MDCT analysis of sinusoids: Exact results and applications to coding artifacts reduction

Although widely used in many coding applications, the Modified Discrete Cosine Transform (MDCT) has the drawback of being sensitive to time shifts. With the popular choice a sine window, we show that it is possible to compute an explicit formulation of this time dependency. Starting from the exact MDCT of a pure sine and a simple interpretation in terms of combined modulations, we propose a regularization method that computes a "pseudo-spectrum" for the set of MDCT coefficients. This pseudo-spectum is shown to provide, at a low computational, cost, a good approximation of the local spectrum of the signal, with an improved behavior with respect to frequency and phase than the classical MDCT spectrum, ie. the absolute value of the coefficients. Amongst other applications, this procedure can be used to reduce some of the artifacts that appear in MDCT-based audio coders at low bit-rates.