Results of a deterministic analysis of FFT coefficient errors

Abstract A novel, deterministic approach towards the analysis of coefficient errors in DFT and FFT was proposed, recently [9]. In this paper, its application is described: After a short introduction into the basic idea, the “modulation plus smoothing-filter” description of the transforms, the impulse responses, signal-flow graphs, and transfer functions for the erroneous low-pass filters are exposed which fully describe the coefficient error effects. General insights into the behaviours of the direct DFT as well as four FFT versions are provided. For the case of a fixed-point data and coefficient representation, detailed results are presented in a compact “necessary wordlength for prescribed criteria and output accuracy” form. Finally, some general conclusions are derived from these results.