ALGORITHMS FOR MODELING FUNCTION AND MEDICAL SIGNALS IN WAVELET METHODS

Аннотация

Objective.This article is devoted to the construction of wavelet models, which are considered important in function processing, and the use of Taylor series as a method of approximating analytical functions. These models are built using Haar wavelets. It is important to reduce the number of coefficients required to approximate the total number of Binary segments (with a given accuracy) as a result of transformation of given signals using Haar wavelets in the form of a known function and analytical function. The process of calculating the coefficients using the Xarra wavelet is found without long operations. Only addition, scaling and transformation operations are used. Methods. Haar wavelet, Taylor series, conversion wavelet, digital processing error, relative error. Results.The obtained results show that it can be seen that the Haar wavelet gives higher accuracy compared to the Taylor series in the digital processing of the given signals in an analytical form. Conclusion. In the problems of image recognition from waves, in the processing and synthesis of various signals such as speech, in the analysis of various images in nature (the color of the retina, radiography of the kidney, studying the surface properties of crystals and nano-objects, satellite .images of clouds or planetary surfaces etc. can be used to study the properties of vortex fields and in other cases. Key words: Haar wavelet, Taylor series absolute error, relative error, scaling function Introduction. Currently, there are several types of wavelets. It is convenient to use uncomplicated methods to determine the coefficients of the function, one of the uncomplicated methods is the Haara wavelet, in which the coefficients of the function are determined without many operations only by 163 THEORETICAL ASPECTS IN THE FORMATION OF PEDAGOGICAL SCIENCES International scientific-online conference adding, subtracting and scaling. It can also be noted that the preference of the type of wavelets also depends on the analysis of the input looking function or signal, because the scaling function is interpreted differently depending on the wavelet types. In medicine, wavelets are widely used when studying various signals, radiography of the kidney, properties of the surface of crystals and nano-objects, when studying the properties of gastroenterological signals and in other cases, interpolation. The waveforms of the Haar wavelet extend along the time axis along with the signal graph. A Haar wavelet plot often approximates a signal as a one-way waveform across the signal, which is good for compressing some signals. Its mathematical interpretation allows analysis of wave states at different frequencies. The amplitude of the graph of the Haar-wavelet function decreases to zero, forming oscillating waves. Methods. Construction of a Haar wavelet. There are fast Haar wavelet transformation algorithms, and its orthogonal wavelets are widely used in solving practical problems. An orthogonal Haar wavelet is expressed as follows: Considered as a wavelet in Haar bases. Haar wavelets attract the attention of experts for two reasons: Reducing the number of coefficients required for approximation (with a given accuracy) compared to the total number of binary segments. Absence of "long" operations in the process of calculating coefficients. Only add, scale, and transform operations are used. In the digital processing of signals, wavelet functions are used to separate the details and local features of the signals, and scaling functions are used to approximate the signals. When choosing wavelet functions, special attention is paid to their characteristics, such as smoothness, carrier size, and the number of cases where their values are equal to zero. The process of wavelet transformation of signals relies on the use of two types of functions: a wavelet function and a scaling function, which means that they are the same wavelet 164 ( t )  - to shift in time across the signal b and time scale a is built by changing: a b ( t )  1 a a , ( a , b )  R , ( t )  L 2 ( R )    V 0 - that's all [ 0 ,1 ] we define a set of invariant functions on the interval, that is, a set of linear vectors. Then the following scaling function - belongs to the collection: THEORETICAL ASPECTS IN THE FORMATION OF PEDAGOGICAL SCIENCES International scientific-online conference 165 ( t )  0 ,0 ( t )   1 , 00 , ti f  1 (1) (1) i  0 zoom function when available. n , j ( t )  1 , 2 j n 0 , t i f j 2 n 1  , j  0 ,1 , . . . , 2 n  1 (2) (2) i  n zoom function when available, here, n j j 1 02 t  j 1, t  n n 2 2 is the interval of change of scaling functions, n , j ( t )  -lar V n are scaling functions related to , in which there is a set of vectors with scalar multiplication, so these sets form the Euclidean space. In our case as a scalar multiplication ( f , g )  1 0 f ( t ) g ( t ) d t (3) (3) we get the form using this formula C n - coefficients of scaling functions are defined.