What is cepstral analysis and what are its applications?

Cepstrum is the spectrum of the log spectrum: c[n] = IDFT(log(|DFT(x)|)). Separates convolved components (e.g., source and filter) that appear multiplicative in spectrum but additive in log domain. The 'quefrency' domain reveals periodicities in log spectrum. Applications: Speech analysis (vocal tract and excitation separation), MFCC extraction (mel-frequency cepstral coefficients for speech recognition), Pitch detection (cepstral peak at fundamental period), Echo detection (impulse in cepstrum at echo delay), and Deconvolution (homomorphic filtering). Real cepstrum (real part only) vs complex cepstrum (preserves phase) for different applications.