Calculation of radix-2 discrete multiresolution Fourier transform

Authors:
X. Wen;M. Sandler
Affiliations:
Centre for Digital Music, Queen Mary, University of London, Electronic Engineering, London E1 4NS, UK;Centre for Digital Music, Queen Mary, University of London, Electronic Engineering, London E1 4NS, UK
Venue:
Signal Processing
Year:
2007

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Abstract

This article discusses the efficient calculation of radix-2 multiresolution Fourier transform (MFT), which can also be regarded as a collection of short-time Fourier transforms (STFTs) with multiple 2-based window sizes, calculated on the same discrete-time signal. We show that by reconfiguring the (decimation-in-frequency)-fast Fourier transform (DIF-FFT) framework to adopt different internal calculations, we are able to save nearly 50% of the calculation compared with a direct DIF-FFT method. Practical issues on real signals, sliding windows and cosine-family windowing are also discussed.