CN109374969B - Down-sampling sinusoidal signal phase difference measurement method based on coherent accumulation DFT - Google Patents

Down-sampling sinusoidal signal phase difference measurement method based on coherent accumulation DFT Download PDF

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CN109374969B
CN109374969B CN201811160519.0A CN201811160519A CN109374969B CN 109374969 B CN109374969 B CN 109374969B CN 201811160519 A CN201811160519 A CN 201811160519A CN 109374969 B CN109374969 B CN 109374969B
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CN109374969A (en
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唐启见
刘佳
李建
刘娟
钟雅瑾
张珏
吴小平
左国才
马庆
苏秀芝
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Hunan Software Vocational Institute
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Abstract

The invention discloses a phase difference measuring method of a down-sampling sinusoidal signal based on DFT of coherent accumulation in the field of signal processing, which comprises the following steps: respectively sampling two groups of sinusoidal signals with the same frequency by using a down-sampling mode to obtain two groups of sampling signals; respectively carrying out coherent accumulation on the two groups of sampling signals to obtain two groups of accumulated signals; respectively carrying out discrete Fourier transform on the two groups of accumulated signals to obtain initial phases of two groups of sinusoidal signals with the same frequency; and calculating the phase difference between the two groups of sinusoidal signals according to the initial phase between the two groups of sinusoidal signals with the same frequency.

Description

Down-sampling sinusoidal signal phase difference measurement method based on coherent accumulation DFT
Technical Field
The invention relates to the field of signal processing, and particularly discloses a phase difference measuring method for a down-sampling sinusoidal signal based on DFT (discrete Fourier transform) of coherent accumulation.
Background
Phase difference measurement of sinusoidal signals is an important research topic in many applications such as power system monitoring, radio frequency communication, radar positioning, laser ranging, and the like. Furthermore, it can also be applied to phase calibration, especially useful in phase calibration on single-pass on-board/on-board InSAR systems.
Many different phase difference measurement methods have been discussed for a long time, such as least squares or Discrete Fourier Transform (DFT) methods, hilbert transform methods, ICA methods, and zero crossing detection methods. However, the DFT-based spectrum analysis method requires one complete sampling period in calculation; the zero-crossing detection method is unreliable in the case where noise is superimposed on the signal; furthermore, when the signal frequency is too high, there is a lack of research on how to select the sampling frequency and what phase difference measurement method to use.
Disclosure of Invention
The invention aims to solve the technical defect that the phase difference of the adopted sinusoidal signals cannot be obtained when the signal frequency is too high in the prior art.
In order to achieve the above object, the present invention provides a down-sampling sinusoidal signal phase difference measurement method based on coherent accumulation DFT, which comprises the following steps:
s1: respectively sampling two groups of sinusoidal signals with the same frequency by using a down-sampling mode to obtain two groups of sampling signals;
s2: respectively carrying out coherent accumulation on the two groups of sampling signals to obtain two groups of accumulated signals;
s3: respectively carrying out discrete Fourier transform on the two groups of accumulated signals to obtain initial phases of two groups of sinusoidal signals with the same frequency;
s4: and calculating the phase difference between the two groups of sinusoidal signals according to the initial phase between the two groups of sinusoidal signals with the same frequency.
Preferably, S1 includes the steps of:
s11: sampling the sinusoidal signal to obtain a sampled signal frequency spectrum;
s12: filtering the signal spectrum to obtain a baseband signal spectrum;
s13: reconstructing a baseband signal by adopting inverse Fourier transform according to the baseband signal frequency spectrum;
s14: and reconstructing the high-frequency signal according to the frequency and the initial phase of the baseband signal.
