Title :
A discrete-time wavelet transform based on a continuous dilation framework
Author :
Zhao, Wei ; Rao, Raghuveer M.
Author_Institution :
Dept. of Electr. Eng., Rochester Inst. of Technol., NY, USA
Abstract :
We present a new form of wavelet transform. Unlike the continuous wavelet transform (CWT) or discrete wavelet transform (DWT), the mother wavelet is chosen to be a discrete-time signal and wavelet coefficients are computed by correlating a given discrete-time signal with continuous dilations of the mother wavelet. The results developed are based on the definition of a discrete-time scaling (dilation) operator through a mapping between the discrete and continuous frequencies. The forward and inverse wavelet transforms are formulated. The admissibility condition is derived, and examples of discrete-time wavelet construction are provided. The new form of wavelet transform is naturally suited for discrete-time signals and provides analysis and synthesis of such signals over a continuous range of scaling factors
Keywords :
correlation methods; discrete wavelet transforms; inverse problems; signal processing; signal synthesis; admissibility condition; continuous dilation; continuous frequencies; correlation; dilation operator; discrete frequencies; discrete-time scaling; discrete-time signal; discrete-time signals; discrete-time wavelet transform; forward wavelet transform; frequencies mapping; inverse wavelet transform; mother wavelet; scaling factors; signal analysis; signal synthesis; wavelet coefficients; Continuous wavelet transforms; Discrete Fourier transforms; Discrete transforms; Discrete wavelet transforms; Fourier transforms; Frequency domain analysis; Signal analysis; Signal synthesis; Wavelet analysis; Wavelet coefficients;
Conference_Titel :
Acoustics, Speech, and Signal Processing, 1999. Proceedings., 1999 IEEE International Conference on
Conference_Location :
Phoenix, AZ
Print_ISBN :
0-7803-5041-3
DOI :
10.1109/ICASSP.1999.756193
