This chapter discusses *frequency-response analysis* of digital
filters. The frequency response is a complex function which yields
the gain and phase-shift as a function of frequency. Useful variants
such as *phase delay* and *group delay* are defined, and
examples and applications are considered.

- Frequency Response
- Amplitude Response
- Phase Response
- Polar Form of the Frequency Response

- Frequency Response as a Ratio of DTFTs

- Phase and Group Delay
- Phase Delay
- Phase Unwrapping
- Group Delay
- Group Delay Examples in Matlab
- Vocoder Analysis
- Numerical Computation of Group Delay

- Frequency Response Analysis Problems

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