Preferably, the signal spectrum obtained at S11 is as follows:
Figure 418300DEST_PATH_IMAGE001
wherein the content of the first and second substances,
Figure 326213DEST_PATH_IMAGE002
the angular frequency is represented by the angular frequency,
Figure 805736DEST_PATH_IMAGE003
in order to be able to sample the frequency,
Figure 508113DEST_PATH_IMAGE004
is the frequency of the signal or signals,
Figure 73086DEST_PATH_IMAGE005
is a natural constant and is a natural constant,
Figure 519111DEST_PATH_IMAGE006
as an initial phase, the phase of the phase,
Figure 118720DEST_PATH_IMAGE007
the number of shifts (which is an integer),
Figure 991998DEST_PATH_IMAGE008
in the form of an impulse signal, the signal is,
Figure 44267DEST_PATH_IMAGE009
in the form of a circumferential ratio,
Figure 25474DEST_PATH_IMAGE010
in units of imaginary numbers.
Preferably, the gain of S12 for filtering the signal is
Figure 745168DEST_PATH_IMAGE011
The band pass range is
Figure 789348DEST_PATH_IMAGE012
。
Preferably, the baseband signal of S13 is as follows:
Figure 328914DEST_PATH_IMAGE013
wherein the content of the first and second substances,
Figure 116741DEST_PATH_IMAGE014
is the frequency of the baseband signal and is,
Figure 690942DEST_PATH_IMAGE015
is the initial phase of the baseband signal.
Preferably, the high frequency signal of S14 is as follows:
Figure 906022DEST_PATH_IMAGE016
wherein the content of the first and second substances,
Figure 932884DEST_PATH_IMAGE017
in order to be the sampling period of time,
Figure 258823DEST_PATH_IMAGE018
in order to be the length of the sample,
Figure 687531DEST_PATH_IMAGE019
is a signal vibration pair.
Preferably, the initial phase of S3 is as follows:
Figure 73513DEST_PATH_IMAGE020
wherein, DFT stands for discrete Fourier transform,
Figure 587671DEST_PATH_IMAGE021
is the accumulated signal.
The invention has the following beneficial effects:
1. the measuring method can effectively filter noise in the signal, improve the measuring precision of the phase difference of the sinusoidal signal and greatly reduce the measuring error;
2. the measuring method of the invention has the advantages that when the signal frequency is too high, the selection of the down-sampling frequency under the down-sampling condition is wider.
The present invention will be described in further detail below with reference to the accompanying drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
fig. 1 is a flow chart of a down-sampling sinusoidal signal phase difference measurement method based on coherent accumulation DFT according to a preferred embodiment of the present invention.
FIG. 2 is a signal spectrum diagram of a preferred embodiment of the present invention;
FIG. 3 is a signal diagram before and after coherent accumulation in accordance with a preferred embodiment of the present invention;
fig. 4 is a schematic phase difference diagram of the preferred embodiment of the present invention.
Detailed Description
The embodiments of the invention will be described in detail below with reference to the drawings, but the invention can be implemented in many different ways as defined and covered by the claims.
The DFT full name Discrete Fourier Transform is Discrete Fourier Transform, which is a form in which the Fourier Transform is Discrete in both time domain and frequency domain.
The invention firstly provides a phase difference measuring method of a down-sampling sinusoidal signal based on DFT of coherent accumulation, referring to figure 1, comprising the following steps:
s1: and respectively sampling two groups of sinusoidal signals with the same frequency by using a down-sampling mode to obtain two groups of sampling signals.
Setting sine signal
Figure 717301DEST_PATH_IMAGE022
At a sampling frequency of
Figure 514DEST_PATH_IMAGE003
The mathematical expression is as follows:
Figure 822977DEST_PATH_IMAGE023
（1）
wherein
Figure 824431DEST_PATH_IMAGE024
Is the amplitude of the signal that is not known,
Figure 757752DEST_PATH_IMAGE004
is the frequency of the signal or signals,
Figure 629893DEST_PATH_IMAGE025
is the time of day or the like,
Figure 623257DEST_PATH_IMAGE015
is an unknown initial phase. According to the Nyquist sampling theorem,
Figure 112007DEST_PATH_IMAGE003
must be 2 or more
Figure 317860DEST_PATH_IMAGE004
The original signal can be accurately restored. However, when it is desired to measure the phase difference of two sinusoidal signals,
Figure 575666DEST_PATH_IMAGE003
must be much greater than 2
Figure 739931DEST_PATH_IMAGE004
. However, when the signal frequency itself is very high, the sampling frequency will be higher and higher as the signal frequency increases, and is difficult to achieve even under the existing equipment and technical conditions, so that the implementation is difficult. Therefore, it is necessary to reduce the sampling frequency according to the band-pass sampling theorem, that is, to sample the signal by using the down-sampling method.
