Recursive sliding discrete Fourier transform with oversampled data

• Published in: Digital signal processing Vol. 25; pp. 275 - 279
• Main Authors: van der Byl, A., Inggs, M.R.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.02.2014
• Subjects: Blocking; Decomposition; Digital signal processing; Discrete Fourier transform; Fourier transforms; Recursive; Recursive discrete Fourier transform; Running Fourier transform; Sampling; Sliding discrete Fourier transform; Spectra; Spectral updating; Windows (intervals); Running Fourier transform; Spectral updating; Sliding discrete Fourier transform; Discrete Fourier transform; Recursive discrete Fourier transform
• ISSN: 1051-2004; 1095-4333
• DOI: 10.1016/j.dsp.2013.10.008

The Discrete Fourier Transform (DFT) has played a fundamental role for signal analysis. A common application is, for example, an FFT to compute a spectral decomposition, in a block by block fashion. However, using a recursive, discrete, Fourier transform technique enables sample-by-sample updating, which, in turn, allows for the computation of a fine time–frequency resolution. An existing spectral output is updated in a sample-by-sample fashion using a combination of the Fourier time shift property and the difference between the most recent input sample and outgoing sample when using a window of finite length. To maintain sampling-to-processing synchronisation, a sampling constraint is enforced on the front–end hardware, as the processing latency per input sample will determine the maximum sampling rate. This work takes the recursive approach one step further, and enables the processing of multiple samples acquired through oversampling, to update the spectral output. This work shows that it is possible to compute a fine-grained spectral decomposition while increasing usable signal bandwidths through higher sampling rates. Results show that processing overhead increases sub-linearly, with signal bandwidth improvement factors of up to 6.7× when processing 8 samples per iteration.