CN114578093B - Laser Doppler velocimeter speed measurement method based on mixed-base FFT - Google Patents
Laser Doppler velocimeter speed measurement method based on mixed-base FFT Download PDFInfo
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- G—PHYSICS
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- G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
- G01P5/00—Measuring speed of fluids, e.g. of air stream; Measuring speed of bodies relative to fluids, e.g. of ship, of aircraft
- G01P5/26—Measuring speed of fluids, e.g. of air stream; Measuring speed of bodies relative to fluids, e.g. of ship, of aircraft by measuring the direct influence of the streaming fluid on the properties of a detecting optical wave
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
- G06F17/141—Discrete Fourier transforms
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- G06—COMPUTING; CALCULATING OR COUNTING
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Abstract
The invention discloses a laser Doppler velocimeter speed measuring method based on mixed-base FFT, which comprises the following steps: acquiring 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 three variable factor matrixes 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 DFT layer-by-layer iterative computation on the subsequences based on the three variable factor matrixes to obtain Doppler signal sequence amplitude spectrums and maximum values thereof, and solving a main frequency sequence of the maximum value of the spectrums; and calculating Doppler frequency and final fluid velocity according to the main frequency sequence number of the maximum value of the frequency spectrum. The invention can effectively simplify complex operation, improve operation efficiency and real-time performance, and is favorable for realizing on-site online measurement.
Description
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 a mixed-base FFT.
Background
The laser Doppler velocimetry technology is a technology for measuring and calculating the speed of fluid (solid) by utilizing a laser and based on the Doppler effect of light, has the unique advantages of non-contact measurement, high accuracy, high spatial resolution, quick dynamic response and the like, and is widely applied to the fields of particle velocimetry, energy environmental protection, clinical medical treatment, biological medicine, deep submerged exploration, satellite navigation, industrial production and the like.
The LDV is mainly composed of a laser, an incident optical unit (a spectroscopic system), a collection optical unit (a light receiving system), a doppler signal processing system, and a data processing system. The Doppler signal processing system is responsible for preprocessing the photocurrent signals collected by the light receiving system, extracting Doppler signals, sending the Doppler signals to the data processing system to calculate Doppler frequency, and finally calculating to obtain speed. The process of data processing is typically done by a computer, and the data processing algorithm is critical to the LDV's resolution of doppler frequency. Conventional data processing algorithms are fast algorithms of discrete fourier transform (Discrete Fourier Transform, DFT), radix-2 fast fourier transform (Fast Fourier Transform, FFT) and mixed-radix FFT. The 3 algorithms have respective defects in LDV speed measurement application: the DFT converts the time domain discrete signal into the frequency domain discrete representation, a large number of complex operations are included in the calculation, and in the LDV actual measurement process, the large number of complex operations can lead to longer Doppler signal resolving time and a certain hysteresis of the actual measurement speed, so that the field measurement efficiency and the real-time performance can not meet the requirements; the base-2 FFT can only receive sequences with the number of 2 powers, so that the limitation of the number of Doppler signal sequences in LDV measurement is caused, and the universal requirement of resolving any number of signal sequences cannot be met; the fast algorithm of the mixed-base FFT is a simplified algorithm of the mixed-base FFT, and when an actual signal sequence is processed, the number of sequence points is only decomposed into two products, and although the efficiency is improved to a certain extent compared with the DFT, the operation efficiency and the instantaneity still do not meet the requirement 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 measuring method capable of effectively simplifying complex operation, improving operation efficiency and instantaneity, and facilitating on-site on-line measurement is a problem to be solved by those skilled in the art.
Disclosure of Invention
In view of the above, the invention provides a laser Doppler velocimeter speed measuring method based on mixed-base FFT, which can effectively simplify complex operation, improve operation efficiency and instantaneity, and is favorable for realizing on-site on-line measurement.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a laser doppler velocimeter speed measurement method based on a hybrid FFT, comprising:
acquiring 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 three variable factor matrixes of a DFT iterative process; the three variable factor matrices are as follows: inputting a sequence matrix, a coefficient twiddle factor matrix and a DFT twiddle factor matrix;
performing DFT layer-by-layer iterative computation on the subsequence based on the three variable factor matrixes to obtain Doppler signal sequence amplitude spectrum and maximum value thereof, and solving a main frequency sequence of the maximum value of the spectrum;
and calculating Doppler frequency and final fluid velocity in sequence according to the main frequency sequence number of the maximum value of the frequency spectrum.
