Question

If x(n) is a stable sequence so that X(z) converges on to a unit circle, then the complex cepstrum signal is defined as ____________

(a) X(ln X(z))

(b) ln X(z)

(c) X^-1(ln X(z))

(d) None of the mentioned

This question was posed to me during an interview.

The above asked question is from Frequency Analysis of Discrete Time Signal in chapter Frequency Analysis of Signals and Systems of Digital Signal Processing

Answer 1

Right answer is (c) X^-1(ln X(z))

For explanation I would say: Let us consider a sequence x(n) having a z-transform X(z). We assume that x(n) is a stable sequence so that X(z) converges on to the unit circle. The complex cepstrum of the  signal x(n) is defined as the sequence cx(n), which is the inverse z-transform of Cx(z), where Cx(z)=ln X(z)

=> cx(z)= X^-1(ln X(z))