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/*Description
Real cepstrum and minimum-phase reconstruction
If called with two output arguments,
the minimum phase reconstruction of the signal x is returned in ym.Calling Sequence
[y,ym] = rceps(x)
Parameters
x : A vector or a Matirx
y : Real cepstrum
ym : Minimum-phase reconstruction
Dependencies fft1 , ifft1
Example:
// create a 45 Hz sine wave sampled at 100 Hz.
t = 0:0.01:1.27;
s1 = sin(2*%pi*45*t);
s2 = s1 + 0.5*[zeros(1,20) s1(1:108)]; //Add an echo of the signal, with half the amplitude, 0.2 seconds after the beginning of the signal.
c = rceps(s2); // real cepstrum of signal
plot(t,c)
*/
function [y, xm]= rceps(x)
if(argn(2)~= 1 )
error("Wrong number of Input Arguments");
end
if(argn(1)>2)
error("Wrong number of Output Arguments")
end
f = abs(fft1(x));
if (or(f == 0))
error ("The spectrum of x contains zeros, unable to compute real cepstrum");
end
y = real(ifft1(log(f)));
if argn(1) == 2 then
n=max(size(x));
if size(x,1)==1 then
if (n-fix(n./2).*2) ==1 then
xm = [y(1), 2*y(2:n/2+1), zeros(1,n/2)];
else
xm = [y(1), 2*y(2:n/2), y(n/2+1), zeros(1,n/2-1)];
end
else
if (n-fix(n./2).*2)==1
xm = [y(1,:); 2*y(2:n/2+1,:); zeros(n/2,size(y,2))];
else
xm = [y(1,:); 2*y(2:n/2,:); y(n/2+1,:); zeros(n/2-1,size(y,2))];
end
end
xm = real(ifft1(exp(fft1(xm))));
end
endfunction
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