Preferably, in the above method for measuring a velocity of a laser doppler velocimeter based on a hybrid FFT, the expression of the mth layer DFT is:
wherein X is m Representing the output sequence matrix of the mth layer,DFT twiddle factor matrix representing m-th layer, X m-1 Input sequence matrix representing layer m, +.>Representing the coefficient twiddle factor matrix of the m-th layer.
Preferably, in the above method for measuring a velocity of a laser doppler velocimeter based on a hybrid FFT, the sequentially decomposing the sequence of the discrete doppler signals into shorter subsequences includes:
representing the discrete doppler signal as a sequence of N points x (N), i.e. x (0), x (1), …, x (N-1);
subjecting N to prime factorization into n=r 1 r 2 …r L Wherein r is 1 ,r 2 ,…,r L For L prime numbers arranged from small to large in turn, use divisionThe solved L prime numbers are used as mixed bases, and any decimal non-negative integer smaller than N is expressed as a multi-base multi-system form.
Preferably, in the above method for measuring a velocity of a laser doppler velocimeter based on a hybrid FFT, the m-th layer inputs the sequence matrix X m-1 The construction process of (1) is as follows:
set X m-1 The discrete Doppler signal sequence is formed by N-dimensional vector quantity X after N is subjected to prime factorization m-1 (k L-1 ,k L-2 ,…,k L-m+1 ,n L-m ,…,n 0 ) Reducing the dimension of the L-dimensional matrix into a two-dimensional matrix by using a dimension reduction rule;
performing iterative computation of DFT on the dimension-reduced two-dimensional matrix to output a two-dimensional matrix X m ；
Two-dimensional matrix X of outputs m Re-increasing dimension to form new L-dimension matrix X according to reverse order of dimension decreasing time sequence m (k L-1 ,k L-2 ,…,k L-m ,n L-m-1 ,…,n 0 ) Then the elements are recombined according to the reverse order of the base order to form an N-dimensional vector, and an N-dimensional input vector X of the next layer is obtained m 。
Preferably, in the above method for measuring a velocity of a laser doppler velocimeter based on a hybrid FFT, the dimension reduction rule is:
to the L-dimensional matrix X m-1 Is the mth dimension element X of (2) m-1 (n L-m ),n L-m ＝0,1,…,r m -1 as first column of the input sequence matrix, r m Represents an mth group;
the elements in the remaining dimension are in the reverse order of the base, i.e. r L r L-1 …r m+1 r m-1 …r 1 Sequentially added to columns of the matrix;
finally obtaining a dimension-reduced two-dimensional matrix X m-1 (n L-m ,(k L-1 …k L-m+1 n L-m-1 …n 1 n 0 ))。
Preferably, in the above method for measuring velocity of a laser doppler velocimeter based on a hybrid FFT, the coefficient twiddle factor matrix of the mth layer is formed by the product of a plurality of twiddle factor sub-terms, and the expression is:
wherein t=1, 2, …, m-1, represents the number of mth coefficient twiddle factor terms,is a twiddle factor item; r is (r) para ＝r m+1 r m+2 …r L ；k para For the number of columns of the matrix, 0 is less than or equal to k para ≤N/r m -1；/>Is k para Is a partial inversion of the bit sequence.
Preferably, in the above-mentioned laser doppler velocimetry speed measuring method based on mixed-base FFT,the value process of (2) is as follows:
representing the residual radicals as primordia r 1 ,r 2 ,…,r m ,…,r L Remove r m The radicals formed being r 1 ,r 2 ,…,r m-1 ,r m+1 ,…,r L ；
Determining the input of the mth layer as X m-1 (k L-1 ,k L-2 ,…,k L-m+1 ,n L-m ,…,n 0 ) The remaining base orthosteric sequences are then:
k para ＝k L-1 (r 2 …r m-1 r m+1 …r L )+…+k L-m+1 (r m+1 …r L )+n L-m-1 (r m+2 …r L )+…+n 0 ；
the remaining base inversion bit sequences are arranged as follows:
k L-1 +…+k L-m+1 (r 1 r 2 …r m-2 )+n L-m-1 (r 1 r 2 …r m-1 )+…+n 0 (r 1 r 2 …r m-1 r m+1 …r L-1 )；
the value of (2) is the sum of k terms in the residual base inverted bit sequence arrangement, and the calculation formula is as follows:
preferably, in the above method for measuring velocity of a laser doppler velocimeter based on a hybrid FFT, the m-th layer DFT rotates the factor matrixThe expression of (2) is:
preferably, in the above method for measuring velocity of a laser doppler velocimeter based on a hybrid FFT, the calculation formula of the final fluid velocity is:
v＝f D ·λ/2sinθ；
wherein f D ＝k D ·f s /N，f s Is the sampling frequency; lambda is the wavelength of the laser in the laser Doppler velocimeter; θ is the incident laser angle; k (k) D The dominant frequency sequence number that is the maximum of the spectrum.
