% Notes for cochlear filterbank design

%% Cochlear Filter Usage
% File name: aud24.mat (~speech/matlab/nsltools/aud24.mat)
% Description: 24 channel/octave auditory (cochlear) filterbank 
% # of channel: 129.
% 	Q: Why 129 channels?
%	A: There is an LIN operation (differentiation between adjacent channels)
%	   which will result in one less channel output at the end of the model.
%	   We want the # of output channel to be a power of 2 which is good for
%	   further Fourier analysis.
%	Q: Why 24 ch/oct?
%	A: The spacing of musical semitones (C, C#, D, D#, ... A#, B, C) is 1/12%	   octave. The 24 ch/oct organization is good enough to resolve musical
%	   note and ensure the equal-height note-tone will induce equal-height
%	   output.
%
% Characteristic Frequency: fr = 440 * 2.^ ([(0:128)-31]/24);	% for 16 kHz
%			or  fr = 440 * 2.^ ([(0:128)-31]/24) * SF / 16000;
%			where SF is the sampling rate for the input signal
load aud24;

% Format of the variable COCHBA: = [ch1 ch2 .. .. ch129]
% for m-th channel, 
% The order of IIR: p = real(COCHBA(1, m)); 	% ranges from 4 to 14
% The error of IIR re. target filter: err = imag(COCHBA(1, m)); % ignored 
% The MA coefficients: B = real(COCHBA((0:p)+2, m));
% The AR coefficients: A = imag(COCHBA((0:p)+2, m));

% For instance,
m = 60;
p = real(COCHBA(1, m));
B = real(COCHBA((0:p)+2, m));
A = imag(COCHBA((0:p)+2, m));

% you may see the frequency response
freqz(B, A, 256);

% impulse response
impz(B, A);

% zero-pole plot
zplane(B', A');

% (to be continues)
%% Cochlear Filter Design

%% IIR coefficient Generation