An orthogonal set of frequency and amplitude modulated (FAM) functions for variable resolution signal analysis

IEEE Trans. Signal Process.

2010

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.

Section: Discrete-time-discrete-frequency Case (Dtdf)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fast Computation of Frequency Warping Transforms

IEEE Trans. Signal Process.

2010

“…Frequency warping has been introduced some years ago [2] and then modeled as a projection on a set of frequency and amplitude modulated functions (FAM) [3]. The commonly adopted Laguerre transform approach to frequency warping allows a reduced set of mapping functions and is based on a recursive computationally expensive algorithm.…”

Section: Introductionmentioning

confidence: 99%

Analytical computation of fast frequency warping

2008 IEEE International Conference on Acoustics, Speech and Signal Processing

2008

In this work we introduce an analytical characterization of the frequency warping operator of arbitrary shaped non-smooth warping maps. The transformation matrix is decomposed in two additive terms: the first term represents its Nonuniform Fourier Transform approximation while the second term is imposed for aliasing suppression. The first transformation is known to be analytically characterized and fast computable by an interpolation approach. For the second transformation an analytical representation is introduced which allows a fast computation and a simple design. Finally, an example of a potential application is shown.

“…Each octave is frequency warped so that a linear segmentation by filter bank or wavelet packet in the warped domain is equivalent to an exponential segmentation, taking into account the mirroring effect. and amplitude modulated functions (FAM) [4] but a computational model has not been proposed. The commonly adopted Laguerre transform approach to frequency warping is based on a recursive computationally expensive algorithm and the only implementable maps are constituted by compositions between sigmoidal functions and its inverse multiplied by a scale parameter such as:…”

Section: Introductionmentioning

confidence: 99%

Fast operators for arbitrary warping maps

2008 IEEE International Symposium on Circuits and Systems (ISCAS)

2008

In this work we describe a mathematical operator for the fast calculation of frequency warping. Such invertible transformation can be used to reshape the tiling of timefrequency analysis in a flexible way. In our approach the warping is computed by splitting the transformation operator in two additive terms: the first term represents its Nonuniform Fourier Transform approximation while the second term is imposed for aliasing suppression. The first transformation is known to be analytically characterized and rapidly computable by interpolation approaches. An analytical characterization of the second transformation operator is proposed for arbitrary shaped non-smooth warping maps commonly used for signal processing applications.