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1、The averaged periodogram,School of Information Science and Technology Yunnan University,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 absolu
2、te 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 w
3、idely 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 se
4、ction 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 :,i=0,1,k-1,n= 0,1,L-1,The periodogram of the th s
5、egmnet is,There are two methods of Averaged Periodogram.The one is segmented overlapping method of small sample .The other is segmented non-overlapping method of big sample。Signal x (n) can also be devided for overlapping segments,such as by 2:1.They are half overlap.Power spectrum estimate every sm
6、all segments,then average them.,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; ran
7、dn(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); subplo
8、t(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;
9、pxx4=abs(fft(xn(385:640),Nsec).2)/Nsec; pxx5=abs(fft(xn(513:768),Nsec).2)/Nsec; pxx6=abs(fft(xn(641:896),Nsec).2)/Nsec; pxx7=abs(fft(xn(769:1024),Nsec).2)/Nsec; Pxx=10*log10(pxx1+pxx2+pxx3+pxx4+pxx5+pxx6+pxx7)/7); %Averaged Periodogram and tramsformed to dB f=(0:length(Pxx)-1)*Fs/length(Pxx); subplot(2,1,2),plot(f(1:Nsec/2),Pxx(1:Nsec/2); xlabel(Frequency/Hz); ylabel(Power spectrum/dB); title(averaged periodogram(overlapping) N=1024); grid on,THANKS!,