CN114578093A - Laser Doppler velocimeter speed measurement method based on mixed basis FFT - Google Patents

Laser Doppler velocimeter speed measurement method based on mixed basis FFT Download PDF

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CN114578093A
CN114578093A CN202210233733.4A CN202210233733A CN114578093A CN 114578093 A CN114578093 A CN 114578093A CN 202210233733 A CN202210233733 A CN 202210233733A CN 114578093 A CN114578093 A CN 114578093A
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崔骊水
张育闻
李春辉
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National Institute of Metrology
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Abstract

The invention discloses a laser Doppler velocimeter speed measurement method based on mixed basis FFT, which comprises the following steps: collecting analog photoelectric signals according to a preset sampling interval, and preprocessing to obtain a discrete Doppler signal sequence; sequentially decomposing the discrete Doppler signal sequence into shorter subsequences; constructing a three-term variable factor matrix of a DFT iterative process; the three variable factor matrices are: inputting a sequence matrix, a coefficient twiddle factor matrix and a DFT twiddle factor matrix; performing layer-by-layer iterative computation of DFT on the subsequences based on the three variable factor matrixes to obtain the amplitude spectrum and the maximum value of the Doppler signal sequence, and solving the main frequency sequence number of the maximum value of the spectrum; and sequentially calculating the Doppler frequency and the final fluid speed according to the main frequency sequence number of the maximum value of the frequency spectrum. The invention can effectively simplify complex number operation, improve operation efficiency and real-time performance and is beneficial to realizing on-site on-line measurement.

Description

Laser Doppler velocimeter speed measurement method based on mixed basis FFT
Technical Field
The invention relates to the technical field of fluid velocity measurement, in particular to a laser Doppler velocimeter velocity measurement method based on mixed basis FFT.
Background
The Laser Doppler Velocimetry (LDV) designed based on the Laser Doppler Velocimetry technology is widely applied to the fields of particle Velocimetry, energy environmental protection, clinical medical treatment, biological medicine, deep-diving exploration, satellite navigation, industrial production and the like.
The LDV mainly consists of a laser, an incident optical unit (spectroscopic system), a collection optical unit (photoreceiving system), a doppler signal processing system, and a data processing system. The Doppler signal processing system is responsible for preprocessing photocurrent signals collected by the light receiving system, extracting Doppler signals and then sending the Doppler signals to the data processing system to calculate Doppler frequency, and finally calculating to obtain speed. The data processing process is usually completed by a computer, and a data processing algorithm is the key for solving the Doppler frequency by the LDV. Conventional data processing algorithms include Discrete Fourier Transform (DFT), Fast Fourier Transform (FFT), and mixed-basis FFT. The 3 algorithms have respective defects in LDV speed measurement application: the DFT converts the time domain discrete signal into frequency domain discrete representation, the calculation comprises a large amount of complex operations, and in the LDV actual measurement process, the large amount of complex operations can cause that the Doppler signal resolving time is long, the actual measurement speed generates certain delay, so that the efficiency and the real-time performance of field measurement cannot meet the requirements; the radix-2 FFT can only receive a sequence with the point number of 2 times, so that the limitation of the point number of a Doppler signal sequence during LDV measurement is caused, and the universal requirement for resolving any point signal sequence cannot be met; the fast algorithm of the mixed-radix FFT is a simplified algorithm of the mixed-radix FFT, only the number of sequence points is decomposed into two products when the actual signal sequence is processed, although the efficiency is improved to a certain extent compared with DFT, the calculation efficiency and the real-time performance still do not meet the requirements of LDV field measurement when the number of sequence points is longer and the number of sequence points is prime.
Therefore, how to provide a speed measurement method capable of effectively simplifying complex number operation, improving operation efficiency and real-time performance, and facilitating on-site on-line measurement is a problem that needs to be solved urgently by those skilled in the art.
Disclosure of Invention
In view of this, the invention provides a method for measuring speed of a laser doppler velocimeter based on mixed-basis FFT, which can effectively simplify complex operations, improve operation efficiency and real-time performance, and facilitate on-site on-line measurement.
