Fast computation of frequency warping transforms

  • Authors:

  • Salvatore Caporale;Luca De Marchi;Nicolò Speciale

  • Affiliations:

  • Department of Electronic Computer Sciences and Systems, University of Bologna, Bologna, Italy;Department of Electronic Computer Sciences and Systems, University of Bologna, Bologna, Italy;Department of Electronic Computer Sciences and Systems, University of Bologna, Bologna, Italy

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 2010

Quantified Score

Hi-index 35.68

Visualization

Abstract

In this paper, we introduce an analytical approach for the frequency warping transform. Criteria for the design of operators based on arbitrary warping maps are provided and an algorithm carrying out a fast computation is defined. Such operators can be used to shape the tiling of time-frequency (TF) plane in a flexible way. Moreover, they are designed to be inverted by the application of their adjoint operator. According to the proposed model, the frequency warping transform is computed by considering two additive operators: the first one represents its nonuniform Fourier transform approximation and the second one suppresses aliasing. The first operator is fast computable by various interpolation approaches. A factorization of the second operator is found for arbitrary shaped nonsmooth warping maps. By properly truncating the operators involved in the factorization, the computation turns out to be fast without compromising accuracy.