Giant FFTs for Sample-Rate Conversion

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Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2023-03
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Language
en
Pages
12
88-99
Series
AES: Journal of the Audio Engineering Society, Volume 71, issue 3
Abstract
The audio industry uses several sample rates interchangeably, and high-quality sample-rate conversion is crucial. This paper describes a frequency-domain sample-rate conversion method that employs a single large (“giant”) fast Fourier transform (FFT). Large FFTs, corresponding to the duration of a track or full-length album, are now extremely fast, with execution times on the order of a few seconds on standard commercially available hardware. The method first transforms the signal into the frequency domain, possibly using zero-padding. The key part of the technique modifies the length of the spectral buffer to change the ratio of the audio content to the Nyquist limit. For up-sampling, an appropriate number of zeros is inserted between the positive and negative frequencies. In down-sampling, the spectrum is truncated. Finally, the inverse FFT synthesizes a time-domain signal at the new sample rate. The proposed method does not result in surviving folded spectral images, which occur in some instances with time-domain methods. However, it causes ringing at the Nyquist limit, which can be suppressed by tapering the spectrum and by low-pass filtering. The proposed sample-rate conversion method is targeted to offline audio applications in which sound files need to be converted between sample rates at high quality.
Description
Funding Information: The main part of this work was conducted during a research visit of the second author to the Aalto Acoustics Lab between May 30 and June 13, 2022. This research belongs to the activities of the Nordic Sound and Music Computing Network—NordicSMC (NordForsk project no. 86892). For the purpose of open access, the second author has applied a creative commons attribution (CC BY) license to any author-accepted manuscript version arising. The authors would like to thank the Associate Technical Editor for noticing the surprising mismatch between the numerical precisions of the FFT spectrum and the time-domain signal reconstructed using the IFFT. Special thanks go to the anonymous reviewer who suggested testing the method by converting a signal to another sample rate and back. Publisher Copyright: © 2023 Authors. All rights reserved.
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Citation
Välimäki , V & Bilbao , S 2023 , ' Giant FFTs for Sample-Rate Conversion ' , AES: Journal of the Audio Engineering Society , vol. 71 , no. 3 , pp. 88-99 . https://doi.org/10.17743/jaes.2022.0061