Adaptive Signal Windowing for Time-Frequency Analysis
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Solution Overview
Problem
Current time-frequency analysis methods struggle with efficiently processing signals with varying bandwidths, particularly adaptive frequency band and ultra-wide band signals, due to limitations in sampling rates and accuracy in reconstructing signals with sub-Nyquist sampling and variable bandwidths.
Innovation Solution
The method involves adaptive partitioning of signals in the time domain into segments using B-splines to construct basis windows, transforming these segments into the frequency domain while preserving orthogonality, and mapping samples back into the time domain, allowing for efficient analysis and reconstruction of signals with varying bandwidths through parallel processing and Fourier series expansions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If sub-Nyquist sampling is used to reduce sampling rates, then productivity is improved, but measurement precision deteriorates due to aliasing errors
Solution Approach 1:
The signal is divided into multiple segments in the time domain, each processed independently through Fourier series expansion. This segmentation allows parallel processing of different signal portions, improving productivity while maintaining measurement precision through orthogonality preservation in each segment
Solution Approach 2:
The patent transforms the signal from time domain to frequency domain through Fourier series expansion, then applies parallel processing in the frequency domain before mapping back to time domain. This dimensional transformation enables sub-Nyquist sampling by exploiting the frequency domain structure to avoid aliasing while achieving faster processing
2Adaptability or versatility
If adaptive partitioning with B-splines is applied, then adaptability is improved for varying bandwidths, but device complexity increases
Solution Approach 1:
The patent uses B-spline basis functions with adjustable order and control points to adapt the partitioning to varying signal bandwidths. By changing the B-spline parameters (order, number of control points), the system can adapt to different bandwidth requirements while maintaining a relatively simple computational structure based on standard Fourier series expansions
3Measurement precision
If orthogonality is preserved in overlapping regions, then measurement precision is improved, but computational complexity increases
Solution Approach 1:
The patent applies windowing functions to the signal segments before Fourier series expansion to ensure orthogonality is preserved in overlapping regions. This preliminary action of windowing prevents spectral leakage and maintains orthogonality, improving measurement precision while keeping the computational complexity manageable through standard Fourier transform algorithms
Data Source
AI summary
The present embodiments include methods of time-frequency analyzing signals. Some embodiments provide methods of processing signals comprising: adaptively partitioning at least a portion of a signal in a time domain into a plurality of segments of the signal; and transforming each of the segments of the signal producing respective expansions in a frequency domain and obtaining respective samples of the windows of signal in the frequency domain.