DFT spectrum estimation from critically sampled lapped transforms

Critically sampled perfect reconstruction lapped transforms (LT), apart from signal representation, are difficult to use for signal analysis and processing. We tackle this problem by establishing a novel connection between the LT and the DFT based on matrix analysis. Specifically, for the modified discrete cosine transform (MDCT) with an arbitrary symmetric window, one of the most widely used LT, a sparse matrix representation for the conversion to and from the DFT is developed, leading to an efficient implementation in the form of low-order frequency domain FIR filtering. We give two example applications, MDCT domain group delay estimation and aliasing reduction for the temporal noise shaping (TNS).