Copyright © 2022-02-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University
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.