分段平均周期图法.ppt

Power spectrum estimation Random signal is unlimited in time，and infinited in sample.Therefore,the energy of random signal is infinite,it is a power signal. The power signal does not meet the conditions of absolute integrable of Fourier transform. Strictly speaking,its Fourier transform does not exist. Analysis of random signals in the frequency domain,it is no longer a simple spectrum, but the power spectrum. Power spectrum estimation is using of finite data to estimate the power spectrum of signal,it is widely used in radar, sonar, communications, geological exploration, astronomy, biomedical engineering and other fields. Averaged Periodogram The method of Average Periodogram is divided a longer data sequence of random signal x (n) into m segments.Then using the Fourier analysis to transform them section by section.Finally, Periodogram averaging. The signal sequence x (n), n = 0,1, ..., N-1, is divided into K small non-overlapping segments, each of small non-overlapping segments has L samples, then K * L = N.To subdivide the existing record data : Using two methods of averaged periodogram to estimate power spectral density of signals.f1=50Hz,f2=120Hz, w(t) is Gaussian white noise,Sampling frequency Fs=1000Hz,Signal length N=1024. clf;Fs=1000; %segmented non-overlapping method N=1024;Nsec=256;n=0:N-1;t=n/Fs; randn(state,0); xn=sin(2*pi*50*t)+2*sin(2*pi*120*t)+randn(1,N); pxx1=abs(fft(xn(1:256),Nsec).^2)/Nsec; pxx2=abs(fft(xn(257:512),Nsec).^2)/Nsec; pxx3=abs(fft(xn(515:768),Nsec).^2)/Nsec; pxx4=abs(fft(xn(769:1024),Nsec).^2)/Nsec; Pxx=10*log10((pxx1+pxx2+pxx3+pxx4)/4); f=(0:length(Pxx)-1)*Fs/length(Pxx); subplot(2,1,1),plot(f(1:Nsec/2),Pxx(1:Nsec/2)); xlabel(Frequency/Hz);ylabel(Power spectrum /dB); title(averaged periodogram(non-overlapping) N=4*256); grid on %segmented overlapping method pxx1=abs(fft(xn(1:256),Nsec).^2)/Nsec; pxx2=abs(fft(xn(129:384),Nsec).^2)/Nsec; pxx3=abs(fft(xn(257:512),Nsec).^2)/Nsec; pxx4=abs(fft(xn(385:640),Ns