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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