Cepstrum

The cepstrum was introduced by Bogert, Healy, and Tukey in 1963, who playfully rearranged the letters of "spectrum" to name this new domain. The independent variable of the cepstrum is called "quefrency" (an anagram of "frequency") and has units of time. Peaks in the cepstrum at specific quefrency values indicate periodic components in the spectrum. In audio measurement, the cepstrum is powerful for detecting reflections. A single reflection creates a periodic ripple pattern (comb filtering) in the frequency response. This periodic structure appears as a clear peak in the cepstrum at a quefrency equal to the time delay of the reflection. By examining the cepstrum, you can identify the exact delay times of problematic reflections without manually searching through the impulse response. For speech analysis, the cepstrum separates the vocal tract response (formants) from the excitation (pitch). This is the foundation of MFCC (Mel-Frequency Cepstral Coefficients) used in speech recognition. In music, cepstral analysis can identify the fundamental pitch of a complex sound even when the fundamental is weak or absent. The cepstrum also assists in echo detection for room acoustics. Multiple reflections from parallel surfaces produce distinct cepstral peaks that reveal the geometry of the reflection pattern. This complements SonaVyx's impulse response analysis by providing an alternative view of room behavior. SonaVyx's RTA mode provides spectral analysis that forms the basis for cepstral computation, helping engineers identify periodic spectral patterns caused by comb filtering or room modes.