From the *convolution representation*, Eq.(5.5), we have that the output
from a linear
time-invariant filter with input
and impulse response
is given
by the *convolution* of
and
, *i.e.*,

where `` '' means convolution as before. Taking the

where H(z) is the

This shows that, as a direct result of the convolution theorem, the

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