On Frequency-Domain Implementation of Digital FIR Filters

This paper considers frequency-domain implementation of finite-length impulse response filters. In practical fixed-point arithmetic implementations, the overall system corresponds to a time-varying system which can be represented with either a multirate filter bank, and the corresponding distortion and aliasing functions, or a periodic time-varying impulse-response representation or, equivalently, a set of impulse responses and the corresponding frequency responses. The paper provides systematic derivations and analyses of these representations along with design examples. These representations are useful when analyzing the effect of coefficient quantizations as well as the use of shorter DFT lengths than theoretically required.