Fast Computation of Frequency Warping Transforms

被引：19
作者：
Caporale, Salvatore [1 ]
De Marchi, Luca [1 ]
Speciale, Nicolo [1 ]
机构：
[1] Univ Bologna, Dept Elect Comp Sci & Syst, I-40136 Bologna, Italy
来源：
IEEE TRANSACTIONS ON SIGNAL PROCESSING | 2010年 / 58卷 / 03期
关键词：
Fast transforms; frequency warping; FAST FOURIER-TRANSFORMS; REPRESENTATIONS;
D O I：
10.1109/TSP.2009.2034323
中图分类号：
TM [电工技术]; TN [电子技术、通信技术];
学科分类号：
0808 ; 0809 ;
摘要：
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.
引用
收藏
页码：1110 / 1121
页数：12
相关论文
共 15 条
[1]   UNITARY EQUIVALENCE - A NEW TWIST ON SIGNAL-PROCESSING [J].
BARANIUK, RG ;
JONES, DL .
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 1995, 43 (10) :2269-2282
[2]   Analytical computation of fast frequency warping [J].
Caporale, Salvatore ;
De Marchi, Luca ;
Speciale, Nicolo .
2008 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING, VOLS 1-12, 2008, :3793-3796
[3]   FRAME BOUNDS ESTIMATION OF FREQUENCY WARPING OPERATORS [J].
Caporale, Salvatore ;
De Marchi, Luca ;
Speciale, Nicolo .
2009 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, VOLS 1- 8, PROCEEDINGS, 2009, :3453-3456
[4]   FAST FOURIER-TRANSFORMS FOR NONEQUISPACED DATA [J].
DUTT, A ;
ROKHLIN, V .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1993, 14 (06) :1368-1393
[5]   Discrete frequency warped wavelets: Theory and applications [J].
Evangelista, G ;
Cavaliere, S .
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 1998, 46 (04) :874-885
[6]   Frequency estimation using warped discrete Fourier transform [J].
Franz, S ;
Mitra, SK ;
Doblinger, G .
SIGNAL PROCESSING, 2003, 83 (08) :1661-1671
[7]   The power classes - Quadratic time-frequency representations with scale covariance and dispersive time-shift covariance [J].
Hlawatsch, F ;
Papandreou-Suppappola, A ;
Boudreaux-Bartels, GF .
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 1999, 47 (11) :3067-3083
[8]  
LAINE U, 1990, P IEEE INT C AC SPEE, P1615
[9]   An accurate algorithm for nonuniform fast Fourier transforms (NUFFT's) [J].
Liu, QH ;
Nguyen, N .
IEEE MICROWAVE AND GUIDED WAVE LETTERS, 1998, 8 (01) :18-20
[10]   Warped discrete-Fourier transform: Theory and applications [J].
Makur, A ;
Mitra, SK .
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS, 2001, 48 (09) :1086-1093
12