Preferably, in the above-mentioned laser doppler velocimetry speed measuring method based on mixed-base FFT,
compared with the prior art, the invention discloses a laser Doppler velocimeter speed measuring method based on a mixed base FFT, which combines a mixed base method based on a Kuril-graph base idea with discrete Fourier transform (Discrete Fourier Transform, DFT) during LDV measurement, performs spectrum analysis on Doppler signal sequences, calculates Doppler frequency and finally realizes real-time online measurement of fluid speed by LDV. The iterative process can effectively simplify complex operation, improves operation efficiency and instantaneity, is favorable for realizing on-site online measurement, improves the operation efficiency of DFT in LDV measurement, breaks through the limitation of base-2 fast Fourier transform (Fast Fourier Transform, FFT) on the length of an input signal sequence, enables a data processing system to efficiently process the input of the signal sequence with any length in the measurement process, has universality and practicability, and also ensures the accurate measurement of the fluid speed by LDV.
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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 that are required to be used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only embodiments of the present invention, and that other drawings can be obtained according to the provided drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flow chart of a laser doppler velocimeter velocimetry method based on a hybrid FFT provided by the invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1, the embodiment of the invention discloses a laser doppler velocimeter speed measuring method based on a mixed-base FFT, which comprises the following steps:
s1, acquiring analog photoelectric signals according to a preset sampling interval, and preprocessing to obtain a discrete Doppler signal sequence;
s2, sequentially decomposing the discrete Doppler signal sequence into shorter subsequences;
s3, constructing three variable factor matrixes in 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;
s4, performing DFT layer-by-layer iterative computation on the subsequence based on the three variable factor matrixes to obtain a Doppler signal sequence amplitude spectrum and a maximum value thereof, and solving a main frequency sequence of the maximum value of the spectrum;
s5, calculating Doppler frequency and final fluid velocity in sequence according to the main frequency sequence number of the maximum value of the frequency spectrum.
The steps described above are further described below.
S1, setting a sampling frequency f s Sampling interval T s ＝1/f s The signal processing system samples and preprocesses the analog photoelectric signals collected by the light receiving system according to the sampling interval, and the data processing system receives the preprocessed discrete Doppler signals N point sequences x (N): x (0), x (1), … and x (N-1).
S2, carrying out prime factorization on N to obtain N=r 1 r 2 …r L Wherein r is 1 ,r 2 ,…,r L For L prime numbers which are sequentially arranged from small to large and are called as bases, the numbers can be expressed as a multi-base multi-system form by using the L prime numbers as mixed bases; that is, any decimal non-negative integer less than N may be represented as a multiple-base multiple form.
S3, before constructing a three-term variable factor matrix in an iterative process, determining an expression of DFT, wherein the DFT expression is shown in the formula (1):
wherein n represents the sequence number of the sequence before transformation; k represents a main frequency sequence number of a sequence after DFT;the rotation factor is a complex factor matrix constructed by a data processing system and is used for processing Doppler signal sequences; x (k) represents sequence frequency domain result of sequence after DFTIs a complex number.
The signal processing system simultaneously represents the decimal representation of the sequence numbers n and k as r 1 ,r 2 ,…,r L N is represented as a positive bit sequence and k is represented as an inverted bit sequence in the form of a multiple-base system of mixed base. Wherein n is i ＝r L-i ,i＝0,1,…,L-1，k j ＝r j+1 J=0, 1, …, L-1 are coefficients of each digit.
The signal processing system substitutes formula (2) into formula (1):
based on polynomial multiplication and the nature of twiddle factorsSystem pair L in (3) 2 The rotation factor of the term power term is simplified, and (L 2 The L)/2 term is reduced to 0 and the remaining non-reduced power term results are shown in Table 1.
TABLE 1 twiddle factor remainder exponentiations
Where "/" indicates that the power term is eliminated due to the nature of the twiddle factor, which has a value of 1.
Dividing the DFT into L layers according to the formula (3), summing and iterating layer by layer, and substituting the simplified result of the table 1 into the formula (3) to obtain a first layer DFT formula.
