Cepstrum Analysis for Signal Frequency Extraction

In this article, we will conduct an in-depth exploration of signal multiplication methods to effectively extract signal frequency information. Frequency extraction represents a crucial task in signal processing, as it enables better understanding of signal characteristics and properties. By employing the multiplicative combination of two signals, we can achieve more accurate frequency information retrieval and enhance practical applications. The cepstral analysis approach involves taking the inverse Fourier transform of the logarithm of the signal's Fourier transform, which effectively separates source and filter components in signals. This technique is particularly valuable in speech processing and vibration analysis where we need to separate excitation sources from system resonances. Python implementation typically involves using FFT (Fast Fourier Transform) from libraries like NumPy or SciPy, followed by logarithmic transformation and inverse FFT operations. Key functions include numpy.fft.fft() for forward transformation, numpy.log() for spectral smoothing, and numpy.fft.ifft() for cepstrum calculation. We hope this article provides valuable insights and practical assistance for your signal processing endeavors.