Polynomial, Neural Network, and Spline Wavelet Models for Continuous Wavelet Transform of Signals

Area of Science:

• Signal Processing
• Applied Mathematics
• Computer Science

Background:

• Continuous wavelet transform (CWT) is crucial for signal analysis.
• Existing wavelet synthesis methods may lack guaranteed approximation accuracy or formalized representation.
• Efficient implementation of CWT on digital hardware is essential.

Purpose of the Study:

• To propose a modified wavelet synthesis algorithm for CWT.
• To achieve guaranteed approximation of the maternal wavelet to the signal sample.
• To obtain a formalized representation of the wavelet for software implementation.

Main Methods:

• Utilizing splines and artificial neural networks (specifically radial basis function networks) for wavelet synthesis.
• Comparative analysis of polynomial, neural network, and wavelet spline models.
• Applying synthesized wavelets to inverse continuous wavelet transform.

Main Results:

• The proposed method guarantees accurate approximation of the maternal wavelet to the signal sample without approximation error.
• Achieved formalized representation of the wavelet, crucial for digital signal processors and microcontrollers.
• Demonstrated the feasibility of using synthesized wavelets (from polynomial, neural network, and spline models) for inverse CWT.

Conclusions:

• The modified wavelet synthesis algorithm effectively addresses limitations of existing methods.
• The integration of neural networks and splines offers a robust approach for CWT applications.
• This work facilitates efficient and accurate signal analysis and processing in digital environments.