Digital Signal Processing Reference
In-Depth Information
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Bild 20-46
Schätzungen der Zeit-AKF und der Leistungsübertragungsfunktion zum System
H
2
(
z
) mit
dem Programm
dsplab15_1
% Estimation of the auto-correlation function (acf) and computation
% of the power density spectrum (pds) using the estimated acf and
% the dft with zero-padding
% dsplab15_1.m * mw * 06/12/2008
M = 51; %
number of acf coefficients
N = 1e6; %
number of signal samples per block
Ndft = 256; %
dft length
b = [0.06 0.12 0.06]; %
numerator coefficients H2
a = [1 -1.3 0.845]; %
denominator coefficients H2
% b = [0.845 -1.3 1]; %
numerator coefficients H3
% a = [1 -1.3 0.845]; %
denominator coefficients H3
x = randn(1,N); %
normally distributed random signal
y= filter(b,a,x); %
filtering
Ryy = xcorr(y,M,'unbiased'); %
auto-correlation sequence
%%
Compute pds from acf estimates with zero-padding to length Ndft
Syy = fft([Ryy zeros(1,Ndft-2*M+1)]);
Syy = abs(Syy);
%
compensate for numerical impairments
%%
Compute analytical values
h = impz(b,a,M); %
impulse response
Rhh = conv(h,flipud(h)); %
time acf
Phi = abs(freqz(b,a,Ndft,'whole')').^2; %
power transmission function
%%
Graphics
FIG1=figure('Name','dsplab15_1: estimates of acf and
pds','NumberTitle','off',...
'Units','normal','Position',[.4 .4 .45 .45]);
subplot(2,1,1), plot(0:M-1,Rhh(M:2*M-1)/Rhh(M),0:M-
1,Ryy(M+1:2*M)/Ryy(M+1),'o'), grid
axis([0 M-1 -1 1]);
xlabel('{\itl} \rightarrow'),ylabel('{\itR}[{\itl}] / {\itR}[0]
\rightarrow')
hold on
