www.pudn.com > tftb2002toolbox.rar > gdpower.m

function [x,gpd,nu]=gdpower(N,k,c)
%GDPOWER Signal with power-law group delay.
%	[X,GPD,F]=GDPOWER(N,K,C) generates a signal with a
%	power-law group delay of the form tx(f) = T0 + C*f^(K-1).
%	The output signal is of unit energy.
%
%	N   : number of points in time		(must be even)
%	K   : degree of the power-law		(default : 0)
%	C   : rate-coefficient of the power-law group delay.  
%	      C must be non-zero. 		(default : 1)	
%	X   : time row vector containing the modulated signal samples
%	GPD : group delay	      (length : round(N/2)-1)
%	F   : frequency bins
%
%	Examples :   
%	 sig=gdpower(64,0); tfrbert(sig,1:64,0.01,0.32,256,1);
%	 [sig,gpd,f]=gdpower(256,1/2); plot(gpd,f); 
%
%	See also FMPOWER.

%	O. Lemoine - April, July 1996
%	Copyright (c) 1996 by CNRS (France).
%
%	------------------- CONFIDENTIAL PROGRAM -------------------- 
%	This program can not be used without the authorization of its
%	author(s). For any comment or bug report, please send e-mail to 
%	f.auger@ieee.org 

if (nargin < 1),
 error ( 'At least one parameter.' );
elseif nargin==1,
 k=0; c=1;
elseif nargin==2,
 c=1;
end

if (N <= 0),
 error ('The signal length N must be strictly positive' );
end  

t0=0;

Lnu=round(N/2);
nu=linspace(0,0.5,Lnu+1); nu=nu(2:Lnu+1);
AM=nu.^((k-2)/6);

if c==0,
 error('C must be non-zero');
end

t=1:N;
TFx=zeros(1,N);

if (k<1 & k~=0),
 d=N^k*c; t0=N/10;
 TFx(1:Lnu)=exp(-j*2*pi*(t0*(nu)+d*(nu).^k/k)).*AM;
 x=ifft(TFx).';
elseif k==0,
 d=c; t0=N/10;
 TFx(1:Lnu)=exp(-j*2*pi*(t0*(nu)+d*log(nu))).*AM;
 x=ifft(TFx).';
elseif k==1,
 t0=N;
 x=anapulse(N,t0);
elseif (k>1),
 d=N*2^(k-1)*c; 
 TFx(1:Lnu)=exp(-j*2*pi*(t0*(nu)+d*(nu).^k/k)).*AM;
 x=ifft(TFx).';
end

if k~=1,
 gpd=t0+abs(sign(c)-1)/2*(N+1)+d*nu.^(k-1);
else
 gpd=t0*ones(1,N/2);
end

x=x-mean(x);
x=x/norm(x);