Giant FFTs for Sample-Rate Conversion

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.