Design of Tight Minimum-Sidelobe Windows by Riemannian Newton's Method
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The short-time Fourier transform (STFT), or the discrete Gabor transform (DGT), has been extensively used in signal analysis and processing. Their properties are characterized by a window function, and hence window design is a significant topic up to date. For signal processing, designing a pair of analysis and synthesis windows is important because results of processing in the time-frequency domain are affected by both of them. A tight window is a special window that can perfectly reconstruct a signal by using it for both analysis and synthesis. It is known to make time-frequency-domain processing robust to error, and therefore designing a better tight window is desired. In this paper, we propose a method of designing tight windows that minimize the sidelobe energy. It is formulated as an optimization problem on an oblique manifold, and a Riemannian Newton algorithm on this manifold is derived to efficiently obtain a solution.
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