Two Implementation Methods of Cepstrum Analysis

In MATLAB, there are two primary methods to implement cepstrum analysis. The first approach utilizes the built-in rceps() function, while the second involves manual implementation based on the mathematical definition. Although both methods yield identical cepstrum plots, their implementation processes differ slightly.

Specifically, calling the rceps() function simplifies the cepstrum calculation process as it directly computes the cepstral coefficients through optimized algorithms. The function internally handles signal framing, Fourier transformation, logarithmic operations, and inverse Fourier transformation. Conversely, manual implementation provides deeper insight into the cepstrum definition and computational workflow. This method typically involves sequential operations: applying the Fast Fourier Transform (FFT) to the signal, computing the logarithm of the magnitude spectrum, and then performing an inverse FFT to obtain the cepstral coefficients. These step-by-step operations enhance understanding of the physical meaning and mathematical foundations of cepstrum analysis.

To practically demonstrate these concepts, experiments can be conducted using the acceleration data provided in the attachment. During experimentation, users can compare the cepstrum plots generated by both methods and analyze their similarities and differences. Furthermore, modifications can be applied to the manual implementation (such as windowing techniques or different logarithm bases) to observe their impact on cepstral results.

Therefore, when implementing cepstrum analysis in MATLAB, users can select either method according to their needs. Understanding both approaches facilitates comprehensive knowledge of cepstrum concepts and applications, forming a solid foundation for subsequent signal processing research and development.