The sampling of the sinusoidal signal by means of down-sampling comprises the following steps:
s11: and sampling the sinusoidal signal to obtain a sampled signal frequency spectrum.
Signal
Figure 450399DEST_PATH_IMAGE022
Spectrum of
Figure 725522DEST_PATH_IMAGE026
As shown in fig. 2 (a). Wherein
Figure 837835DEST_PATH_IMAGE002
Angular frequency is indicated, arrows represent amplitude spectra, and solid black dots represent phase spectra. The spectral expression of the sampled signal is as follows:
Figure 898633DEST_PATH_IMAGE001
（2）
wherein the content of the first and second substances,
Figure 96396DEST_PATH_IMAGE002
the angular frequency is represented by the angular frequency,
Figure 909631DEST_PATH_IMAGE003
in order to be able to sample the frequency,
Figure 142029DEST_PATH_IMAGE004
is the frequency of the signal or signals,
Figure 382518DEST_PATH_IMAGE005
is a natural constant and is a natural constant,
Figure 333156DEST_PATH_IMAGE006
as an initial phase, the phase of the phase,
Figure 684503DEST_PATH_IMAGE007
in order to be the number of shifts,
Figure 771408DEST_PATH_IMAGE008
in the form of an impulse signal, the signal is,
Figure 448377DEST_PATH_IMAGE009
in the form of a circumferential ratio,
Figure 355153DEST_PATH_IMAGE010
in units of imaginary numbers.
Frequency spectrum of sampled signal
Figure 510191DEST_PATH_IMAGE027
As shown in fig. 2(b), obviously, to avoid spectrum aliasing, the following condition must be satisfied between the sampling frequency and the signal frequency:
Figure 717181DEST_PATH_IMAGE028
　　 （3）
namely:
Figure 299472DEST_PATH_IMAGE029
（4）
s12: and filtering the signal spectrum to obtain a baseband signal spectrum.
The sampled spectrum is gained by
Figure 693544DEST_PATH_IMAGE011
The band pass range is
Figure 652273DEST_PATH_IMAGE030
The rest is the spectrum of the baseband signal. At this time, there may be two cases, as shown in fig. 2(c), (d). Wherein the part marked with "1" is the signal spectrum
Figure 713770DEST_PATH_IMAGE026
As a result of shifting right n times, the portion labeled "2" is the signal spectrum
Figure 732542DEST_PATH_IMAGE026
Left shift n times.
In the case shown in fig. 2(c), the condition is satisfied:
Figure 613910DEST_PATH_IMAGE031
（5）
namely:
Figure 110750DEST_PATH_IMAGE032
（6）
the spectrum of the baseband signal obtained at this time is:
Figure 26754DEST_PATH_IMAGE033
（7）
in the case shown in fig. 2(d), the condition is satisfied:
Figure 216427DEST_PATH_IMAGE031
（10）
namely:
Figure 585091DEST_PATH_IMAGE034
（11）
the spectrum of the baseband signal obtained at this time is:
Figure 885623DEST_PATH_IMAGE035
（12）
s13: and reconstructing the baseband signal by adopting inverse Fourier transform according to the baseband signal frequency spectrum.
