Elementary Filter Sections

This section gives condensed analysis summaries of the four most
elementary digital filters: the one-zero, one-pole, two-pole, and
two-zero filters. Despite their relative simplicity, they are quite
valuable to master in practice. In particular, recall from
Chapter 9 that every causal, finite-order, LTI filter (any
difference equation of the form
Eq.
(5.1)) may be factored into a *series and/or parallel
combination*of such sections. Implementing high-order filters as parallel and/or
series combinations of low-order sections offers several advantages,
such as numerical robustness and easier/safer control in real time.

- One-Zero
- One-Pole
- Two-Pole

- Two-Zero
- Complex Resonator

- The BiQuad Section
- Biquad Software Implementations

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University