A new class of affine higher order time-frequency representations

Author

Murray, Robin L. ; Papandreou-Suppappola, Antonia ; Boudreaux-Bartels, G. Faye

Author_Institution

Dept. of Electr. & Comput. Eng., Rhode Island Univ., Kingston, RI, USA

Volume

3

fYear

1999

fDate

15-19 Mar 1999

Firstpage

1613

Abstract

We propose a new class of affine higher order time-frequency representations (HO-TFRs) unifying HO-TFRs which satisfy the desirable properties of scale covariance and time-shift covariance. This new class extends to higher order (N>2) the affine class of quadratic (N=2) time-frequency representations. In this paper, we provide five alternative formulations of the class in terms of multi-dimensional smoothing kernels. We discuss important class members, including the new higher order scalogram that is related to the wavelet transform. We also list additional desirable properties and derive the associated kernel constraints. Finally, we consider a subclass of affine HO-TFRs that intersects with a Cohen´s class of time and frequency shift covariant HO-TFRs. A formulation for HO-TFRs satisfying three covariances in this higher order affine-Cohen intersection is derived

Keywords

covariance analysis; higher order statistics; signal representation; time-frequency analysis; Cohen intersection; affine higher order time-frequency representations; higher order scalogram; kernel constraints; multi-dimensional smoothing kernels; quadratic time-frequency representations; scale covariance; signal representation; time-shift covariance; wavelet transform; Fractals; Kernel; Signal analysis; Signal representations; Smoothing methods; Spectrogram; Time frequency analysis; Wavelet analysis; Wavelet transforms; Wideband;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech, and Signal Processing, 1999. Proceedings., 1999 IEEE International Conference on

Conference_Location

Phoenix, AZ

ISSN

1520-6149

Print_ISBN

0-7803-5041-3

Type

conf

DOI

10.1109/ICASSP.1999.756297

Filename

756297