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In this paper, new insights in frequency-domain implementations of digitalfinite-length impulse response filtering (linear convolution) using overlap-addand overlap-save techniques are provided. It is shown that, in practicalfinite-wordlength implementations, the overall system corresponds to atime-varying system that can be represented in essentially two different ways.One way is to represent the system with a distortion function and aliasingfunctions, which in this paper is derived from multirate filter bankrepresentations. The other way is to use a periodically time-varyingimpulse-response representation or, equivalently, a set of time-invariantimpulse responses and the corresponding frequency responses. The paper providessystematic derivations and analyses of these representations along with filterimpulse response properties and design examples. The representations areparticularly useful when analyzing the effect of coefficient quantizations aswell as the use of shorter DFT lengths than theoretically required. Acomprehensive computational-complexity analysis is also provided, and accurateformulas for estimating the optimal DFT lengths for given filter lengths arederived. Using optimal DFT lengths, it is shown that the frequency-domainimplementations have lower computational complexities (multiplication rates)than the corresponding time-domain implementations for filter lengths that areshorter than those reported earlier in the literature. In particular, forgeneral (unsymmetric) filters, the frequency-domain implementations are shownto be more efficient for all filter lengths. This opens up for newconsiderations when comparing complexities of different filter implementations.

On Frequency-Domain Implementation of Digital FIR Filters Using Overlap-Add and Overlap-Save Techniques