Modern Methods Used in the Complex Analysis of the Phonocardiography Signal
Nicolae Marius, S. Gergely · InTech eBooks · 2012
Sometimes we need an accurate or approximate representation of a quantity in a different form; either the quantity is given by an analytical expression or by the finite set of values. Using transformations, we usually measure the similarity of a given function with an entire class of functions depending on one or more parameters (such as the frequency in the Fourier transform) which may change continuously or discretely. The wavelet representation is given in the spacefrequency domain, opposite to the Fourier analysis that gives only a frequency representation. Compact supports of wavelets provide a space, and their oscillatory nature provides a frequency representation of a transformed function. It is clear that such representation is essential for the non stationary signal. The wavelet representation of a function has the multiresolution property, which means that it is given on several resolution scales. Details defined on various refinement levels (fine meshes) are added to the rough approximation determined on a coarse mesh. The dimension of the data set that store information about the function is considerably decreased while the most important information is not lost. This is very important for a good compression that saves storage in a system memory. A data compression is fundamental for an efficient analyzing of a signal with an extremely high noise density and a large variety of shapes (Abbas K.Abbas & Rasha Bassam, 2009).