Complex Cepstrum Signal
The complex cepstrum is a mathematical tool used in signal processing and analysis. It is defined as the inverse Fourier transform of the logarithm of the magnitude of the Fourier transform of a signal.

Stable Sequence and Convergence
A stable sequence in signal processing refers to a sequence that does not grow infinitely as time progresses. In other words, a stable sequence has bounded values.

When we consider the z-transform of a stable sequence, denoted as X(z), it converges onto the unit circle in the complex plane. This means that the values of X(z) lie on the unit circle, which is a circle with a radius of 1 centered at the origin.

Complex Cepstrum Signal Definition
The complex cepstrum signal, denoted as C(z), is defined as the inverse z-transform of the logarithm of X(z).

Explanation
The correct answer is option 'C', which states that the complex cepstrum signal is X-1(ln X(z)). Let's break down the expression to understand it better.

1. X(z): This represents the z-transform of the stable sequence x(n).

2. ln X(z): Taking the natural logarithm of X(z) means finding the complex logarithm of each value of X(z). This operation is performed element-wise for each value on the unit circle.

3. X-1(ln X(z)): The inverse z-transform, denoted as X-1, is then applied to the logarithm of X(z). This means finding the sequence x(n) whose z-transform is ln X(z).

This process of taking the inverse z-transform of the logarithm of the z-transform is known as the complex cepstrum.

The complex cepstrum has various applications in signal processing, such as analyzing the properties of speech signals, identifying resonances in audio signals, and detecting periodicities in time series data.

Conclusion
In summary, the complex cepstrum signal is defined as the inverse z-transform of the logarithm of the z-transform of a stable sequence. It is a powerful tool in signal processing for analyzing and extracting features from signals.