Implementation and evaluation of the Vandermonde transform

Tom Bäckström, Johannes Fischer, Daniel Boley

Abstract: The Vandermonde transform was recently presented as a time-frequency transform which, in difference to the discrete Fourier transform, also decorrelates the signal. Although the approximate or asymptotic decorrelation provided by Fourier is sufficient in many cases, its performance is inadequate in applications which employ short windows. The Vandermonde transform will therefore be useful in speech and audio processing applications, which have to use short analysis windows because the input signal varies rapidly over time. Such applications are often used on mobile devices with limited computational capacity, whereby efficient computations are of paramount importance. Implementation of the Vandermonde transform has, however, turned out to be a considerable effort: it requires advanced numerical tools whose performance is optimized for complexity and accuracy. This contribution provides a baseline solution to this task including a performance evaluation.