Series and Parallel Transfer Functions

The transfer function conveniently captures the algebraic structure of a filtering operation with respect to series or parallel combination. Specifically, we have the following cases:

1. Transfer functions of filters in series multiply together.
2. Transfer functions of filters in parallel sum together.

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Subsections

• Series Case
• Parallel Case
  • Series Combination is Commutative

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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.