Performing inverse fourier transform on equation (7) to obtain a reconstructed baseband signal:
Figure 656132DEST_PATH_IMAGE036
（8）
wherein the content of the first and second substances,
Figure 16707DEST_PATH_IMAGE037
is the frequency of the baseband signal and is,
Figure 138246DEST_PATH_IMAGE038
for the initial phase of the baseband signal, it can be known from equation (8)
Figure 708380DEST_PATH_IMAGE039
（9）
I.e. baseband signals
Figure 598976DEST_PATH_IMAGE040
Initial phase and signal of
Figure 130452DEST_PATH_IMAGE041
The initial phases of (a) are the same.
Performing inverse fourier transform on equation (11) to obtain a reconstructed baseband signal:
Figure 473708DEST_PATH_IMAGE042
（13）
from the formula (13)
Figure 116042DEST_PATH_IMAGE043
（14）
I.e. baseband signals
Figure 861144DEST_PATH_IMAGE040
Initial phase and signal of
Figure 563521DEST_PATH_IMAGE041
The initial phases of (1) are opposite.
S14: and reconstructing the high-frequency signal according to the frequency and the initial phase of the baseband signal.
From low-frequency baseband signals
Figure 394074DEST_PATH_IMAGE040
Frequency of (2)
Figure 308940DEST_PATH_IMAGE037
And initial phase
Figure 174128DEST_PATH_IMAGE038
Can reconstruct high frequency signals
Figure 47406DEST_PATH_IMAGE041
(ii) a And the phase difference of two sinusoidal signals of the same frequency can be measured by selecting a sampling frequency satisfying the condition (6) or (11).
Assuming that the sampling frequency satisfies the condition of equation (11), the sampling length is
Figure 365255DEST_PATH_IMAGE018
A point, and the number of sampling points in one baseband signal period is
Figure 83812DEST_PATH_IMAGE044
And satisfy the relationship
Figure 803507DEST_PATH_IMAGE045
（
Figure 847686DEST_PATH_IMAGE046
Positive integer), the sampled signal is:
Figure 652831DEST_PATH_IMAGE047
（15）
Figure 440658DEST_PATH_IMAGE048
（16）
wherein the content of the first and second substances,
Figure 749280DEST_PATH_IMAGE017
is a sampling period
Figure 964361DEST_PATH_IMAGE049
，
Figure 991222DEST_PATH_IMAGE018
In order to be the length of the sample,
Figure 317162DEST_PATH_IMAGE019
is a signal vibration pair.
S2: and respectively carrying out coherent accumulation on the two groups of sampling signals to obtain two groups of accumulated signals.
The sampled signal
Figure 745869DEST_PATH_IMAGE050
And
Figure 131851DEST_PATH_IMAGE051
with baseband signals
Figure 911588DEST_PATH_IMAGE040
Period of (2)
Figure 41218DEST_PATH_IMAGE052
Coherent accumulation is performed for the period to filter gaussian noise. Namely, it is
Figure 61782DEST_PATH_IMAGE053
（17）
The sampling result is shown in fig. 3 (a).
Figure 884245DEST_PATH_IMAGE054
（18）
The sampling result is shown in fig. 3 (b).
S3: and respectively carrying out discrete Fourier transform on the two groups of accumulated signals to obtain the initial phases of the two groups of sinusoidal signals with the same frequency.
For the accumulated signals
Figure 885699DEST_PATH_IMAGE055
And
Figure 287861DEST_PATH_IMAGE056
respectively performing discrete Fourier transform to calculate the initial phases of two sinusoidal signals
Figure 691161DEST_PATH_IMAGE057
And
Figure 684525DEST_PATH_IMAGE058
：
Figure 907696DEST_PATH_IMAGE059
（19）
the sampling result is shown in fig. 3 (c).
Figure 644707DEST_PATH_IMAGE060
（20）
The sampling result is shown in fig. 3 (d).
S4: and calculating the phase difference between the two groups of sinusoidal signals according to the initial phase between the two groups of sinusoidal signals with the same frequency.
