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 timedomain 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.