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Hilbert transform和全相位Hilbert transform

已有 588 次阅读2011-2-24 10:21 |个人分类:应用论文|

张国亮.基于FPGA的无功功率测量仪的设计[D]. 哈尔滨理工大学, 2015，硕士

论文提出

对 Hilbert 变换进行全相位改进

对 Hilbert 变换之前，对数据进行了全相位加窗处理，实验表明，有效的提高了无功功率的计量精度。

论文致力于提高无功功率的计量精度，针对无功功率的多种测量方式，选取了测量精度更高的 Hilbert 变法，并针对电网中电能信号无法实现同步采样的实际情况，对 Hilbert 变换之前，对数据进行了全相位加窗处理，实验表明，有效的提高了无功功率的计量精度。

同时针对电网中无法实现同步采样这一特点，采用全相位 FFT 来代替代替 DFT 运算，比传统的 Hilbert 算法计算精度更高。

论文中提出了全相位予处理+Hilbert变换,全相位Hilbert teansform(ap-Hilbert ),

並给出了和传统Hilbert法比较结果

hilbert和ap-Hilbert比较程序:

clc;clear;clf;close all;
N=200;f1=50.3;fs=1000;
t = (0:N-1)*1/fs;
y = sin(2*pi*f1*t);
yh = hilbert(y);
yi=imag(yh);
subplot(421);plot(t,y,'R.-'),grid;title('(a)orignal sin signal')
subplot(422);plot(t,yi,'B.-');grid;ylim([-1,1]),title('(b)Hilbert transform signal')
yih=hilbert(yi);
yii=imag(yih);
disp('The results of Hilbert transform for two times the orignal signal')
max(y+yii)
disp('orthogonal signal Hilbert transform and orignal signal');
sum(y.*yi)
NFFT=2^nextpow2(N);
f=fs*linspace(0,1,NFFT);
Y=fft(y,NFFT)/N;
YH=fft(yh,NFFT)/N;
subplot(423);plot(f,(abs(Y*2)),'R.-'),grid;title('(c)Bilateal spectrum of the orignal signal')
subplot(424);plot(f,(abs(YH)),'B.-'),grid;title('(d)Bilateal spectrum of complex signal composed of the signal after Hilbert transformation')
tt = (-N+1:N-1)*1/fs;
y = sin(2*pi*f1*tt);
win=ones(1,N);
win1=conv(win,win)/N;
%win1=win1/sum(win1);
y1=y.*win1;
ya=y1(N:end)+[0 y1(1:N-1)];
yha = hilbert(ya);
yai=imag(yha);
subplot(425);plot(t,ya,'R.-');grid;title('(e)orignal all phase signal')
subplot(426);plot(t,yai,'B.-'),grid;title('(f)Hilbert transform all phase signal')
yih=hilbert(yai);
yii=imag(yih);
disp('The results of Hilbert transform for two times the orignal ap-signal')
max(ya+yii)
disp('orthogonal ap-signal Hilbert transform and orignal ap-signal');
sum(ya.*yai)
NFFT=2^nextpow2(N);
f=fs*linspace(0,1,NFFT);
Y=fft(ya,NFFT)/N;
YH=fft(yha,NFFT)/N;
subplot(427);plot(f,(abs(Y*2)),'R.-');grid;title('(g)Bilateal spectrum of the orignal all phase signal')
subplot(428);plot(f,(abs(YH)),'B.-'),grid;title('(h)Bilateal spectrum of complex signal composed of the all phasesignal after Hilbert transformation')

clc;clear all;close all
ts = 0.001;
fs = 1/ts;
N = 200;
t =(0:N-1)*1/fs;
f1 = 10.;
f2 = 70.;
a = cos(2*pi*f1*t);
a = 2 + cos(2*pi*f1*t);
%a = 1./(1+t.^2*50);
m = sin(2*pi*f2*t+pi/3);
y = a.*m;% 信号调制
subplot(241);plot(t, a);title('envelope');
subplot(242);plot(t, m);title('modulatation signal');
subplot(243);plot(t, y);title('modulation results');
yh = hilbert(y);
aabs = abs(yh);                 % envelope abstract value
aangle = unwrap(angle(yh));     % envelope phase
af = diff(aangle)/2/pi ;    % instantaneous frequency of envelope, difference instead differental calculation
dd=af*fs;
% NFFT = 2^nextpow2(N);
NFFT = 2^nextpow2(1024*4);      % improve fence effect
f = fs*linspace(0,1,NFFT);
YH = fft(yh, NFFT)/N;           % Hilbert transform spectrum of complex signals
A = fft(aabs, NFFT)/N;          % envelope spectrum
subplot(245);plot(t, aabs, t, a, '.');title('absolute value of envelope');legend('envelope analysis results', 'real envelope');ylim([0,3])
subplot(246);plot(t, aangle);title('phase modulation signal')
subplot(247);plot(t(1:end-1), af*fs);title('instantaneous frequency modulation signal')
subplot(244);plot(f,abs(YH));title('original signal Hilbert spectrum');xlabel('frequency f (Hz)');ylabel('|YH(f)|');xlim([0,N])
subplot(248);plot(f,abs(A));title('envepole spectrum');xlabel('frequency (Hz)');ylabel('|A(f)|');xlim([0,N])
figure
t = (-N+1:N-1)*1/fs;
a = cos(2*pi*f1*t);       % envelope1
a = 2 + cos(2*pi*f1*t);     % envelope2
%a = 1./(1+t.^2*50);       % envelope3
m = sin(2*pi*f2*t+pi/3) ;         % modulation signal
y =a.*m;                 % signal modulation
win=ones(1,N);
win1=conv(win,win)/N;
y1=y.*win1;
ya=y1(N:end)+[0 y1(1:N-1)];
subplot(241);plot(t, a);title('envelope');
subplot(242);plot(t, m);title('modulatation signal');
tt=(0:N-1)*1/fs;
subplot(243);plot(tt,ya);title('modulation results');%tt=(0:N-1)*1/fs;xlim([1,N])
yh = hilbert(ya);
aabs = abs(yh);                 % envelope abstract value
aangle1 = unwrap(angle(yh));     % envelope phase
af1 = diff(aangle1)/2/pi;         % instantaneous frequency of envelope, difference instead differental calculation
dd=af1*fs;
% NFFT = 2^nextpow2(N);
NFFT = 2^nextpow2(1024*4);      % improve fence effect
f = fs*linspace(0,1,NFFT);
YH = fft(yh, NFFT)/N;           % Hilbert transform spectrum of complex signals
A = fft(aabs, NFFT)/N;          % envelope spectrum
subplot(245);plot(tt, aabs,tt,a(N:end), '.');title('absolute value of envelope');legend('envelope analysis results', 'real envelope');ylim([0,3])
subplot(246);plot(tt,aangle1);title('phase modulation signal');
subplot(247);plot(tt(1:end-1),af1*fs);title('instantaneous frequency modulation signal');
subplot(244);plot(f,abs(YH));title('original signal Hilbert spectrum');xlabel('frequency(Hz)');ylabel('|YH(f)|');xlim([1,N])
subplot(248);plot(f,abs(A));title('envepole spectrum');xlabel('frequency f (Hz)');ylabel('|A(f)|');xlim([1,N])