CN102830282A - 2560-point grouping 2-based rapid fast Fourier transform method - Google Patents

Abstract

The invention discloses a 2560-point grouping 2-based rapid fast Fourier transform method. The 2560-point grouping 2-based rapid fast Fourier transform method is mainly used for measurement calculation of components of harmonic waves and inter-harmonic waves of an online electric energy quality monitoring device. The 2560-point grouping 2-based rapid fast Fourier transform method is characterized by comprising the following steps: as to a multi-spectrum Fourier transform of which the quantity of data window sampling points is 2560, firstly, grouping, extracting points from the 2560 points at equal intervals and dividing the 2560 points into five groups, wherein 2560 is equal to 512*5, carrying out 2-based rapid fast Fourier transform on 512 points in each group, and finally, determining the fast Fourier transform result of 2560 points from the five groups of results. According to the invention, the problem in the prior art that the online electric energy quality monitoring device measures and analyzes the harmonic wave and inter-harmonic wave slowly and cannot meet the use requirement is solved, and the fast Fourier transform method meeting the accuracy and the rapidity is provided, so that the electric energy quality device can measure the harmonic wave and inter-harmonic wave easily.

Description

A kind of 2560 basic 2 Fast Fourier Transform (FFT) methods of dividing into groups

Technical field

The present invention relates to a kind of 2560 basic 2 Fast Fourier Transform (FFT) methods of dividing into groups, specifically relate to a kind of measurement computing method that are mainly used in electric energy quality on-line monitoring device harmonic wave, a harmonic wave.

Background technology

Harmonic wave, a harmonic wave are the important monitoring parameters of the quality of power supply; The spectrum analysis time window of act.std regulation harmonic measure is 200ms; Promptly use the spectrum analysis result of 10 power frequency periods; As the basic basis of unstable signal harmonic wave, a harmonic wave assessment, spectral resolution has just reached 5Hz like this.The overtone order that at present general electric energy quality on-line monitoring device requires to detect reaches 50 times; Be 2500Hz; Generally to select for use weekly the data sampling of ripple 256 could satisfy sampling requirement; Counting of such 10 cycles just reached 2560 points; As will be in strict accordance with the harmonic wave among the IEC 61000-4-7, inter-harmonic wave measuring method, will carry out more than 500 times 2560 Fourier transform at every turn, adopt general DFT DFT can't in 200ms, accomplish 2560 Fourier transform for 500 times of a plurality of passages.2560 is not 2 index simultaneously, can not directly use 2 Fast Fourier Transform (FFT)s of general base.

Summary of the invention

Slow in order to solve in the prior art electric energy quality on-line monitoring device for the Measurement and analysis speed of harmonic wave, a harmonic wave; Can't satisfy the problem of use needs; The invention provides a kind of accuracy that both satisfied, satisfied the Fast Fourier Transform (FFT) method of rapidity again.

In order to address the above problem, the technical scheme that the present invention taked is:

It for the data window sampling number 2560 multiple spectra Fourier transform; Employing is divided into groups earlier, 2560 is uniformly-spaced taken out a little be divided into 5 groups, 2560=512*5; Carry out basic 2 Fast Fourier Transform (FFT)s to 512 every group again, obtain 2560 fast Fourier transformation result by these 5 groups of results more at last.

A kind of 2560 basic 2 Fast Fourier Transform (FFT) methods of dividing into groups is characterized in that: may further comprise the steps:

(1), samples time window demonstration sampling number 2560 points through electric energy quality on-line monitoring device;

(2), 2560 are uniformly-spaced taken out a little be divided into 5 groups, every group 512 point;

(3), carry out basic 2 Fast Fourier Transform (FFT)s to 512 every group;

(4), obtain 2560 fast Fourier transformation result by these 5 groups of bases 2 Fast Fourier Transform (FFT) results again.

Aforesaid a kind of 2560 basic 2 Fast Fourier Transform (FFT) methods of dividing into groups is characterized in that: may further comprise the steps:

Be provided with a sampling time window, number of data points is { x (n) }, n=0, and 1,2,3..., 2559,

Then its DFT is:

$X\left(k\right)=\mathrm{DFT}\left[x\left(n\right)\right]=\underset{n=0}{\overset{2559}{\mathrm{\Σ}}}x\left(n\right)W_{2560}^{\mathrm{kn}};$

Wherein $W_N=e^{-j\frac{2\mathrm{\π}}{N}},$ N=2560,

If 0≤k≤511 are divided into 5 groups { x (5r) }, { x (5r+1) } with { x (n) }, { x (5r+2) }, { x (5r+3) }, { x (5r+4) }, r=0 wherein, 1,2,3 ..., 511,

Then have:

$X\left(k\right)=\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x\left(5r\right)W_{2560}^{k5r}+\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+1)W_{2560}^{k(5r+1)}+\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+2)W_{2560}^{k(5r+2)}$

$+\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+3)W_{2560}^{k(5r+3)}+\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+4)W_{2560}^{k(5r+4)}$

$X\left(k\right)=W_{2560}^0\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x\left(5r\right)W_{2560}^{k5r}+W_{2560}^k\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+1)W_{2560}^{k5r}+W_{2560}^{2k}\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+2)W_{2560}^{k5r}$

$+W_{2560}^{3k}\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+3)W_{2560}^{k5r}+W_{2560}^{4k}\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+4)W_{2560}^{k5r}$

Because $W_{2560}^{k5r}=W_{512}^{\mathrm{Kr}},$ Following formula becomes:

$X\left(k\right)=W_{2560}^0\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x\left(5r\right)W_{512}^{kr}+W_{2560}^k\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+1)W_{512}^{\mathrm{kr}}+W_{2560}^{2k}\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+2)W_{512}^{\mathrm{kr}}$

$+W_{2560}^{3k}\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+3)W_{512}^{kr}+W_{2560}^{4k}\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+4)W_{512}^{kr}$

Order $Q_l\left(k\right)=\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+l)W_{512}^{\mathrm{Kr}},$ L=0,1,2,3,4,

Q _l(k) be 512 fourier transformations of grouping { x (5r+l) }, because 512=29, so Q _l(k) can try to achieve by the base 2 quick fourier transformations of routine, can calculate X (k) thus.