In order to achieve the purpose, the invention adopts the following technical scheme:
a laser Doppler velocimeter velocity measurement method based on mixed basis FFT comprises the following steps:
collecting analog photoelectric signals according to a preset sampling interval, and preprocessing to obtain a discrete Doppler signal sequence;
sequentially decomposing the discrete Doppler signal sequence into shorter subsequences;
constructing a three-term variable factor matrix of a DFT iterative process; the three variable factor matrices are: inputting a sequence matrix, a coefficient twiddle factor matrix and a DFT twiddle factor matrix;
performing layer-by-layer iterative computation of DFT on the subsequence based on the three variable factor matrixes to obtain an amplitude spectrum and a maximum value of the amplitude spectrum of the Doppler signal sequence, and solving a main frequency sequence number of the maximum value of the spectrum;
and sequentially calculating the Doppler frequency and the final fluid speed according to the main frequency sequence number of the maximum frequency spectrum.
Preferably, in the above method for measuring speed of a laser doppler velocimeter based on mixed-basis FFT, the expression of DFT at the mth layer is:
Figure BDA0003541360120000021
wherein, XmA matrix of output sequences representing the m-th layer,
Figure BDA0003541360120000022
DFT twiddle factor matrix, X, representing the mth layerm-1An input sequence matrix representing the mth layer,
Figure BDA0003541360120000023
a coefficient twiddle factor matrix representing the mth layer.
Preferably, in the above method for measuring speed of a laser doppler velocimeter based on mixed-basis FFT, the sequentially decomposing the discrete doppler signal sequence into shorter subsequences includes:
representing the discrete Doppler signals in the form of an N-point sequence x (N), namely x (0), x (1), …, x (N-1);
decomposing N into N-r1r2…rLWherein r is1,r2,…,rLThe method is characterized in that L prime numbers are sequentially arranged from small to large, the decomposed L prime numbers are used as a mixed base, and any decimal nonnegative integer smaller than N is represented as a multi-base multi-system form.
Preferably, in the above method for measuring speed of laser doppler velocimeter based on mixed-basis FFT, the m-th layer of input sequence matrix Xm-1The construction process of (1) is as follows:
let Xm-1Initially an N-dimensional vector, and after factorization of N, the discrete doppler signal sequence is changed from the N-dimensional vector to Xm-1(kL-1,kL-2,…,kL-m+1,nL-m,…,n0) The dimension of the L-dimensional matrix is reduced into a two-dimensional matrix by applying a dimension reduction rule;
performing DFT iterative computation on the two-dimensional matrix after dimension reduction, and outputting a two-dimensional matrix Xm；
To the output two-dimensional matrix XmRe-ascending the dimension to form a new L-dimension matrix X according to the reverse order of the dimension descending time sequencem(kL-1,kL-2,…,kL-m,nL-m-1,…,n0) Recombining the elements in the reverse order of the base order to form an N-dimensional vector to obtain an N-dimensional input vector X of the next layerm。
Preferably, in the above method for measuring speed of a laser doppler velocimeter based on mixed-basis FFT, the dimension reduction rule is:
will L dimension matrix Xm-1The m-th dimension element X ofm-1(nL-m),nL-m＝0,1,…,rm-1 as the first column of the input sequence matrix, rmRepresents the m-th group;
the elements in the remaining dimensions being in reverse order of the basis, i.e. rLrL-1…rm+1rm-1…r1The order of (a) is added to the columns of the matrix in turn;
finally obtaining a two-dimensional matrix X after dimension reductionm-1(nL-m,(kL-1…kL-m+1nL-m-1…n1n0))。
Preferably, in the above method for measuring speed of laser doppler velocimeter based on mixed-basis FFT, the coefficient twiddle factor matrix of the mth layer is composed of products of multiple twiddle factor sub-terms, and its expression is:
Figure BDA0003541360120000031
wherein t is 1,2, …, m-1, which represents the number of the m-th layer coefficient twiddle factor sub-item,
Figure BDA0003541360120000032
is a twiddle factor sub-term; r ispara＝rm+1rm+2…rL；kparaIs the number of matrix columns, k is more than or equal to 0para≤N/rm-1；
Figure BDA0003541360120000033
Is k isparaPartial inverted order of (3).
