Precision Measuring Matrix for Waveform Analysis
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Solution Overview
Problem
Existing methods for analyzing compound waveforms struggle with accurately measuring and separating sound sources when signals from different sources overlap in time and frequency, and exhibit trade-offs between time and frequency resolution, leading to challenges in representing dynamic changes in waveforms.
Innovation Solution
A machine-implemented method using multiple measuring matrices of varying sizes, generated through repeated transformations of the input signal, to identify and link correlated maxima, creating a Precision Measuring Matrix (PMM) that enhances both time and frequency resolution by correlating maxima across matrices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a large dimension DFT is used, then frequency resolution is improved, but time resolution deteriorates
Solution Approach 1:
The patent divides the frequency analysis into multiple segments by using different DFT dimensions. Instead of using a single large DFT, the method segments the frequency range and processes different frequency bands with appropriately sized DFTs, allowing simultaneous achievement of good frequency resolution in specific bands and good time resolution in others.
Solution Approach 2:
The patent introduces an additional dimension to the analysis by creating a three-dimensional time-frequency-energy representation. This involves computing multiple DFTs of different dimensions and combining them in a way that adds a new dimension of information, resolving the traditional two-dimensional trade-off between time and frequency resolution.
2Loss of time
If a small dimension DFT is used, then time resolution is improved, but frequency resolution deteriorates
Solution Approach 1:
The patent segments the frequency spectrum and applies different DFT dimensions to different segments. Small dimension DFTs are used for frequency bands requiring good time resolution, while large dimension DFTs are used for bands requiring good frequency resolution, eliminating the need to choose a single suboptimal dimension.
Solution Approach 2:
The patent applies local quality by making the DFT dimension adaptive to local requirements in the frequency spectrum. Different portions of the spectrum receive different levels of frequency resolution based on their specific characteristics, rather than applying a uniform resolution across the entire spectrum.
3Loss of information
If multiple FT data are combined using spectral correlation, then measurement completeness is improved, but information smearing occurs
Solution Approach 1:
The patent performs preliminary correlation of maxima before combining FT data. By identifying and correlating maxima across multiple DFT results in advance, the method ensures that only consistent, non-smeared information is combined, preventing the information smearing that occurs in traditional spectral correlation methods.
Solution Approach 2:
The patent uses feedback by iteratively refining the combination of multiple FT data based on the correlation of maxima. The process continuously adjusts the weighting and combination of different DFT results based on how well their maxima correlate, ensuring high accuracy while maintaining completeness.
Data Source
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Figure 3A~3E
AI summary
A machine-implemented method for computerized digital signal processing, comprising: obtaining a digital signal from data storage or from conversion of an analog signal; and determining, from the digital signal, measuring matrices. Each measuring matrix has a plurality of cells, each cell having an amplitude corresponding to the signal energy in a frequency bin for a time slice. Cells in each measuring matrix having maximum amplitudes along a time slice and/or frequency bin are identified as maximum cells. Maxima that coincide in time and frequency are identified and a correlated maxima matrix, called a "Precision Measuring Matrix" is constructed showing the coinciding maxima and the adjacent marked maxima are linked into partial chains. If only one MM is constructed, multiple types of maxima are identified to generate the Precision Measuring Matrix.