$X\left(k\right)=W_{2560}^0{Q}_0\left(k\right)+W_{2560}^k{Q}_1\left(k\right)+W_{2560}^{2k}{Q}_2\left(k\right)+W_{2560}^{3k}{Q}_3\left(k\right)+W_{2560}^{4k}{Q}_4\left(k\right)$

The invention has the beneficial effects as follows: the present invention's deadline window sampling number in a short period of time is the multiple spectra analysis of 2560 point data, makes quality of power supply device realize easily for the measurement of harmonic wave, a harmonic wave.

Embodiment

Below embodiments of the invention are done concrete introduction:

Be provided with a sampling time window, number of data points is { x (n) }, n=0,1,2,3..., 2559.

Then its DFT is:

$X\left(k\right)=\mathrm{DFT}\left[x\left(n\right)\right]=\underset{n=0}{\overset{2559}{\mathrm{\Σ}}}x\left(n\right)W_{2560}^{\mathrm{kn}};$

Wherein $W_N=e^{-j\frac{2\mathrm{\π}}{N}},$ N=2560.

If 0≤k≤511 are divided into 5 groups { x (5r) }, { x (5r+1) }, { x (5r+2) }, { x (5r+3) }, { x (5r+4) } with { x (n) }, r=0 wherein, 1,2,3 ..., 511.

Then have:

$X\left(k\right)=\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x\left(5r\right)W_{2560}^{k5r}+\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+1)W_{2560}^{k(5r+1)}+\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+2)W_{2560}^{k(5r+2)}$

$+\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+3)W_{2560}^{k(5r+3)}+\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+4)W_{2560}^{k(5r+4)}$

$X\left(k\right)=W_{2560}^0\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x\left(5r\right)W_{2560}^{k5r}+W_{2560}^k\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+1)W_{2560}^{k5r}+W_{2560}^{2k}\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+2)W_{2560}^{k5r}$

$+W_{2560}^{3k}\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+3)W_{2560}^{k5r}+W_{2560}^{4k}\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+4)W_{2560}^{k5r}$

Because $W_{2560}^{k5r}=W_{512}^{\mathrm{Kr}},$ Following formula becomes:

$X\left(k\right)=W_{2560}^0\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x\left(5r\right)W_{512}^{kr}+W_{2560}^k\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+1)W_{512}^{\mathrm{kr}}+W_{2560}^{2k}\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+2)W_{512}^{\mathrm{kr}}$

$+W_{2560}^{3k}\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+3)W_{512}^{kr}+W_{2560}^{4k}\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+4)W_{512}^{kr}$

Order $Q_l\left(k\right)=\underset{r=0}{\overset{511}{\mathrm{\Σ}}}x(5r+l)W_{512}^{\mathrm{Kr}},$ L=0,1,2,3,4.

Q _l(k) be 512 fourier transformations of grouping { x (5r+l) }, because 512=29, so Q _l(k) can try to achieve by the base 2 quick fourier transformations of routine, can calculate X (k) thus.

$X\left(k\right)=W_{2560}^0{Q}_0\left(k\right)+W_{2560}^k{Q}_1\left(k\right)+W_{2560}^{2k}{Q}_2\left(k\right)+W_{2560}^{3k}{Q}_3\left(k\right)+W_{2560}^{4k}{Q}_4\left(k\right)$

More than show and described ultimate principle of the present invention, principal character and advantage.The technician of the industry should understand; The present invention is not restricted to the described embodiments; That describes in the foregoing description and the instructions just explains principle of the present invention; Under the prerequisite that does not break away from spirit and scope of the invention, the present invention also has various changes and modifications, and these variations and improvement all fall in the scope of the invention that requires protection.The present invention requires protection domain to be defined by appending claims and equivalent thereof.

Claims (2)

1. one kind 2560 basic 2 Fast Fourier Transform (FFT) methods of dividing into groups is characterized in that: may further comprise the steps:

(1), samples time window demonstration sampling number 2560 points through electric energy quality on-line monitoring device;

(2), 2560 are uniformly-spaced taken out a little be divided into 5 groups, every group 512 point;

(3), carry out basic 2 Fast Fourier Transform (FFT)s to 512 every group;

(4), obtain 2560 fast Fourier transformation result by these 5 groups of bases 2 Fast Fourier Transform (FFT) results again.

2. according to described a kind of 2560 the basic 2 Fast Fourier Transform (FFT) methods of dividing into groups of claim, it is characterized in that: may further comprise the steps:

Be provided with a sampling time window, number of data points is { x (n) }, n=0, and 1,2,3..., 2559,

Then its DFT is:

N=2560 wherein

If 0≤k≤511 are divided into 5 groups { x (5r) }, { x (5r+1) } with { x (n) }, { x (5r+2) }, { x (5r+3) }, { x (5r+4) }, r=0 wherein, 1,2,3 ..., 511,

Then have:

Because

following formula becomes:

Make

l=0; 1,2,3; 4

Ql (k) is for 512 fourier transformations of divide into groups { x (5r+l) }, because 512=29 so Ql (k) can be tried to achieve by the base 2 quick fourier transformations of routine, can calculate X (k) thus.

。