Preferably, in the above method for measuring speed of laser doppler velocimeter based on mixed-basis FFT,
Figure BDA0003541360120000041
the value taking process is as follows:
the residue is denoted as primordia r1,r2,…,rm,…,rLRemove rmThe radical formed is r1,r2,…,rm-1,rm+1,…,rL；
Determining the input of the mth layer as Xm-1(kL-1,kL-2,…,kL-m+1,nL-m,…,n0) Then, the remaining radix sequences are arranged as:
kpara＝kL-1(r2…rm-1rm+1…rL)+…+kL-m+1(rm+1…rL)+nL-m-1(rm+2…rL)+…+n0；
the remaining radix inversion order is arranged as:
kL-1+…+kL-m+1(r1r2…rm-2)+nL-m-1(r1r2…rm-1)+…+n0(r1r2…rm-1rm+1…rL-1)；
Figure BDA0003541360120000042
the value of (b) is the sum of k terms contained in the residual radix-inverted sequence arrangement, and the calculation formula is as follows:
Figure BDA0003541360120000043
preferably, in the above method for measuring speed of laser doppler velocimeter based on mixed-basis FFT, the mth layer DFT twiddle factor matrix
Figure BDA0003541360120000044
The expression of (c) is:
Figure BDA0003541360120000045
preferably, in the above method for measuring speed of a laser doppler velocimeter based on mixed-basis FFT, the final fluid speed is calculated by the following formula:
v＝fD·λ/2sinθ；
wherein, fD＝kD·fs/N，fsIs the sampling frequency; lambda is the wavelength of laser in the laser Doppler velocimeter; theta is an incident laser included angle; k is a radical of formulaDThe main frequency sequence number of the maximum value of the frequency spectrum.
Preferably, in the above method for measuring speed of laser doppler velocimeter based on mixed-basis FFT,
according to the technical scheme, compared with the prior art, the invention discloses a laser Doppler velocimeter speed measurement method based on mixed-basis FFT, and the method combines a mixed-basis method based on the Kully-graph-based idea with Discrete Fourier Transform (DFT) during LDV measurement, performs spectrum analysis on a Doppler signal sequence and calculates Doppler frequency, and finally realizes real-time online measurement of the LDV on fluid speed. The iterative process can effectively simplify complex number operation, improve the operation efficiency and real-time performance, is beneficial to realizing on-site on-line measurement, improves the operation efficiency of DFT in LDV measurement, breaks the limitation of Fast Fourier Transform (FFT) to the length of an input signal sequence, enables a data processing system to efficiently process signal sequence input with any length in the measurement process, has universality and practicability, and also ensures the accurate measurement of the LDV fluid speed.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
Fig. 1 is a schematic flow chart of a laser doppler velocimeter velocity measurement method based on mixed-basis FFT provided by the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, an embodiment of the present invention discloses a method for measuring a velocity of a laser doppler velocimeter based on mixed-basis FFT, which includes the following steps:
s1, collecting analog photoelectric signals according to a preset sampling interval, and preprocessing the analog photoelectric signals to obtain a discrete Doppler signal sequence;
s2, decomposing the discrete Doppler signal sequence into shorter subsequences in sequence;
s3, constructing a three-item variable factor matrix of the DFT iterative process; the three variable factor matrices are: inputting a sequence matrix, a coefficient twiddle factor matrix and a DFT twiddle factor matrix;
s4, performing layer-by-layer iterative computation of DFT on the subsequences based on the three variable factor matrixes to obtain the amplitude frequency spectrum and the maximum value of the Doppler signal sequence, and solving the main frequency sequence number of the maximum value of the frequency spectrum;
and S5, sequentially calculating the Doppler frequency and the final fluid speed according to the main frequency sequence number of the maximum value of the frequency spectrum.
The above steps are further described below.
S1, setting sampling frequency fsThen sampling interval Ts＝1/fsThe signal processing system samples and preprocesses the analog photoelectric signal collected by the light receiving system according to the sampling interval, and the data processing system receives the preprocessed discrete Doppler signal N point sequence x (N) x (0), x (1), …, x (N-1).
S2, decomposing N into N-r by prime factor1r2…rLWherein r is1,r2,…,rLL prime numbers which are sequentially arranged from small to large are called as bases, and the numbers can be expressed into a multi-base multi-system form by taking the L prime numbers as mixed bases; that is, any decimal nonnegative integer less than N may be represented in a multibase multilevel form.
