- Since the feedforward coefficient's of the FIR filter are the same as
the non-zero elements of the impulse response, a general expression
for the FIR filter's output can also be given by
where is the impulse responses and replaces the coefficients
- When the relation between the input and the output of
the FIR filter is expressed in terms of the input and impulse
response, we say the the output is obtained by convolving the
sequences and .
- Note that this is circular or cyclic convolution.
To simulate acyclic convolution (as we do when simulating sampled
continuous-time systems), we need to zero-pad sufficiently () so
that non-zero samples do not ``wrap around'' as a resulting of
``Mus 270a: Introduction to Digital Filters''
by Tamara Smyth,
Department of Music, University of California, San Diego.
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Copyright © 2019-02-25 by Tamara Smyth.
Please email errata, comments, and suggestions to Tamara Smyth<firstname.lastname@example.org>