MATLAB Code Implementation for Cepstrum Calculation

Cepstrum analysis is an effective signal processing technique for detecting periodic structures in signals. Implementing cepstrum calculation through MATLAB enables clear visualization of periodic characteristics in the frequency domain, making it particularly suitable for applications such as mechanical fault diagnosis and speech signal processing.

Implementation Approach: Signal Preprocessing: First, perform Fast Fourier Transform (FFT) on the input time-domain signal to convert it to the frequency domain. To enhance analysis effectiveness, typically take the logarithmic magnitude spectrum using MATLAB's `abs()` and `log()` functions, which helps emphasize harmonic structures. Cepstrum Calculation: Apply Fourier transform (or inverse Fourier transform) to the logarithmic magnitude spectrum to obtain the cepstrum. The x-axis of the cepstrum represents "quefrency," which reflects periodic components in the original signal. In MATLAB, this can be implemented using `ifft(log(abs(fft(signal))))` or `rceps()` function for real cepstrum. Visualization: Utilize MATLAB's plotting functions (such as `plot()` or `stem()`) to display cepstrum results, with annotation of major peak points using `findpeaks()` function to facilitate analysis.

Application Extensions: In mechanical vibration analysis, cepstrum can separate sidebands in signals, helping identify fault frequencies in gears or bearings through peak detection algorithms. In speech processing, cepstrum is used for extracting formant characteristics of vocal tracts, serving as a crucial preprocessing step for speech recognition systems using MATLAB's signal processing toolbox.

By directly generating graphs through MATLAB, users can quickly observe peak distributions in cepstrum, facilitating signal feature extraction and fault diagnosis in practical engineering applications. The implementation typically involves spectral smoothing and windowing techniques to improve result accuracy.