Position-Modulated Wavelet Sampling for Low-Aliasing Bandpass Signals
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Solution Overview
Problem
Existing bandpass sub-sampling methods, such as Non-Uniform Wavelet Bandpass Sampling (NUWBS), suffer from spectral aliasing due to sub-sampling below the Nyquist frequency, leading to information loss and distortion in signal reconstruction.
Innovation Solution
The proposed method involves temporally modulating the positions of wavelets using a CAZAC sequence, specifically a Zadoff-Chu sequence, to break the phase coherence of spectral rays, thereby reducing aliasing and enabling better signal reconstruction from sampled data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If bandpass sub-sampling is performed below the Nyquist frequency, then the sampling rate is reduced, but spectral aliasing occurs causing information loss and signal distortion
Solution Approach 1:
The patent converts the harmful spectral aliasing effect into a beneficial structure by using position-modulated wavelets where the aliased spectral components are deliberately positioned and modulated to carry useful information. The CAZAC sequence modulation ensures that aliasing components are decorrelated and can be separated during reconstruction, transforming the previously harmful aliasing into a manageable and even useful phenomenon for compressed sensing.
Solution Approach 2:
The patent changes the temporal position parameter of wavelets using CAZAC sequence modulation. By modulating the positions of wavelets according to CAZAC sequences, the spectral characteristics of the sampling process are altered, causing spectral rays to be decorrelated and reducing aliasing interference while maintaining the reduced sampling rate.
2Productivity
If non-uniform sampling is used to reduce sampling rate, then the average sampling rate decreases, but the device complexity increases due to synchronization requirements
Solution Approach 1:
The patent makes the sampling system self-synchronizing by using the inherent properties of CAZAC sequences. The autocorrelation properties of CAZAC sequences allow the receiver to automatically recover synchronization information from the received signal without requiring complex external synchronization mechanisms, thus reducing device complexity while maintaining non-uniform sampling benefits.
3Productivity
If wavelet bandpass sampling is performed, then the sampling rate can be reduced, but spectral aliasing causes distortion in signal reconstruction
Solution Approach 1:
The patent modifies the temporal position parameter of wavelets using CAZAC sequence modulation. This parameter change causes the spectral rays to be decorrelated, which reduces aliasing distortion and improves signal reconstruction accuracy while maintaining the reduced sampling rate capability of wavelet bandpass sampling.
Data Source
AI summary
The present invention relates to a wavelet bandpass sampling method, with low aliasing and a corresponding device. The analogue signal to sample is correlated with a sequence of wavelets succeeding each other with a rate fp of which the positions in the sequence are temporally modulated from arguments of a CAZAC sequence, notably a Zadoff-Chu sequence. The correlation results are next sampled at a frequency fs≤fp and digitally converted to provide a compressed representation of the signal. The temporal modulation of the positions of the wavelets makes it possible to obtain incoherent aliasing of the correlation signal in the sampling band and thereby to reduce aliasing.