Abstract
The multiwindow discrete Gabor transform (M-DGT) is a useful time-frequency analysis tool for non-stationary signal processing. Given an arbitrary Gabor frame, a parallel lattice structure of block time-recursive algorithm for fast and efficient computation of dual/analysis Gabor windows for M-DGT is presented. By using a multiple window dual Gabor frame, the dual Gabor windows can be expressed by synthesis and analysis windows with a block-circulant matrix. Then, a parallel lattice structure of block time-recursive can be derived to solve the dual Gabor windows by the block-circulant matrix computed by the fast discrete Fourier transform (FFT). When compared to three existing methods, the proposed algorithm can reduce computational complexity and save computational time. Experimental results indicate that the proposed algorithm is valid to compute the dual windows of the M-DGT, which make the algorithm attractive for fast time-frequency signal analysis and processing.
Highlights
The Gabor transform (GT) [1] is a widely-utilized timefrequency analysis tool to represent, analyze, and process signal which can be constructed from a window function by translation in both time domain and frequency domain
In multiwindow Gabor analysis, solving the dual Gabor windows for a given multiwindow Gabor frame is an important issue in the multiwindow discrete Gabor transform (M-DGT)
Traditional methods to compute dual Gabor windows based on minimum 2 norm, require the inverse matrix computation of a frame operator with a high computational complexity especially if the matrix dimensions are high which could lead to numerical instability
Summary
The Gabor transform (GT) [1] is a widely-utilized timefrequency analysis tool to represent, analyze, and process signal which can be constructed from a window function by translation in both time domain and frequency domain. K. Kwan: Parallel Lattice Structure for Dual Windows Computation in Multiwindow GT structure of a block time-recursive method was presented in [37] to compute the dual/analysis window of the DGT for a constructed Gabor frame, but can only apply to a window function that can form a Gabor frame. An efficient algorithm for computing the Gabor dual windows of the M-DGT is proposed for a given multiwindow Gabor frame, in which the inversion of a Gabor frame matrix with block circulant characters can be computed by the FFT, followed by the design of the parallel lattice structure of the block time-recursive method for implementation.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