The phase difference between the two sinusoidal signals can be obtained according to the initial phases of the two sinusoidal signals:
Figure 636934DEST_PATH_IMAGE061
（21）
the obtained phase difference results are shown in FIG. 4(c), and the phase difference errors are shown in FIG. 4 (d). While the phase difference measured by the conventional DFT method is shown in fig. 4(a), and the phase difference error is shown in fig. 4 (b). Compared with the traditional DFT method, the method has the advantages that the phase difference is more accurate and the phase difference error is smaller.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. 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.

Claims (6)

1. A down-sampling sinusoidal signal phase difference measuring method based on coherent accumulation DFT is characterized by comprising the following steps:
s1: respectively sampling two groups of sinusoidal signals with the same frequency by using a down-sampling mode to obtain two groups of sampling signals;
s2: respectively carrying out coherent accumulation on the two groups of sampling signals to obtain two groups of accumulated signals;
s3: respectively carrying out discrete Fourier transform on the two groups of accumulated signals to obtain initial phases of two groups of sinusoidal signals with the same frequency;
s4: calculating the phase difference between the two groups of sinusoidal signals according to the initial phase between the two groups of sinusoidal signals with the same frequency; the S1 includes the steps of:
s11: sampling the sinusoidal signal to obtain a sampled signal frequency spectrum;
s12: filtering the signal spectrum to obtain a baseband signal spectrum;
s13: reconstructing a baseband signal by adopting inverse Fourier transform according to the baseband signal frequency spectrum;
s14: and reconstructing the high-frequency signal according to the frequency and the initial phase of the baseband signal.
2. The method of claim 1, wherein the signal spectrum obtained at S11 is as follows:
Figure 494558DEST_PATH_IMAGE001
wherein the content of the first and second substances,
Figure 847042DEST_PATH_IMAGE002
the angular frequency is represented by the angular frequency,
Figure 789590DEST_PATH_IMAGE003
in order to be able to sample the frequency,
Figure 168137DEST_PATH_IMAGE004
is the frequency of the signal or signals,
Figure 588754DEST_PATH_IMAGE005
is a natural constant and is a natural constant,
Figure 61324DEST_PATH_IMAGE006
as an initial phase, the phase of the phase,
Figure 112457DEST_PATH_IMAGE007
in order to be the number of shifts,
Figure 37687DEST_PATH_IMAGE008
in the form of an impulse signal, the signal is,
Figure 261995DEST_PATH_IMAGE009
in the form of a circumferential ratio,
Figure 261175DEST_PATH_IMAGE010
in units of imaginary numbers.
3. The method as claimed in claim 1, wherein the step S12 is performed to filter the signal with a gain of
Figure 545526DEST_PATH_IMAGE011
The band pass range is
Figure 958053DEST_PATH_IMAGE012
。
4. The method of claim 1, wherein the baseband signal of S13 is as follows:
Figure 923735DEST_PATH_IMAGE013
wherein the content of the first and second substances,
Figure 105318DEST_PATH_IMAGE014
is the frequency of the baseband signal and is,
Figure 294990DEST_PATH_IMAGE015
is the initial phase of the baseband signal and,
Figure 132496DEST_PATH_IMAGE016
is time.
5. The method for measuring the phase difference of the down-sampled sinusoidal signals based on the DFT of the coherent accumulation as claimed in claim 1, wherein the high frequency signals of S14 are as follows:
Figure 698607DEST_PATH_IMAGE017
wherein the content of the first and second substances,
Figure 275DEST_PATH_IMAGE018
in order to be the sampling period of time,
Figure 298533DEST_PATH_IMAGE019
in order to be the length of the sample,
Figure 685652DEST_PATH_IMAGE020
is the signal amplitude.
6. The method of claim 1, wherein the initial phase of S3 is as follows:
Figure 55453DEST_PATH_IMAGE021
wherein, DFT stands for discrete Fourier transform,
Figure 883732DEST_PATH_IMAGE022
is the accumulated signal.
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