Two-dimensional Fourier Processing of Rasterised Audio

There is continuous research effort into the expansion and refinement of transform techniques for audio signal processing needs, yet the two-dimensional Fourier transform has seldom been applied to audio. This is probably because audio does not readily allow the application of a 2D transform, unlike images for which its use is common. A signal mapping is first required to obtain a two-dimensional representation. However the 2D Fourier transform opens up potential for new or improved analysis and transformation of audio. In this paper, raster scanning is used to provide a simple mapping between oneand two-dimensional representations. This allows initial experimentation with the 2D Fourier transform, in which the 2D spectrum can be observed. A straightforward method is used to display the spectral data as a colour image. The transform gives information on two frequency axes, one in the typical audible frequency range and the other in the low frequency rhythmic range. This representation can be used to more easily observe rhythmic modulations in the signal. Some novel audio transformations are presented, allowing manipulation of rhythmic frequency content. The techniques developed using the 2D Fourier transform allow interaction with audio in a new domain, both analytically and creatively. This work shows how two common signal processing mechanisms can be combined to exciting effect for audio applications.