# Documentation of GammaChirp

Index of all files: short | long | this subdirectory only: short | long

## Function Synopsis

`[GC, LenGC, Fps, InstFreq ] ...`

## Help text

```
Gammachirp : Theoretical auditory filter
Toshio IRINO
20 Aug. 97 (Simplify & Carrier Selection)
10 Jun. 98 (SwNorm)
26 Nov. 98 (phase = phase + c ln fr/f0)
7  Jan. 2002 (adding 'envelope' option)
22  Nov. 2002 (debugging 'peak' option)

gc(t) = t^(n-1) exp(-2 pi b ERB(Frs)) cos(2*pi*Frs*t + c ln t + phase)

function [GC, LenGC, Fps, InstFreq ] ...
= GammaChirp(Frs,SR,OrderG,CoefERBw,CoefC,Phase,SwCarr,SwNorm);
INPUT : Frs	: Asymptotic Frequency ( vector )
SR 	: Sampling Frequency
OrderG 	: Order of Gamma function t^(OrderG-1)        == n
CoefERBw: Coeficient -> exp(-2*pi*CoefERBw*ERB(f))    == b
CoefC	: Coeficient -> exp(j*2*pi*Frs + CoefC*ln(t)) == c
Phase	: Start Phase(0 ~ 2*pi)
SwCarr  : Carrier ('cos','sin','complex','envelope': 3 letters)
SwNorm  : Normalization of peak spectrum level ('no', 'peak')
OUTPUT: GC 	: GammaChirp                     ( matrix )
LenGC 	: Length of GC for each channel  ( vector )
Fps     : Peak Frequency                 ( vector )
InstFreq: Instanteneous Frequency        ( matrix )

```

## Cross-Reference Information

This function calls This function is called by

## Listing of function GammaChirp

```
function [GC, LenGC, Fps, InstFreq ] ...
= GammaChirp(Frs,SR,OrderG,CoefERBw,CoefC,Phase,SwCarr,SwNorm);

if nargin < 2,            help GammaChirp; return; end;
Frs = Frs(:);
NumCh = length(Frs);
if nargin < 3,            OrderG = [];	               end;
if length(OrderG) == 0,   OrderG = 4;                  end; % Default GammaTone
if length(OrderG) == 1,   OrderG = OrderG*ones(NumCh,1); end;
if nargin < 4,            CoefERBw = [];	       end;
if length(CoefERBw) == 0, CoefERBw = 1.019;            end; % Default GammaTone
if length(CoefERBw) == 1, CoefERBw = CoefERBw*ones(NumCh,1); end;
if nargin < 5,            CoefC  = [];                 end;
if length(CoefC) == 0,    CoefC  = 0;                  end; % Default GammaTone
if length(CoefC) == 1,    CoefC  = CoefC*ones(NumCh,1); end;
if nargin < 6,            Phase  = [];                  end;
if length(Phase) == 0,    Phase  = 0;                  end;
if length(Phase) == 1,    Phase  = Phase*ones(NumCh,1); end;
if nargin < 7,            SwCarr = [];                 end;
if length(SwCarr) == 0,   SwCarr = 'cos';	       end;
if nargin < 8,            SwNorm = [];                 end;
if length(SwNorm) == 0,   SwNorm = 'no';	       end;

[ERBrate ERBw] = Freq2ERB(Frs);                             % G&M (1990)
LenGC1kHz = (40*max(OrderG)/max(CoefERBw) + 200)*SR/16000;  % 2 Aug 96
[dummy ERBw1kHz] = Freq2ERB(1000);

if strcmp(SwCarr,'sin'), Phase = Phase - pi/2*ones(1,NumCh); end;
%%% Phase compensation
Phase = Phase + CoefC.*log(Frs/1000); % relative phase to 1kHz

LenGC = fix(LenGC1kHz*ERBw1kHz./ERBw);

%%%%%  Production of GammaChirp  %%%%%
GC       = zeros(NumCh,max(LenGC));
if nargout > 2, Fps = Fr2Fpeak(OrderG,CoefERBw,CoefC,Frs); end; % Peak Freq.
if nargout > 3, InstFreq = zeros(NumCh,max(LenGC));        end;

for nch = 1:NumCh,
t = (1:LenGC(nch)-1)/SR;

GammaEnv = t.^(OrderG(nch)-1).*exp(-2*pi*CoefERBw(nch)*ERBw(nch)*t);
GammaEnv = [ 0 GammaEnv/max(GammaEnv)];

if strcmp(SwCarr(1:3),'env') % envelope
Carrier = ones(size(GammaEnv));
elseif strcmp(SwCarr(1:3),'com') % complex
Carrier = [ 0 exp(i * (2*pi*Frs(nch)*t + CoefC(nch)*log(t) +Phase(nch)) )];
else
Carrier = [ 0 cos(2*pi*Frs(nch)*t + CoefC(nch)*log(t) +Phase(nch))];
end;

GC(nch,1:LenGC(nch)) = GammaEnv.*Carrier;

if nargout > 3,
InstFreq(nch,1:LenGC(nch)) = [0, [Frs(nch) + CoefC(nch)./(2*pi*t)]];
end;

if strcmp(SwNorm,'peak') == 1,  % peak gain normalization
[frsp freq] = freqz(GC(nch,1:LenGC(nch)),1,LenGC(nch),SR);
fp = Fr2Fpeak(OrderG(nch),CoefERBw(nch),CoefC(nch),Frs(nch));
[dummy np] = min(abs(freq-fp));
GC(nch,:) = GC(nch,:)/abs(frsp(np));
end;

end; % nch = ...

return

%% ERBw = 0.128*Frs;     % Complete Constant Q only for check.

% old
% Amp = ones(NumCh,1);                                  % No normalization
% if strcmp(SwNorm,'peak'),  Amp = ERBw./ERBw1kHz; end; % Peak spectrum==const.
% when it is gammatone
%  if strcmp(SwNorm,'peak'),   ...
%         Amp = 2.815*sqrt(4/OrderG).*CoefERBw.*ERBw/SR; end;
% Peak spectrum==const. The gain is 1.0 when filtering sinusoid at cf.
% GC(nch,:) = GC(nch,:)/max(abs(freqz(GC(nch,:),1,LenGC(nch))));
%
```

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