% M06-freqresp.diary % 2007-10-09 % Passing a mixture of two sinusoid through a system with a known % frequency response (i.e. DTFT of its impulse response) modifies % the balance between the sinusoids in proportion to the frequency % response at those frequencies. % 5 point moving average filter: frequency response h = 1/5*ones(1,5); % setup timebase nn = -20:100; % offset to get zero point zz = 21; % Mixture of two equal-amplitude sines at 0.1pi rad/samp and 0.5pi rad/samp s1(zz+[0:100]) = sin(0.1*pi*[0:100]); s2(zz+[0:100]) = sin(0.5*pi*[0:100]); x = s1 + s2; % Pass it through the system y = conv(h,x); % truncate y to be the same length as x y = y(1:length(x)); % Plot results subplot(411) % The two component sinusoids plot(nn,s1,nn,s2) % Their sum (system input) and system output subplot(412) plot(nn,x,nn,y); grid axis([-20 100 -2 2]) % Compare to sinusoids scaled by freq resp H = fft(h,256); % with a 256pt fft, 2pi corresponds to 256, so 0.1pi corresponds to 256/20 H1 = H(1+round(0.1*(256/2))); H2 = H(1+round(0.5*(256/2))); % Individual sinusoids scaled and phase shifted by freq resp samples s1b(zz+[0:100]) = abs(H1)*sin(0.1*pi*[0:100]+angle(H1)); s2b(zz+[0:100]) = abs(H2)*sin(0.5*pi*[0:100]+angle(H2)); % Plot the modified sinusoids subplot(413) plot(nn,s1b,nn,s2b) % .. and compare their sum to the actual system output subplot(414) plot(nn,s1b+s2b,nn,y) grid axis([-20 100 -2 2]) % Pretty much fall fright on top of each other, except for a few % points around zero (i.e. the transient response, which is limited to the % impulse response length or 5 points).