Frequency Warping Biorthogonal Frames

• Published in: IEEE transactions on signal processing Vol. 59; no. 6; pp. 2575 - 2584
• Main Authors: Caporale, S, De Marchi, L, Speciale, N
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-06-2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Biological system modeling; Biorthogonal transforms; Computational modeling; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Facsimile; Factorization; fast transforms; Frames; frequency warping; Information, signal and communications theory; Mathematical analysis; Mathematical model; Mathematical models; Operators; perfect reconstruction; Reconstruction; Signal and communications theory; Signal, noise; Studies; Telecommunications and information theory; Time frequency analysis; Transforms; Warpage; Warping; Zinc; Warping; Redundancy; Biorthogonal transforms; perfect reconstruction; Factorization; Implementation; Orthogonal transformation; Accuracy; frequency warping; Signal processing; Infinite dimension; Mathematical model; fast transforms
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2011.2114658

Frequency warping is theoretically designed to be a unitary operator of infinite input and output dimensions, thus performing the resolution of identity. In real implementations finite dimensions have to be considered, then perfect reconstruction cannot be fulfilled. The accuracy of reconstruction is particularly compromised in case of non-smooth warping maps, which are more useful for practical applications. In order to overcome this limitation, a new frequency warping biorthogonal frame operator for non-smooth warping maps is introduced in this work. The proposed transformation is based on a mathematical model which has been previously introduced for computational purposes. By adding some redundancy with respect to the truncation of the infinite dimensions operator, the effect of an infinite output dimension can be taken into account in a compressed way, based on an analytical factorization. In the reconstruction process, the additional redundant samples are expanded, thus guaranteeing near perfect reconstruction.