Application of Improved Sliding DFT Algorithm for Non-Integer k

Abstract

An algorithm and network is described in this paper that implements a sliding Discrete Fourier Transform, such that it outputs an estimate of the DFT value for every input sample. Regular DFT algorithms calculate a complex value that is proportional to the amplitude and phase of an equivalent sine wave at the selected analysis frequency. The analysis frequency that can be selected is typically an integer multiple of the frequency increment of the DFT algorithm, and this might not necessarily correspond to the desired analysis frequency. The sliding DFT algorithm proposed here overcomes this limitation, and permits the analysis frequency to be any value up to half the sampling frequency. The proposed sliding DFT algorithm is demonstrated by analysing a synthetic sine wave, and the exhaust noise from a V8 diesel engine.