icceps

Inverse complex cepstrum

Syntax

x = icceps(xhat,nd)

Description

x = icceps(xhat,nd) returns the inverse complex cepstrum of the real data sequence xhat, removing nd samples of delay.

Examples

Inverse Complex Cepstrum of Echo

Generate a sine of frequency 45 Hz, sampled at 100 Hz. Add an echo with half the amplitude and 0.2 s later. Compute the complex cepstrum of the signal.

Fs = 100;
t = 0:1/Fs:1.27;

s1 = sin(2*pi*45*t);		
s2 = s1 + 0.5*[zeros(1,20) s1(1:108)];

c = cceps(s2);

Compute the inverse complex cepstrum. Plot the echo data and its inverse complex cepstrum.

x = icceps(c);
plot(t,s2,t,x,'r--')
xlabel('Time (s)')
legend('Echo signal','Inverse complex cepstrum')

Input Arguments

xhat — Data sequence

real vector

Data sequence, specified as a real vector. If xhat was obtained with cceps, then the amount of delay that was added to x was the element of round(unwrap(angle(fft(x)))/pi) corresponding to π radians.

nd — Number of samples of delay

real positive scalar

Number of samples of delay, specified as a real positive scalar.

Output Arguments

x — Inverse complex cepstrum

vector

Inverse complex cepstrum, returned as a vector.

References

[1] Oppenheim, A.V., and R.W. Schafer, Discrete-Time Signal Processing, Prentice-Hall, 1989.