Equivalence of Parallel Combs to TDLs

It is easy to show that the TDL of Fig.1.13 is equivalent to a parallel combination of three feedforward comb filters, each as in Fig.1.17. To see this, we simply add the three comb-filter transfer functions of Eq.(1.3) and equate coefficients:

which implies

We see that parallel comb filters require more delay memory ( elements) than the corresponding TDL, which only requires elements.

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written by 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.