The phase of the frequency response is called the *phase
response*. Like the phase of any complex number, it is given by the
arctangent of the imaginary part of
divided by its
real part, and it specifies the *delay* of the filter at each
frequency. The phase response is a good way to look at short filter
delays which are not directly perceivable as causing an
``echo''.^{4.4} For longer delays in audio, it is
usually best to study the filter *impulse response*, which is
output of the filter when its input is
(an
``impulse''). We will show later that the impulse response is also
given by the inverse
*z* transform of the filter transfer function (or, equivalently, the inverse
Fourier transform of the filter frequency response).

In this example, the phase response is

A specific case is plotted in Fig.3.10b, corresponding to the amplitude response in Fig.3.10a. The impulse response is plotted in Fig.3.8. The matlab code for producing these figures is shown in Fig.3.11. (The plotting utility

`freqz(B,A,Nspec)`

.

% efr.m - frequency response computation in Matlab/Octave % Example filter: g1 = 0.5^3; B = [1 0 0 g1]; % Feedforward coeffs g2 = 0.9^5; A = [1 0 0 0 0 g2]; % Feedback coefficients Nfft = 1024; % FFT size Nspec = 1+Nfft/2; % Show only positive frequencies f=[0:Nspec-1]/Nfft; % Frequency axis Xnum = fft(B,Nfft); % Frequency response of FIR part Xden = fft(A,Nfft); % Frequency response, feedback part X = Xnum ./ Xden; % Should check for divide by zero! clf; figure(1); % Matlab-compatible plot plotfr(X(1:Nspec),f);% Plot frequency response cmd = 'print -deps ../eps/efr.eps'; disp(cmd); eval(cmd); |

[How to cite this work] [Order a printed hardcopy] [Comment on this page via email]

Copyright ©

Center for Computer Research in Music and Acoustics (CCRMA), Stanford University