Cepstrum Calculation with MATLAB Implementation

Based on the mathematical definition of cepstrum and MATLAB's computational capabilities, I conducted multiple implementations to develop various cepstrum calculation approaches. These methods required programming implementation since cepstrum computation involves Fourier transforms of input signals. Using MATLAB's programming environment, I created straightforward code that can be directly executed in MATLAB - typically involving FFT operations, logarithmic magnitude calculations, and inverse FFT applications to obtain the queFrency domain representation. Despite trying multiple methodologies, I initially found it challenging to identify target frequencies from the generated cepstral plots. This prompted me to reevaluate my approach and introduce several enhancements to the computation pipeline. First, I increased the number of sampling points in input signals to improve spectral resolution and calculation accuracy. Additionally, I implemented various digital filtering techniques (such as Wiener filtering and band-pass filters) to reduce noise interference in the signal processing chain. Finally, I incorporated advanced visualization tools including custom plot scaling and frequency annotation functions to better observe cepstral peaks and identify target frequency components. Through these modifications, I successfully identified the target frequencies, validating the effectiveness of the refined methodology. Although this process required more time and effort than initially anticipated, it provided deeper insights into cepstrum computation techniques and emphasized the importance of iterative refinement in scientific research. The implementation highlights key signal processing concepts including windowing functions, spectral smoothing, and peak detection algorithms crucial for effective cepstral analysis.