Theme: calculation of spectral coefficients of signals using the machine learning method based on xaar bases

Theme: CALCULATION OF SPECTRAL COEFFICIENTS OF SIGNALS USING THE MACHINE LEARNING METHOD BASED ON XAAR BASES.

Presenter: Nurmurodov Javohir

• Xaar base. The Haar base is widely used in various fields of technology and science to solve a large class of theoretical and practical problems. Haar has piece- invariant, piece-linear and piece-quadratic bases. It is distinguished by a number of excellent properties of the bases functions and the presence of spectral analysis calculation algorithms for them.
• The normalized Haar bases function is considered a multivalued function, and it is more convenient to perform calculations using three values (-1, 0, and 1) for spectral processing. These bases are given analytically by the following expression and are constructed based on the binary number system in the interval [0, 1] or [0,1)

CONSTRUCTION OF HAAR BASES

k - where the Xaar function is the ordinal number.

p while 1 is equal to the value.
N - is the number of incoming values.
j=0,1,……, 2p-1 repeated to the power of two.
If the spectral coefficients are calculated based on the piece-quadratic bases using the above formula, the following expression is obtained.
Haar bases presented as a result of the research. For this, we calculate the spectral coefficients by taking the actual values of the functions and determine the compression coefficients.[1]
Кс=N/(N-N1)
The number of N - function calculations is N1- the number of zero coefficients obtained as a result of quick changes in Xaar bases.
RESULTS FROM THE HAAR-ANDREWS METHOD OF CALCULATING SPECTRAL COEFFICIENTS USING HAARS PIECE-INVARIANT BASES.

Function

piece - invariant

piece - linear