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International Journal of Digital Multimedia Broadcasting
Volume 2014, Article ID 529852, 10 pages
Research Article

Efficient Time-Frequency Localization of a Signal

Division of Computer Engineering, Netaji Subhas Institute of Technology, Sector-3, Dwarka, New Delhi 110 078, India

Received 12 February 2014; Revised 15 July 2014; Accepted 23 July 2014; Published 25 August 2014

Academic Editor: Ekram Khan

Copyright © 2014 Satish Chand. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new representation of the Fourier transform in terms of time and scale localization is discussed that uses a newly coined A-wavelet transform (Grigoryan 2005). The A-wavelet transform uses cosine- and sine-wavelet type functions, which employ, respectively, cosine and sine signals of length . For a given frequency , the cosine- and sine-wavelet type functions are evaluated at time points separated by on the time-axis. This is a two-parameter representation of a signal in terms of time and scale (frequency), and can find out frequency contents present in the signal at any time point using less computation. In this paper, we extend this work to provide further signal information in a better way and name it as -wavelet transform. In our proposed work, we use cosine and sine signals defined over the time intervals, each of length , , and are nonnegative integers, to develop cosine- and sine-type wavelets. Using smaller time intervals provides sharper frequency localization in the time-frequency plane as the frequency is inversely proportional to the time. It further reduces the computation for evaluating the Fourier transform at a given frequency. The A-wavelet transform can be derived as a special case of the -wavelet transform.