S3, before constructing a three-term variable factor matrix of the iterative process, determining a DFT expression, wherein the DFT expression is as shown in formula (1):
Figure BDA0003541360120000061
wherein n represents the sequence number of the pre-transform sequence; k represents the main frequency serial number of the sequence after DFT;
Figure BDA0003541360120000062
the rotation factor is a complex factor matrix constructed by a data processing system and used for processing the Doppler signal sequence; x (k) represents the frequency domain result of the DFT-performed sequence, and is a complex number.
The signal processing system simultaneously represents the decimal serial numbers n and k as r1,r2,…,rLIn the multi-base multi-system form of the mixed base, n is represented as positive order, and k is represented as negative order. Wherein n isi＝rL-i,i＝0,1,…,L-1，kj＝rj+1J is 0,1, …, and L-1 is a coefficient of each digit.
Figure BDA0003541360120000063
The signal processing system substitutes formula (2) for formula (1):
Figure BDA0003541360120000064
according to polynomial multiplication and the nature of the twiddle factor
Figure BDA0003541360120000065
L in system pair formula (3)2The twiddle factors of the terms of the powers are simplified to (L)2the-L)/2 terms are reduced to 0, and the remaining non-reduced power term results are shown in Table 1.
TABLE 1 twiddle factor residual power terms
Figure BDA0003541360120000071
Where "/" indicates that the power term is eliminated due to the nature of the twiddle factor, which has a value of 1.
The DFT is divided into L layers according to equation (3), and the layers are summed and iterated, and the first layer DFT formula can be obtained by substituting the simplified result of table 1 into equation (3).
Figure BDA0003541360120000072
The second layer DFT formula is as follows.
Figure BDA0003541360120000073
The third layer DFT equation is as follows:
Figure BDA0003541360120000074
by analogy, the same variables are marked by X (n) as X0The formula of the DFT of the mth layer is as follows (m is more than or equal to 1 and less than or equal to L).
Figure BDA0003541360120000081
According to the formulas (4) to (7), the 3 variable factors in the DFT iteration process are respectively constructed as follows: input sequence X of m-th layerm-1Coefficient twiddle factor
Figure BDA0003541360120000082
DFT twiddle factor
Figure BDA0003541360120000083
The method comprises the following specific steps:
Figure BDA0003541360120000084
equation (7) is converted into a matrix form.
Figure BDA0003541360120000085
Wherein, Xm-1And
Figure BDA0003541360120000086
the multiplication is the corresponding multiplication of each element of the matrix.
Figure BDA0003541360120000087
Figure BDA0003541360120000088
And
Figure BDA0003541360120000089
the multiplication of (a) is a matrix multiplication operation,
Figure BDA00035413601200000810
is equal to
Figure BDA00035413601200000811
The number of rows of (c).
The following describes in detail the construction process of three variable factors, i.e., the input sequence matrix, the coefficient twiddle factor matrix, and the DFT twiddle factor matrix.
1) Input sequence X of m-th layerm-1The construction of the matrix.
Xm-1Is the input sequence of the m-th layer, is an N-dimensional vector, and after N is subjected to prime factor decomposition, X is calculated according to the principle of DFT co-location operationm-1Is changed into Xm-1(kL-1,kL-2,…,kL-m+1,nL-m,…,n0) The L-dimensional matrix is changed into a two-dimensional matrix by applying the following dimensionality reduction rule:
first, an L-dimensional matrix X is formedm-1The m-th dimension element X ofm-1(nL-m),nL-m＝0,1,…,rm-1 to doIs the first column of the input sequence matrix;
② the elements in the remaining dimensions are in the reverse order of the basis, namely rLrL-1…rm+1rm-1…r1The order of (a) is added to the columns of the matrix in turn;
thirdly, a two-dimensional matrix X after dimension reduction is finally obtainedm-1(nL-m,(kL-1…kL-m+1nL-m-1…n1n0))；
The matrix after dimension reduction is used for operation according to the formula (9) to obtain an output two-dimensional matrix XmRe-ascending the dimension of the matrix into an L-dimensional matrix X according to the reverse order of the dimension-descending time sequencem(kL-1,kL-2,…,kL-m,nL-m-1,…,n0) Rearranging the vector elements in the reverse order of the base sequence to obtain the next layer of N-dimensional input vector Xm。
2) Coefficient twiddle factor of mth layer
Figure BDA00035413601200000812
Construction of the matrix
Coefficient twiddle factor according to equation (8)
Figure BDA00035413601200000813
Is formed by the product of a plurality of twiddle factors, as shown in the following formula.
