Elementary Theory of Wavelets and Filter Bank

Many of us are interested in detecting the irregularity in very small region of a transient signal which cannot be detected by necked eyes. That can be possible by discretizing the region in which the irregularity lie. There are two ways to discretize the signal. In theory one can use Fourier transform on the signal and cut in M-pieces. Where as in practice discretization can be obtained by applying multiple number of filters (Filter Bank).This paper will give knowledge of wavelets and filter banks and later on connection between them. These are rapidly developing topics in real time. The technique of filter banks (for discrete signals) and wavelets (to represent functions) are used throughout signal and image processing for compression, denoising, enhancement, motion estimation and pattern recognition. New wavelets continue to be constructed for new applications. To understand this process we need to have a brief knowledge about the basic concepts like Fourier Transform, Short-Time Fourier Transform, Wavelet Transform, MRA, Filter and Filter bank Pinal Choksi"Elementary Theory of Wavelets and Filter Bank" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-4 , June 2018, URL: http://www.ijtsrd.com/papers/ijtsrd12997.pdf http://www.ijtsrd.com/mathemetics/applied-mathematics/12997/elementary-theory-of-wavelets-and-filter-bank/pinal-choksi