Preservation of whiteness in spectral and time-frequency transforms of second order processes Préservation de la blancheur dans les transformations spectrales et temps- fréquences de processus du second ordre

In many signal processing applications, recent techniques often rely on the estimation of a probabilistic model. Many times, this model does not focus on the observed data itself, but rather on a spectral or time-frequency transform of this data, such as the discrete Fourier transform (DFT) or the short-time Fourier transform (STFT). A common statistical assumption regarding these transforms is that all spectral or time-frequency bins are uncorrelated. However this assumption is generally inaccurate, either because of the intrinsic properties of the data, or because of the transform itself. In this document, we aim to design transforms from the time domain to the spectral or timefrequency domain, which best fit this statistical assumption. To formulate this idea, we introduce the concept of preservation of whiteness, and we characterise the transforms that satisfy this property. We show that several widely used transforms such as the discrete cosine transform (DCT), DFT, modified discrete cosine transform (MDCT), and STFT belong to this class under some conditions.