The second layer DFT formula is as follows.
The third layer DFT formula is as follows:
and so on, as a unified variable, record X (n) as X 0 The m-th layer DFT formula is as follows (1.ltoreq.m.ltoreq.L).
According to the formulas (4) to (7), 3 variable factors in the construction DFT iterative process are respectively as follows: input sequence X of the mth layer m-1 Coefficient twiddle factorDFT twiddle factor->The method comprises the following steps:
equation (7) is converted into a matrix form.
Wherein X is m-1 And (3) withIn the form of homotype matrix, their multiplication is the corresponding multiplication of each element of matrix. /> And (3) withMultiplication is matrix multiplication,>column number of (2) is equal to->Is a number of rows of (a).
The construction process of three variable factors of the input sequence matrix, the coefficient twiddle factor matrix and the DFT twiddle factor matrix is described in detail below.
1) Input sequence X of the mth layer m-1 And (5) constructing a matrix.
X m-1 Is the input sequence of the m-th layer, is an N-dimensional vector, and X is calculated according to the principle of DFT same-address operation after carrying out the prime factor decomposition on N m-1 Becomes X m-1 (k L-1 ,k L-2 ,…,k L-m+1 ,n L-m ,…,n 0 ) Is changed into a two-dimensional matrix by applying the following dimension reduction rule:
(1) to the L-dimensional matrix X m-1 Is the mth dimension element X of (2) m-1 (n L-m ),n L-m ＝0,1,…,r m -1 as a first column of the input sequence matrix;
(2) the elements in the remaining dimension are in the reverse order of the base, i.e. r L r L-1 …r m+1 r m-1 …r 1 Sequentially added to columns of the matrix;
(3) finally obtaining a dimension-reduced two-dimensional matrix X m-1 (n L-m ,(k L-1 …k L-m+1 n L-m-1 …n 1 n 0 ))；
The operation is carried out according to the formula (9) by using the matrix after dimension reduction to obtain an output two-dimensional matrix X m The dimension of the matrix is increased again to form an L-dimension matrix X according to the reverse order of the dimension reduction time sequence m (k L-1 ,k L-2 ,…,k L-m ,n L-m-1 ,…,n 0 ) Then rearranging vector elements according to the reverse order of the base order to obtain N-dimensional input vector X of the next layer m 。
2) Coefficient twiddle factor of m-th layerConstruction of matrix
According to equation (8), the coefficient twiddle factorIs composed of the product of a number of twiddle factors, as follows.
The value process of (2) is as follows:
(1) the remainder of the radicals can be denoted as primordia r 1 ,r 2 ,…,r m ,…,r L Remove r m Post-formed radicals of the form r 1 ,r 2 ,…,r m-1 ,r m+1 ,…,r L 。
(2) Let the column number of the matrix be k para ,0≤k para ≤N/r m -1。
The input of the m layer is X m-1 (k L-1 ,k L-2 ,…,k L-m+1 ,n L-m ,…,n 0 ) The remaining base is orthotopic
The columns are as follows:
k para ＝k L-1 (r 2 …r m-1 r m+1 …r L )+…+k L-m+1 (r m+1 …r L )+n L-m-1 (r m+2 …r L )+…+n 0 (11)。
the remaining base inversion bit sequences are arranged as follows:
k L-1 +…+k L-m+1 (r 1 r 2 …r m-2 )+n L-m-1 (r 1 r 2 …r m-1 )+…+n 0 (r 1 r 2 …r m-1 r m+1 …r L-1 ) (12)。
③the value of (2) is the sum of k entries in the remaining base inverted sequence arrangement.
I.e. Is k para Is a partial inversion of the bit sequence.
3) Layer m DFT twiddle factorConstruction of a matrix:
as can be seen from the formula (8),can be constructed directly as a symmetric matrix as follows.
S4, after constructing 3 variable factors in the iterative process, carrying out L-layer iterative operation according to a formula (9) to obtain an X (k) sequence, finally outputting a frequency spectrum of the Doppler signal sequence through a mixed-base FFT by a signal processing system, calculating the maximum value max { |X (k) | } of the amplitude frequency spectrum of the Doppler signal sequence, and obtaining a main frequency sequence k of the maximum value of the frequency spectrum D 。
S5, according to a frequency calculation formula f D ＝k D ·f s N calculating Doppler frequency f D And calculating the final fluid velocity v=f according to the flow velocity conversion formula D Lambda/2 sin theta. Wherein lambda is the wavelength of laser in LDV, theta is the included angle of incident laser, and f is the set value s Representing the sampling frequency.
