**Definition: **The

*frequency response* of an

LTI filter may be defined
as the

Fourier transform of its

impulse response. In particular, for
finite, discrete-time

signals
, the sampled frequency
response may be defined as

The complete (continuous) frequency response is defined using the

DTFT (see
§

B.1),

*i.e.*,

where the summation limits are truncated to

because

is zero for

and

. Thus, the DTFT can be obtained from
the

DFT by simply replacing

by

, which corresponds
to infinite

zero-padding in the time domain. Recall from
§

7.2.10 that zero-padding in the time domain gives
ideal interpolation of the

frequency-domain samples

(assuming the original DFT included all nonzero samples of

).

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