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 the inverse DFT to obtain the corresponding (finite) impulse response [207, pp. 105-23], [179, 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.

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.