Figure BDA0003541360120000091
Figure BDA0003541360120000092
The value taking process is as follows:
the residual group can be represented as primordia r1,r2,…,rm,…,rLRemove rmThe latter radicals being of the form r1,r2,…,rm-1,rm+1,…,rL。
② let the number of matrix columns be kpara,0≤kpara≤N/rm-1。
The input of the m-th layer is Xm-1(kL-1,kL-2,…,kL-m+1,nL-m,…,n0) Then the remaining radix is arranged in the positive order
The columns are as follows:
kpara＝kL-1(r2…rm-1rm+1…rL)+…+kL-m+1(rm+1…rL)+nL-m-1(rm+2…rL)+…+n0 (11)。
the remaining radix inversion order is arranged as:
kL-1+…+kL-m+1(r1r2…rm-2)+nL-m-1(r1r2…rm-1)+…+n0(r1r2…rm-1rm+1…rL-1) (12)。
③
Figure BDA0003541360120000093
the value of (d) is the sum of k terms in the remaining inverted base permutation.
Namely, it is
Figure BDA0003541360120000094
Figure BDA0003541360120000095
Is kparaPartial inverted order of (3).
3) DFT twiddle factor of mth layer
Figure BDA0003541360120000096
The construction of the matrix:
as can be seen from the formula (8),
Figure BDA0003541360120000097
it can be directly constructed as a symmetric matrix as follows.
Figure BDA0003541360120000098
S4, after 3 variable factors in the iteration process are constructed, L-layer iteration operation is carried out according to a formula (9) to obtain an X (k) sequence, finally, a signal processing system outputs the frequency spectrum of the Doppler signal sequence through mixed-basis FFT, the maximum value max { | X (k) | } of the amplitude frequency spectrum of the Doppler signal sequence is calculated, and the main frequency serial number k of the maximum value of the frequency spectrum is obtainedD。
S5, calculating formula f according to frequencyD＝kD·fs/N calculating the Doppler frequency fDAnd calculating the final fluid velocity v-f according to a velocity conversion formulaDλ/2sin θ. Wherein lambda is the wavelength of laser in the LDV, theta is the included angle of incident laser, which are all set values, fsRepresenting the sampling frequency.
In other embodiments, further comprising: by the Doppler frequency fDAnd displaying the corresponding speed v on a screen in real time, and drawing an image to achieve the aim of on-site real-time measurement.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. The device disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant points can be referred to the method part for description.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (9)

1. A laser Doppler velocimeter velocity measurement method based on mixed basis FFT is characterized by comprising the following steps:
collecting analog photoelectric signals according to a preset sampling interval, and preprocessing to obtain a discrete Doppler signal sequence;
sequentially decomposing the discrete Doppler signal sequence into shorter subsequences;
constructing a three-term variable factor matrix of a DFT iterative process; the three variable factor matrices are: inputting a sequence matrix, a coefficient twiddle factor matrix and a DFT twiddle factor matrix;
performing layer-by-layer iterative computation of DFT on the subsequence based on the three variable factor matrixes to obtain an amplitude spectrum and a maximum value of the amplitude spectrum of the Doppler signal sequence, and solving a main frequency sequence number of the maximum value of the spectrum;
and sequentially calculating the Doppler frequency and the final fluid speed according to the main frequency sequence number of the maximum frequency spectrum.
2. The method according to claim 1, wherein the expression of DFT at the mth layer is:
Figure FDA0003541360110000011
wherein XmAn output sequence matrix representing the m-th layer,
Figure FDA0003541360110000012
DFT twiddle factor matrix, X, representing the mth layerm-1An input sequence matrix representing the mth layer,
Figure FDA0003541360110000013
a coefficient twiddle factor matrix representing the mth layer.
