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An algebraic approach to discrete short-time Fourier transform analysis and synthesis

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2 Author(s)
Shpiro, Z. ; Technion-Israel Institute of Technology, Haifa, Israel ; Malah, D.

An algebraic representation of the discrete short-time Fourier transform (DSTFT) is presented for the case in which the analysis window length N equals the transform block size M . This representation allows the application of algebraic tools for determining an optimal synthesis system which minimizes the mean square error between a given modified DSTFT (which is not necessarily a valid DSTFT sequence) and the DSTFT of the synthesized signal. If no modification is applied, the result is a unity analysis-synthesis system for any given time update R of the sliding analysis window (provided that R\leq M ). It is shown that the optimal synthesis system can be implemented by the well known weighted overlap-add (WOLA) method using an optimal synthesis window. The algebraic approach enables the extension of some recent results and the relaxation of a constraint on the analysis window. The proposed approach is found also to have a potential for solving the synthesis problem for the more general case of N> M .

Published in:

Acoustics, Speech, and Signal Processing, IEEE International Conference on ICASSP '84.  (Volume:9 )

Date of Conference:

Mar 1984