Frequency Domain Data Transformation Using Linear Prediction
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Solution Overview
Problem
High-frequency measurement data transformation into the time domain often results in limited temporal and spatial resolution, making it difficult to accurately interpret and evaluate results, especially when the frequency bandwidth is maximized.
Innovation Solution
The method involves increasing the frequency range of measurement data using linear prediction, allowing for a low-pass transformation that assigns a value to frequency 0, thereby improving temporal resolution by extrapolating in the direction of lower frequencies for both harmonic and non-harmonic frequency grids.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional inverse Fourier transformation or inverse chirp-z transformation is used to transform measurement data from frequency domain to time domain, then the transformation can be performed, but the temporal and spatial resolution is limited and inversely proportional to the analyzed frequency bandwidth
Solution Approach 1:
The patent applies preliminary action by performing linear prediction extrapolation on the frequency domain measurement data before transforming to the time domain. This preprocessing step extends the effective frequency bandwidth by predicting additional frequency points beyond the originally measured range, thereby improving temporal resolution without requiring additional physical measurement bandwidth.
Solution Approach 2:
The patent changes the parameter of frequency bandwidth through linear prediction extrapolation. By mathematically extending the frequency spectrum beyond the measured range, the effective bandwidth parameter is increased, which directly improves the temporal resolution of the time-domain transformation according to the uncertainty principle.
2Measurement precision
If the frequency range is increased by extrapolation using bandpass transformation, then the frequency bandwidth is extended, but only the magnitude of the time domain response is supplied with poor temporal resolution
Solution Approach 1:
The patent replaces the bandpass transformation method with low-pass transformation. This substitution changes the transformation mechanism from bandpass (which preserves only magnitude) to low-pass (which preserves both magnitude and phase), thereby recovering complete time-domain response information including phase while maintaining the frequency extension benefits.
Solution Approach 2:
The patent changes the transformation type parameter from bandpass to low-pass. This parameter change enables the transformation to preserve both magnitude and phase information of the frequency domain data, resulting in complete time-domain response with improved temporal resolution rather than just magnitude with poor resolution.
Data Source
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AI summary
Transforming method involves the frequency range of the measuring data which is increased by extrapolation before the transformation. Transforming method involves the frequency range of the measuring data which is increased before the transformation by linear prediction. The frequency range of the measuring data is increased before the transformation by extrapolation to higher or lower frequencies.