new signal
Figure 14607DEST_PATH_IMAGE002
According to new
Figure 109602DEST_PATH_IMAGE002
Calculating the new value again according to equation (3)
Figure 231142DEST_PATH_IMAGE002
With input signal u (t)
Figure 804206DEST_PATH_IMAGE003
Performing norm, and repeatedly executing the step until the norm is minimum after iteration for u times;
Figure 429222DEST_PATH_IMAGE018
Figure 960698DEST_PATH_IMAGE020
Figure 38375DEST_PATH_IMAGE021
（4）。
s6, judging the mode-changing signal
Figure 946288DEST_PATH_IMAGE004
Is equal to Z: if yes, sequentially outputting all the variable modulus signals; if not, the mode-changing signal is adjusted
Figure 425811DEST_PATH_IMAGE004
Performing a subtraction operation with the input signal u (t) as a new input signal, returning to step S3, while letting i = i + 1;
illustratively, when the value of Z is set to 4, when i = Z, all the modulus-varying signals output in sequence are
Figure 128188DEST_PATH_IMAGE026
、
Figure DEST_PATH_IMAGE027
、
Figure 162003DEST_PATH_IMAGE028
、
Figure DEST_PATH_IMAGE029
(ii) a When the value of Z is set to be 10, when i = Z, all the modulus-changing signals output in sequence are
Figure 811290DEST_PATH_IMAGE026
、
Figure 676478DEST_PATH_IMAGE027
、、、、、、、
Figure 284177DEST_PATH_IMAGE030
、
Figure DEST_PATH_IMAGE031
。
S7, performing Hilbert transform on all the variable-mode signals output in the step S6, and then fusing to obtain the amplitude and phase angle of the variable-mode signals
Figure 70867DEST_PATH_IMAGE005
A method for extracting and processing signals according to any embodiment of the present invention, wherein the amplitude and phase angle of the modulus-variable signal are calculated
Figure 789424DEST_PATH_IMAGE032
Equation (5) of (a) is:
Figure 509119DEST_PATH_IMAGE023
（5）
wherein m isiAnd (t) is a variable-mode signal, and t and w are respectively a time axis and a frequency axis of the current result.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and should not be taken as limiting the invention, but rather the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the present invention.

Claims (6)

1. A method for extracting and processing signals, comprising the steps of:
s1, obtaining an original signal x (t), and simultaneously setting a Z value, wherein the Z value is the number of the variable modulus signals to be obtained;
s2, inputting an original signal x (t) as an input signal u (t), and setting i = 1;
s3, extracting the upper and lower profiles of the input signal u (t) and averaging to obtain the characteristic signal of the input signal u (t)
Figure 332582DEST_PATH_IMAGE001
；
S4, judging the characteristic signal
Figure 742835DEST_PATH_IMAGE001
Whether the difference between the number of the medium maximum value points and the number of the minimum value points is 1 or 0: if not, the characteristic signal is sent
Figure 325126DEST_PATH_IMAGE001
Return to execution of step S3 as an input signal;
if yes, the characteristic signal is sent
Figure 515936DEST_PATH_IMAGE001
Step S5 is executed as a maximum characteristic signal;
s5, setting a proportionality coefficient and aiming at the maximum characteristic signal
Figure 209085DEST_PATH_IMAGE001
Fitting the maximum value point and the minimum value point to obtain a signal
Figure 739424DEST_PATH_IMAGE002
Then make a request for
Figure 492616DEST_PATH_IMAGE002
With input signal u (t)
Figure 905143DEST_PATH_IMAGE003
A norm; fine tuning norm using newton iterationObtained when norm is minimized
Figure 401983DEST_PATH_IMAGE002
As a variable mode signal
Figure 786828DEST_PATH_IMAGE004
；
S6, judging the mode-changing signal
Figure 710922DEST_PATH_IMAGE004
Is equal to Z: if yes, sequentially outputting all the variable modulus signals; if not, the mode-changing signal is adjusted
Figure 79587DEST_PATH_IMAGE004
Performing a subtraction operation with the input signal u (t) as a new input signal, returning to step S3, while letting i = i + 1;
s7, performing Hilbert transform on all the variable-mode signals output in the step S6, and then fusing to obtain the amplitude and phase angle QUOTE of the variable-mode signals
