Equivalence of Series Combs to TDLs

It is also straightforward to show that a series combination of feedforward comb filters produces a sparsely tapped delay line as well. Considering the case of two sections, we have

which yields

Thus, the TDL of Fig.2.19 is equivalent also to the series combination of two feedforward comb filters. Note that the same TDL structure results irrespective of the series ordering of the component comb filters.

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.