Subband DFT - Part II: Accuracy, complexity and applications

A new DFT computation method based on a subband decomposition described in a companion paper (Shentov et al., 1995) is investigated. The two distinct parts of the algorithm, a preprocessing Hadamard transform stage and a 'correction' stage, were interpreted as a filter-bank-plus-recombination network. This interpretation provides a better understanding of the errors caused by dropping subbands in the approximate partial-band DFT computation. In this paper we analyze the approximation errors and computational complexity of the new algorithm in partial-band DFT computation, in addition to outlining a number of its possible applications. Specifically, formulae for the approximation errors due to linear distortions and to aliasing are derived. Two new general formulae are found for the aliasing terms under different conditions; one of them gives an interesting matrix formulation for the coefficients describing the aliasing effects of all frequency bands separately. The computational complexity of the algorithm is analyzed both theoretically and in terms of running-time measurements. This concerns both the full- and partial-band analysis cases in various realization structures as introduced in Shentov et al. (1995). With these insights, the novel algorithm is compared to existing methods, especially for the computation of a limited number of frequency points. A number of application examples are included to illustrate the efficiency of the proposed method in computing approximately the DFT of signals with energies concentrated in small parts of the spectrum.