Figure DEST_PATH_IMAGE006A
Figure DEST_PATH_IMAGE006AA
。
2. The method for extracting and processing the signal according to claim 1, wherein the step S3 is to extract the upper and lower contours of the input signal u (t) and average the upper and lower contours to obtain the characteristic signal of the input signal u (t)
Figure 317801DEST_PATH_IMAGE001
The method comprises the following steps: collecting a maximum value point and a minimum value point of an input signal u (t), and recording the maximum value point as Xmax(1) To Xmax(n 1), the minimum value point is denoted as Xmin(1) To Xmin(n 2), n1 and n2 being the number of maximum and minimum points, respectively;
maximum value to be collectedPoint Xmax(1) To Xmax(n 1) fitting to obtain the upper envelope x of the input signal u (t)1(t) collecting the minimum value point Xmin(1) To Xmin(n 2) fitting to obtain a lower envelope x of x (t)2(t) obtaining the upper envelope x by the formula (1)1(t) and the lower envelope x2(t) obtaining a characteristic signal from the mean value
Figure 822732DEST_PATH_IMAGE001
，
Figure 652147DEST_PATH_IMAGE007
（1）。
3. Method for extracting and processing signals according to claim 2, characterized in that said upper envelope x1(t) and the lower envelope x2(t) the fitting formula (1) is:
Figure 242529DEST_PATH_IMAGE008
（2）。
4. a method for extracting and processing signals according to claim 3, wherein the scaling factor is set for the maximum feature signal
Figure 81172DEST_PATH_IMAGE001
Fitting the maximum value point and the minimum value point to obtain a fitted signal
Figure 502926DEST_PATH_IMAGE002
The method comprises the following steps:
s11, extracting maximum characteristic signal
Figure 503243DEST_PATH_IMAGE001
Is recorded as the maximum value point of
Figure 580920DEST_PATH_IMAGE009
To
Figure 957675DEST_PATH_IMAGE010
Minimum value point is marked as
Figure 233936DEST_PATH_IMAGE011
To
Figure 670733DEST_PATH_IMAGE012
，
Figure 970127DEST_PATH_IMAGE013
And
Figure 150573DEST_PATH_IMAGE014
respectively representing the number of maximum points and minimum points;
s12, k1 to
Figure 750182DEST_PATH_IMAGE015
Each of the scale coefficients in the set of scale coefficients corresponds to a maximum point of the maximum characteristic signal
Figure 154618DEST_PATH_IMAGE009
To
Figure 941309DEST_PATH_IMAGE010
Or minimum point
Figure 659866DEST_PATH_IMAGE011
To
Figure 113981DEST_PATH_IMAGE012
Multiplying, fitting by equation (2) to obtain a signal
Figure 689319DEST_PATH_IMAGE002
Wherein k1 is set to
Figure 963305DEST_PATH_IMAGE015
The initial values of (a) are all 1;
accordingly, the formula (3) is used to obtain
Figure 219974DEST_PATH_IMAGE002
With input signal u (t)
Figure 528596DEST_PATH_IMAGE003
A norm;
Figure 478097DEST_PATH_IMAGE016
（3）
wherein the content of the first and second substances,
Figure 504959DEST_PATH_IMAGE017
is a norm, tsIs the termination moment of the current data acquisition.
5. The method for extracting and processing the signal according to claim 4, wherein the step S5 of performing norm fine-tuning using newton iteration to minimize the norm comprises:
s13, iterating the norm through a formula (4) to obtain new proportionality coefficients k1 to
Figure 362057DEST_PATH_IMAGE015
Step S12 is executed to obtain a new one
Figure 790764DEST_PATH_IMAGE002
According to new
Figure 645588DEST_PATH_IMAGE002
Calculating the new value again according to equation (3)
Figure 894166DEST_PATH_IMAGE002
With input signal u (t)
Figure 554955DEST_PATH_IMAGE003
Norm, and repeatedly executing S13 until the norm is minimum after iteration u times;
Figure 838169DEST_PATH_IMAGE018
Figure 863893DEST_PATH_IMAGE019
Figure 599768DEST_PATH_IMAGE020
（4）。
6. method for extracting and processing signals according to claim 1, characterized in that the amplitude and phase angle of said modulus-varying signal
Figure 267510DEST_PATH_IMAGE021
Equation (5) for (t, w) is:
Figure 201968DEST_PATH_IMAGE022
（5）
wherein m isiAnd (t) is a variable-mode signal, and t and w are respectively a time axis and a frequency axis of the current result.
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