3. The method according to claim 2, wherein the step of sequentially decomposing the discrete doppler signal sequence into shorter subsequences comprises:
representing the discrete Doppler signals as a sequence of N points x (N) in the form of x (0), x (1), …, x (N-1);
decomposing N into N-r1r2…rLWherein r is1,r2,…,rLThe method is characterized in that L prime numbers are sequentially arranged from small to large, the decomposed L prime numbers are used as a mixed base, and any decimal nonnegative integer smaller than N is represented as a multi-base multi-system form.
4. The method as claimed in claim 3, wherein the m-th input sequence matrix X is a matrix of the input sequence of the m-th layerm-1The construction process of (1) is as follows:
let Xm-1Initially an N-dimensional vector, and after factorization of N, the discrete doppler signal sequence is changed from the N-dimensional vector to Xm-1(kL-1,kL-2,…,kL-m+1,nL-m,…,n0) The dimension of the L-dimensional matrix is reduced into a two-dimensional matrix by using a dimension reduction rule;
performing DFT iterative computation on the two-dimensional matrix after dimension reduction, and outputting a two-dimensional matrix Xm；
To the output two-dimensional matrix XmRe-ascending the dimension to form a new L-dimension matrix X according to the reverse order of the dimension descending time sequencem(kL-1,kL-2,…,kL-m,nL-m-1,…,n0) Recombining the elements in the reverse order of the base order to form an N-dimensional vector to obtain an N-dimensional input vector X of the next layerm。
5. The method according to claim 4, wherein the dimension reduction rule is as follows:
will L dimension matrix Xm-1The m-th dimension element X ofm-1(nL-m),nL-m＝0,1,…,rm-1 as the first column of the input sequence matrix, rmRepresents the m-th group;
the elements in the remaining dimensions being in reverse order of the basis, i.e. rLrL-1…rm+1rm-1…r1The order of (a) is added to the columns of the matrix in turn;
finally obtaining a two-dimensional matrix X after dimension reductionm-1(nL-m,(kL-1…kL-m+1nL-m-1…n1n0))。
6. The method according to claim 5, wherein the coefficient twiddle factor matrix of the mth layer is composed of products of a plurality of twiddle factor sub-terms, and the expression is:
Figure FDA0003541360110000021
wherein t is 1,2, …, m-1, which represents the number of the m-th layer coefficient twiddle factor sub-item,
Figure FDA0003541360110000022
is a twiddle factor sub-term; r ispara＝rm+1rm+2…rL；kparaIs the number of matrix columns, k is more than or equal to 0para≤N/rm-1；
Figure FDA0003541360110000023
Is kparaPartial inverted order of (3).
7. The method of claim 6, wherein the laser Doppler velocimeter measures speed based on mixed-basis FFT,
Figure FDA0003541360110000024
the value taking process is as follows:
the remaining radicals are denoted as primordia r1,r2,…,rm,…,rLRemove rmThe new radical formed later can be represented as r1,r2,…,rm-1,rm+1,…,rL；
Determining the m-thInput of layer Xm-1(kL-1,kL-2,…,kL-m+1,nL-m,…,n0) Then, the remaining radix sequences are arranged as:
kpara＝kL-1(r2…rm-1rm+1…rL)+…+kL-m+1(rm+1…rL)+nL-m-1(rm+2…rL)+…+n0；
the remaining radix inversion order is:
kL-1+…+kL-m+1(r1r2…rm-2)+nL-m-1(r1r2…rm-1)+…+n0(r1r2…rm-1rm+1…rL-1)；
Figure FDA0003541360110000031
the value of (b) is the sum of k terms contained in the residual radix-inverted sequence arrangement, and the calculation formula is as follows:
Figure FDA0003541360110000032
8. the method as claimed in claim 1, wherein the DFT rotation factor matrix of the mth layer is a DFT rotation factor matrix
Figure FDA0003541360110000033
The expression of (a) is:
Figure FDA0003541360110000034
9. the method according to claim 1, wherein the final fluid velocity is calculated by the following formula:
v＝fD·λ/2sinθ；
wherein f isD＝kD·fs/N，fsIs the sampling frequency; lambda is the wavelength of laser in the laser Doppler velocimeter; theta is an incident laser included angle; k is a radical ofDThe main frequency sequence number of the maximum value of the frequency spectrum.
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