% M10-apfilt.diary % Looking at allpass filters % dpwe@ee.columbia.edu % 2007-10-30 % Define a simple pair of conjugate poles z0 = .9*exp(j*.1*pi); % poly() gives the polynomial coefficients for these roots a = poly([z0 z0']) %a = % 1.0000 -1.7119 0.8100 % So, for an allpass filter, numerator coefficients are simply the reverse b = fliplr(a); % Look at the response freqz(b,a) % Magnitude response is flat to numerical resolution (10^-14) % Where are poles/zeros? zplane(b,a) % zeros visibly at reciprocals (reflected in unit circle) of poles % What is the group delay (matlab built-in does d theta/d omega for us) grpdelay(b,a) % Peak delay at point of peak rate of phase change % What does the "rubber sheet" ZT surface look like % (i.e., the magnitude of the closed-form - does not include divergence) vizZTsurf(b,a) % Apply the filter repeatedly, to accentuate group delay [x,sr]=wavread('mpgr1_sx419.wav'); y = x; for i = 1:100; y = filter(b,a,y); end soundsc(x,sr) soundsc(y,sr) % Weird sqeakiness from local group delay % Check that long-term spectra unchanged subplot(211) plotspec(x,sr,16384); % (plotspec.m is in the course matlab directory) subplot(212) plotspec(y,sr,16384); % but spectrograms show clear effect subplot(211) specgram(x,512,sr) subplot(212) specgram(y,512,sr)