Re: Cepstrum computation ("Richard F. Lyon" )

Subject: Re: Cepstrum computation
From:    "Richard F. Lyon"  <dicklyon(at)ACM.ORG>
Date:    Mon, 21 Jun 1999 15:28:13 -0700

Argaris and Jont opined: >> Incredible. I couldn't imagine that the "quick & dirty" way >> ie log(x+epsilon) was the proper way to compute the cepstrum. > >You cannot compute the cepstrum of a signal that has no DC term, as >that would be a zero at f=0, or of a narrow band signal. Actually, for any real signals and any real filters, the power spectral density as seen through any channel of the analysis filters will be somewhat nonzero, in which case the probability of any power coefficient in any frame of the analysis being exactly equal to zero is identically zero. Even true if you use an AC-coupling or DC-cut filter. So if you use floats, a zero will 'never' occur, and 'when it does' you can whack it down with negligible consequence. If you're using fixed point, you'll often quantize right into the singularity, so you'll need to be more careful. If you have no DC (or otherwise bandlimited signals--which are not theoretically possible in 'real-valued' signals), then add some, since it doesn't matter how much. It just puts your cepstrum into a different place, and doesn't affect cepstral differences, which is all you should care about. But there's really no 'proper' way to compute a thing that's always operating on the edge of a singularity like that. So go with a quick & dirty way or find your own way... Dick

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