In other embodiments, further comprising: will Doppler frequency f D And the corresponding speed v is displayed on a screen in real time, and an image is drawn, so that the purpose of on-site real-time measurement is achieved.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
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. The laser Doppler velocimeter speed measurement method based on the mixed-base FFT is characterized by comprising the following steps of:
acquiring 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 three variable factor matrixes of a DFT iterative process; the three variable factor matrices are as follows: inputting a sequence matrix, a coefficient twiddle factor matrix and a DFT twiddle factor matrix;
performing DFT layer-by-layer iterative computation on the subsequence based on the three variable factor matrixes to obtain Doppler signal sequence amplitude spectrum and maximum value thereof, and solving a main frequency sequence of the maximum value of the spectrum;
and calculating Doppler frequency and final fluid velocity in sequence according to the main frequency sequence number of the maximum value of the frequency spectrum.
2. The method for measuring the speed of the laser Doppler velocimeter based on the mixed-base FFT according to claim 1, wherein the expression of the mth layer DFT is:
wherein X is m Representing the output sequence matrix of the mth layer,DFT twiddle factor matrix representing m-th layer, X m-1 Input sequence matrix representing layer m, +.>Representing the coefficient twiddle factor matrix of the m-th layer.
3. The method for measuring the velocity of the laser doppler velocimeter based on the mixed-base FFT according to claim 2, wherein the sequence of the discrete doppler signals is decomposed into shorter subsequences in sequence, comprising:
representing the discrete doppler signal as a sequence of N points x (N), i.e. x (0), x (1), …, x (N-1);
subjecting N to prime factorization into n=r 1 r 2 ···r L Wherein r is 1 ,r 2 ,…,r L For L prime numbers which are sequentially arranged from small to large, the decomposed L prime numbers are used as a mixed base, and any decimal non-negative integer smaller than N is expressed as a multi-base multi-system form.
4. A method of laser doppler velocimetry based on a hybrid FFT according to claim 3, characterized in that the m-th layer of input sequence matrix X m-1 The construction process of (1) is as follows:
set X m-1 The discrete Doppler signal sequence is formed by N-dimensional vector quantity X after N is subjected to prime factorization m-1 (k L-1 ,k L-2 ,…,k L-m+1 ,n L-m ,…,n 0 ) Reducing the dimension of the L-dimensional matrix into a two-dimensional matrix by using a dimension reduction rule;
performing iterative computation of DFT on the dimension-reduced two-dimensional matrix to output a two-dimensional matrix X m ；
Two-dimensional matrix X of outputs m Re-increasing dimension to form new L-dimension matrix X according to reverse order of dimension decreasing time sequence m (k L-1 ,k L-2 ,…,k L-m ,n L-m-1 ,…,n 0 ) Then the elements are recombined according to the reverse order of the base order to form an N-dimensional vector, and an N-dimensional input vector X of the next layer is obtained m 。
5. The method for measuring the speed of the laser doppler velocimeter based on the mixed-base FFT according to claim 4, wherein the dimension reduction rule is as follows:
to the L-dimensional matrix X m-1 Is the mth dimension element X of (2) m-1 (n L-m ),n L-m ＝0,1,…,r m -1 as first column of the input sequence matrix, r m Represents an mth group;
the elements in the remaining dimension are in the reverse order of the base, i.e. r L r L-1 ···r m+1 r m-1 ···r 1 Sequentially added to columns of the matrix;
finally obtaining a dimension-reduced two-dimensional matrix X m-1 (n L-m ,(k L-1 ···k L-m+1 n L-m-1 ···n 1 n 0 ))。
6. The method for measuring the speed of the laser Doppler velocimeter based on the mixed-base FFT according to claim 5, wherein the coefficient twiddle factor matrix of the m-th layer consists of the product of a plurality of twiddle factor sub-terms, and the expression is as follows:
wherein t=1, 2, …, m-1, represents the number of mth coefficient twiddle factor terms,is a twiddle factor item; r is (r) para ＝r m+1 r m+2 ···r L ；k para For the number of columns of the matrix, 0 is less than or equal to k para ≤N/r m -1；/>Is k para Is a partial inversion of the bit sequence.
