Time-Signal Comparison Using Zero Crossings and Spectral Power
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Solution Overview
Problem
Existing methods for comparing time-domain signals, such as those based on zero crossings, are inadequate for accurately discriminating between signals with similar dominant frequencies and varying spectral powers, particularly when the spectral powers at these frequencies differ.
Innovation Solution
A method that iteratively calculates normalized zero crossings, differential signals, and spectral powers, followed by Fourier coefficients and a weighted comparison indicator, incorporating both frequency and spectral power components to enhance discrimination between signals.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Use of energy by moving object
If zero crossing methods are used for signal comparison, then computational cost is reduced, but discrimination performance between signals with similar frequencies and different spectral powers deteriorates
Solution Approach 1:
The patent segments the signal analysis into multiple iterative steps, each focusing on specific frequency ranges. The comparison indicator is divided into frequency component and power component, allowing separate optimization of computational efficiency and discrimination accuracy for different signal characteristics.
Solution Approach 2:
The patent transitions from analyzing only zero crossing counts (one-dimensional) to incorporating both frequency indices and spectral powers (two-dimensional analysis). This dimensional expansion enables differentiation of signals that have similar zero crossing patterns but differ in spectral power distribution.
2Measurement precision
If spectral analysis is performed to improve signal discrimination, then discrimination performance improves, but computational cost increases
Solution Approach 1:
The patent performs spectral analysis partially by calculating Fourier coefficients only at specific frequency indices derived from zero crossing information, rather than performing a complete spectral analysis across all frequencies. This partial action maintains discrimination performance while reducing computational burden.
Solution Approach 2:
The patent performs preliminary zero crossing analysis to identify dominant frequency indices before performing spectral power calculations. This preliminary action guides the subsequent spectral analysis to focus only on relevant frequency components, reducing overall computational cost.
3Measurement precision
If complete spectral analysis is performed for all frequencies, then signal discrimination accuracy improves, but processing time increases
Solution Approach 1:
The patent applies local quality by calculating spectral powers only at specific frequency indices that are locally relevant to each signal's characteristics, rather than uniformly across all frequencies. This localized approach reduces processing time while maintaining accuracy for the specific comparison task.
Solution Approach 2:
The patent performs partial spectral analysis at selected frequency indices rather than complete spectral analysis. This partial action is sufficient for discrimination purposes and significantly reduces the number of calculations required, thereby reducing processing time.
Data Source
Figure 1
Figure 2A~2B
Figure 2C
AI summary
A method for comparing a first time-domain signal (x) and a second time-domain signal (y), involving determining the number of zero crossings for each signal, and optionally, the differential signals formed for each signal. From each number of zero crossings, frequency indices are determined, as well as spectral powers corresponding to each frequency index. A comparison index is then constructed, based on a comparison of each normalized number of zero crossings and each spectral power.