Abstract
Currently, one of the main approaches used in analyzing properties and synthesis of signals in various classes is the subband methodology, which is carried out from the position of Fourier transform of signal samples (frequency representations) into subbands of the transform definition domain (transformants). In this case, the main tool, which is widely used for subband analysis (including wavelet analysis), is usage of bandpass filters (mainly those with finite impulse response or FIR filters). The present paper introduces the basics of building a theory forsubband analysis / signal synthesis for various classes, and using transformations based on any orthonormal basis with weight. This proposed approach is based on the concept of Euclidean signal norm square fraction in a given subband of the transformant definition domain. It is shown that the basis for mathematical apparatus of subband analysis is a new class of matrices, called subband ones. Some eigenvalue properties of these matrices are established, and the problem of optimal selection for additive signal components is formulated and solved
Highlights
As an important object of analysis and synthesis, you can specify speech signals that are recorded at the outputs of microphones under th e acoustic influence of oral speech [1,2,3,4,5,6,7]
Fundamentations of the generalized subband analysis and synthesistheorfor symbol F means the set in the general case of complex functions, F n(t), t (a,b);n 0,1,... , (5)
In this paper, the theoretical foundations of subband analysis are developed from the standpoint of dividing the transformation definitions domains of the initial sampled data into subbands, according to orthonormal bases
Summary
As an important object of analysis and synthesis, you can specify speech signals that are recorded at the outputs of microphones under th e acoustic influence of oral speech [1,2,3,4,5,6,7]. Their distinguishing feature is the non-stationarity due to alternation of speech sounds. Description of the signals properties from standpoint of splitting their transformations definitions domains into subregions, is a useful technique for analysis and synthesis of them.
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