7. The method for measuring the speed of the laser Doppler velocimeter based on the mixed-base FFT according to claim 6, wherein,the value process of (2) is as follows:
representing the residual radicals as primordia r 1 ,r 2 ,···,r m ,···,r L Remove r m The new radicals formed later, can be expressed as r 1 ,r 2 ,···,r m-1 ,r m+1 ,···,r L ；
Determining the input of the mth layer as X m-1 (k L-1 ,k L-2 ,…,k L-m+1 ,n L-m ,…,n 0 ) The remaining base orthosteric sequences are then:
k para ＝k L-1 (r 2 …r m-1 r m+1 …r L )+…+k L-m+1 (r m+1 …r L )+n L-m-1 (r m+2 …r L )+…+n 0 ；
the remaining base inversion bit sequences are arranged as follows:
k L-1 +…+k L-m+1 (r 1 r 2 …r m-2 )+n L-m-1 (r 1 r 2 …r m-1 )+…+n 0 (r 1 r 2 …r m-1 r m+1 …r L-1 )；
the value of (2) is the sum of k terms in the residual base inverted bit sequence arrangement, and the calculation formula is as follows:
8. the method for measuring the velocity of a laser Doppler velocimeter based on a mixed-base FFT according to claim 7, wherein the m-th layer DFT twiddle factor matrixThe expression of (2) is:
9. the method for measuring the velocity of a laser doppler velocimeter based on a mixed-base FFT according to claim 1, wherein the calculation formula of the final fluid velocity is:
v＝f D ·λ/2sinθ；
wherein f D ＝k D ·f s /N，f s Is the sampling frequency; lambda is the wavelength of the laser in the laser Doppler velocimeter; θ is the incident laser angle; k (k) D The dominant frequency sequence number that is the maximum of the spectrum.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2012078187A (en) * | 2010-09-30 | 2012-04-19 | Toshiba Corp | Parameter detector, radar device, guidance system and parameter detection method |
| CN103186503A (en) * | 2011-12-27 | 2013-07-03 | 中兴通讯股份有限公司 | Inverted order arrangement system and method for fast Fourier transformation/discrete Fourier transformation (FFT/DFT) and operating system for FFT/DFT |
| CN106249209A (en) * | 2016-07-12 | 2016-12-21 | 电子科技大学 | A kind of adaptive iteration method of estimation of anti-velocity gate deception interference |
| WO2017202068A1 (en) * | 2016-05-26 | 2017-11-30 | 飞依诺科技(苏州)有限公司 | Pulse doppler ultrahigh spectrum resolution imaging processing method and processing system |
| CN107632963A (en) * | 2017-08-08 | 2018-01-26 | 浙江运达风电股份有限公司 | Length is the power system sampled signal Hilbert transform method based on FFT of composite number |
| CN109342813A (en) * | 2018-12-24 | 2019-02-15 | 常州工学院 | A kind of sinusoidal signal frequency estimation method based on DFT and dichotomy |
| CN112051446A (en) * | 2020-08-18 | 2020-12-08 | 许继集团有限公司 | Mixed base FFT implementation method and device for broadband measurement of power system |
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Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2012078187A (en) * | 2010-09-30 | 2012-04-19 | Toshiba Corp | Parameter detector, radar device, guidance system and parameter detection method |
| CN103186503A (en) * | 2011-12-27 | 2013-07-03 | 中兴通讯股份有限公司 | Inverted order arrangement system and method for fast Fourier transformation/discrete Fourier transformation (FFT/DFT) and operating system for FFT/DFT |
| WO2017202068A1 (en) * | 2016-05-26 | 2017-11-30 | 飞依诺科技(苏州)有限公司 | Pulse doppler ultrahigh spectrum resolution imaging processing method and processing system |
| CN106249209A (en) * | 2016-07-12 | 2016-12-21 | 电子科技大学 | A kind of adaptive iteration method of estimation of anti-velocity gate deception interference |
| CN107632963A (en) * | 2017-08-08 | 2018-01-26 | 浙江运达风电股份有限公司 | Length is the power system sampled signal Hilbert transform method based on FFT of composite number |
| CN109342813A (en) * | 2018-12-24 | 2019-02-15 | 常州工学院 | A kind of sinusoidal signal frequency estimation method based on DFT and dichotomy |
| CN112051446A (en) * | 2020-08-18 | 2020-12-08 | 许继集团有限公司 | Mixed base FFT implementation method and device for broadband measurement of power system |
Non-Patent Citations (1)
| Title |
|---|
| 混合基FFT算法运算量分析;程志鹏;马琪;竺红卫;;太赫兹科学与电子信息学报(第06期);第925-928页 * |
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