Waveform Deconvolution Using Windowed FFTs for Precision Measurement
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Solution Overview
Problem
Existing methods face challenges in accurately measuring and separating sound sources within complex compound waveforms, particularly when signals from different sources overlap in time and frequency, or exhibit rapid changes in amplitude and frequency, leading to difficulties in representing frequency and amplitude changes effectively.
Innovation Solution
The method involves constructing Precision Measuring Matrices (PMMs) using time deconvolution of Fast Fourier Transforms (FFTs) and specific windowing functions, which facilitates improved time deconvolution and reduces artifacts, allowing for the identification and separation of sound sources by marking correlated maxima in the matrices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a large dimension DFT is used to achieve higher frequency resolution, then frequency resolution is improved, but time resolution deteriorates due to larger time window inspection
Solution Approach 1:
The patent segments the compound waveform into multiple individual waveforms through deconvolution processing. By dividing the mixed signal into separate components, each component can be analyzed with appropriate DFT dimensions for its specific time-frequency characteristics, resolving the tradeoff between time and frequency resolution.
Solution Approach 2:
The patent employs dynamic adjustment of DFT dimensions based on the specific characteristics of each separated waveform. Rather than using a fixed large dimension DFT for all signals, the system adapts the transform dimension to match the time-frequency resolution requirements of individual waveforms, optimizing both time and frequency measurement precision.
2Ease of manufacture
If traditional DFT methods are used for compound waveforms, then computational simplicity is maintained, but measurement accuracy deteriorates when signals overlap in time and frequency
Solution Approach 1:
The patent performs preliminary deconvolution processing to separate the compound waveform into individual waveforms before applying DFT analysis. This preliminary separation action enables subsequent frequency analysis to be performed on distinct, non-overlapping signals, maintaining measurement accuracy while preserving computational efficiency through the use of standard DFT methods on simplified individual signals.
3Adaptability or versatility
If deconvolution is performed on compound waveforms to separate sound sources, then waveform separation capability is improved, but computational complexity and instability increase
Solution Approach 1:
The patent modifies the deconvolution process by applying windowing functions to the frequency domain representations before performing the deconvolution operation. This parameter change in the processing method stabilizes the deconvolution results and reduces computational complexity by transforming the problem into a more manageable form, while still achieving effective waveform separation.
Data Source
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AI summary
The invention consists of new ways of constructing a Measuring Matrices (MMs) including time deconvolution of Digital Fourier Transforms DFTs. Also, windowing functions specifically designed to facilitate time deconvolution may be used, and/or the DFTs may be performed in specific non-periodic ways to reduce artifacts and further facilitate deconvolution. These deconvolved DFTs may be used alone or correlated with other DFTs to produce a MM.