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## Digital Filter Theory Summary

This section summarizes digital filter theory in a rather terse fashion suitable for review study.

linearity,time-invarianceand four basic representations of digital filters are defined: thedifference equation coefficients,impulse response, transfer function,andfrequency response. Next the concepts ofphase delayandgroup delayare defined. This material is a subset of that in [1].

Definition.A realsignalis defined as any real-valued function of the integers. Similarly a complex signal is any complex-valued function of the integers.

Definition.A realfilteris defined as any real-valued functional of a signal for each integer . We express the input-output relation of the filter by

where is the entire input signal, and is the output at time .

Subsections