A frequency measurement algorithm for non-stationary signals by using wavelet transform.

Area of Science:

• Signal Processing
• Wavelet Theory
• Time-Frequency Analysis

Background:

• Scalograms are commonly used for measuring instantaneous frequencies, but their properties are primarily understood for stationary signals.
• Existing methods struggle with accurate frequency analysis of non-stationary signals.

Purpose of the Study:

• To analytically derive a fundamental property of the scalogram for non-stationary signals.
• To propose a novel frequency measurement algorithm based on this derived property.
• To develop a wavelet transform-based filter for distinguishing signals with similar frequencies.

Main Methods:

• Analytical derivation of scalogram properties for non-stationary signals.
• Development of a new algorithm for instantaneous frequency measurement.
• Application of wavelet transform to design a signal separation filter.

Main Results:

• An intrinsic property of the scalogram for non-stationary signals has been analytically established.
• A new, effective algorithm for measuring instantaneous frequencies in complex signals is proposed.
• A novel filter capable of separating signals with closely related frequencies was successfully developed.

Conclusions:

• The derived scalogram property provides a theoretical foundation for analyzing non-stationary signals.
• The proposed algorithm enhances the accuracy of frequency measurement in dynamic systems.
• The developed wavelet-based filter offers improved resolution for signal discrimination.