##
Frequency Sampling Method for

FIR Filter Design

The *frequency-sampling* method for FIR filter design is perhaps
the simplest and most direct technique imaginable when a desired
frequency response has been specified. It consists simply of
uniformly *sampling* the desired frequency response, and
performing an inverse DFT to obtain the corresponding (finite)
impulse response [224, pp. 105-23],
[198, pp. 251-55]. The results are not optimal,
however, because the response generally deviates from what is desired
*between* the samples. When the desired frequency-response is
*undersampled*, which is typical, the resulting impulse response
will be *time aliased* to some extent. It is important to
evaluate the final impulse response via a simulated DTFT (FFT with
lots of zero padding), comparing to the originally desired frequency
response.

The frequency-sampling method for FIR filter design is illustrated in §4.6.2 below in the context of the window method for FIR filter design, to which we now turn.

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Window Method for FIR Filter Design

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Optimal (but poor if unweighted) Least-Squares Impulse Response Design