Cepstrumbased

Cepstrumbased refers to methods that operate in the cepstrum domain to analyze, modify, or interpret signals. The cepstrum is obtained by taking the inverse Fourier transform of the log magnitude spectrum of a signal, yielding a function of quefrency, a time-like coordinate that exposes periodicities and spectral structures separately from the spectral envelope. This separation enables common signal-processing tasks such as deconvolution, pitch estimation, and source-filter separation.

Computationally, a cepstrum is formed by transforming a windowed segment of a signal: X(f) is its Fourier transform, A(f) is the magnitude |X(f)| or power |X(f)|^2, then c(n) = F^{-1}{log A(f)}. The resulting cepstral coefficients contain information about periodicities (high-quefrency components) and spectral shape (low-quefrency components). Liftering—applying a window in the cepstral domain to keep or discard certain quefrency bands—allows isolation of these aspects. For example, high-quefrency components emphasize periodic structures such as pitch, while low-quefrency components capture the spectral envelope.

Applications are diverse. In speech processing, cepstrum-based methods are used for pitch detection, formant analysis, speaker recognition, and source–filter deconvolution to separate vocal-tract shape from glottal excitation. In audio and music, cepstral techniques assist onset detection and tempo estimation. In seismology and radar, cepstrum analysis helps identify reflectors and deconvolve system responses. Cepstrum variants include real cepstrum, power cepstrum, and complex cepstrum, each with specific properties for different signal types. While robust to certain spectral variations, cepstrumbased methods assume some stationarity over analysis windows and can be sensitive to noise.