Time-Frequency Matrix Extension for Signal Resolution
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Solution Overview
Problem
Conventional frequency transforms, such as FFT, face limitations in providing simultaneous high resolution in both the frequency and time domains due to the Heisenberg uncertainty principle, which restricts their ability to accurately analyze localized signals like transients, as they either sacrifice time resolution for frequency resolution or vice versa.
Innovation Solution
The method introduces a time-frequency matrix extension after frequency transformation, applying cross-frequency phase coupling to synchronize adjacent frequency bins, allowing for sample-accurate analysis and editing by revealing structural information hidden in conventional frequency transforms, thereby overcoming the uncertainty principle's limitations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the number of time domain measurements is increased to improve frequency resolution, then frequency resolution is improved, but time resolution deteriorates
Solution Approach 1:
The patent transitions from conventional 1D frequency analysis to a 2D time-frequency matrix representation. By creating a matrix where rows represent time samples and columns represent frequency bins, the system adds a temporal dimension to the frequency domain analysis. This dimensional expansion allows simultaneous access to both time and frequency information, resolving the Heisenberg uncertainty principle limitation that prevents simultaneous high resolution in both domains.
Solution Approach 2:
The patent segments the frequency domain representation by creating individual frequency representations for each time sample rather than averaging across the entire analysis interval. Each row in the time-frequency matrix contains the frequency content at a specific time instant, effectively segmenting the conventional frequency spectrum into time-localized frequency components. This segmentation enables precise identification of transient features while maintaining high frequency resolution.
2Loss of time
If the number of time domain measurements is decreased to improve time resolution, then time resolution is improved, but frequency resolution deteriorates
Solution Approach 1:
By constructing a time-frequency matrix with full temporal resolution (one row per time sample), the system maintains high time resolution without sacrificing frequency resolution. The matrix structure preserves all frequency information for each time instant, eliminating the need to reduce the number of time domain measurements for improved time resolution.
3Loss of information
If conventional frequency transforms are used to analyze localized signals, then frequency domain representation is obtained, but structural information in the time domain is lost
Solution Approach 1:
The patent creates a time-frequency matrix that preserves structural information by maintaining the temporal dimension in the frequency domain representation. Each row corresponds to a specific time sample, allowing visualization and analysis of how frequency content evolves over time. This preserves the structural information about when specific frequency components occur, which is lost in conventional averaged frequency transforms.
Solution Approach 2:
The time-frequency matrix serves as an intermediary representation between the time domain and conventional frequency domain. It acts as a bridge that contains both temporal and spectral information, allowing users to analyze signals with sample-accurate frequency information while maintaining the ability to identify transient events and their temporal locations.
Data Source
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AI summary
A signal processing method generates a time-frequency domain representation of an input signal for the purpose of signal detection, signal display, and application of filtering operations, such as sample accurate spectral editing. The method may include receiving an input signal in the time domain in a processor. The input signal may include a plurality of transform frames. The input signal is transformed into the frequency domain using a frequency transform. Time-frequency matrices are generated from the frequency transform. Crossfrequency phase coupling is applied between adjacent frequency bins to introduce synchronization between adjacent frequencies and to generate smoothed time-frequency matrices with sample-accurate frequency magnitudes. The frequency information can be edited in the time-frequency domain specific to a single sample of the transform frame to alter unwanted signal features. A modified time domain representation of the edited input signal can be generated from the modified time-frequency matrices.