Efficient Time-Frequency Localization of a Signal. (25th August 2014) - Chand, Satish
Abstract : 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 length2 π . For a given frequencyω, the cosine- and sine-wavelet type functions are evaluated at time points separated by2 π / ω 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 asA * -wavelet transform. In our proposed work, we use cosine and sine signals defined over the time intervals, each of length2 π m / ( 2 n ω ), m ≤ 2 n, m andn 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 theA * -wavelet transform.