Implementation Structures for Recursive Digital Filters

This chapter introduces the four direct-form filter implementations,
and discusses implementation of filters as parallel or series
combinations of smaller filter sections. A careful study of filter
forms can be important when *numerical issues* arise, such as
when implementing a digital filter in a *fixed-point* processor.
(The least expensive ``DSP chips'' use fixed-point numerical
processing, sometimes with only a 16-bit word length in low-cost
audio applications.) For
implementations in floating-point arithmetic, especially at 32-bit
word-lengths or greater, the choice of filter implementation structure
is usually not critical. In matlab software, for example, one rarely
uses anything but the `filter` function, which is implemented
in double-precision floating point (typically 64 bits at the time of
this writing, and more bits internally in the floating-point unit).

- The Four Direct Forms

- Series and Parallel Filter Sections
- Series Second-Order Sections
- Parallel First and/or Second-Order Sections
- Formant Filtering Example
- Butterworth Lowpass Filter Example
- Summary of Series/Parallel Filter Sections

- Pole-Zero Analysis Problems

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