Wavelet Bandpass Sampling with CAZAC Modulation for Low Aliasing
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Solution Overview
Problem
Conventional band-pass subsampling methods, such as non-uniform wavelet bandpass sampling, suffer from spectral aliasing due to subsampling relative to the Nyquist frequency, leading to information loss and distortion in signal reconstruction.
Innovation Solution
A wavelet bandpass sampling method that modulates the temporal positions of wavelets using a Constant Amplitude Zero Auto-Correlation (CAZAC) sequence, such as a Zadoff-Chu sequence, to break phase coherence and reduce aliasing, allowing for improved signal reconstruction with reduced aliasing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If bandpass subsampling is performed at a frequency lower than the Nyquist frequency, then the sampling rate is reduced and data acquisition efficiency is improved, but spectral aliasing occurs leading to information loss and signal reconstruction distortion
Solution Approach 1:
The patent applies preliminary action by modulating the wavelet sequence with a CAZAC sequence before performing bandpass subsampling. This pre-modulation decorrelates the spectral bands and breaks phase coherence, preventing aliasing artifacts from forming during the subsequent downsampling process. The CAZAC sequence modulation is performed in advance to ensure that when spectral folding occurs at lower sampling rates, the aliased components do not coherently add up to create distortion.
Solution Approach 2:
The CAZAC sequence acts as an intermediary between the original signal and the subsampling process. By introducing this intermediate modulation step, the patent transforms the signal representation in a way that allows safe downsampling. The intermediary modulation ensures that spectral components are sufficiently decorrelated, enabling the use of lower sampling frequencies without information loss.
2Productivity
If non-uniform wavelet bandpass sampling is used to reduce sampling rate, then acquisition efficiency is improved, but spectral aliasing and signal distortion still occur
Solution Approach 1:
The patent changes the parameter of the wavelet sequence by modulating it with a CAZAC sequence. This parameter change transforms the spectral characteristics of the wavelets, creating a modified wavelet sequence that, when used for bandpass subsampling, prevents the coherent addition of spectral aliases. The parameter modification maintains acquisition efficiency while dramatically improving reconstruction accuracy.
Solution Approach 2:
The patent converts the potentially harmful effect of bandpass subsampling (which normally causes aliasing) into a beneficial process. By using CAZAC-modulated wavelets, the aliasing that inevitably occurs during downsampling no longer produces coherent distortion but rather incoherent noise that can be filtered out. The harmful aliasing effect is transformed into a manageable artifact that does not compromise reconstruction quality.
3Manufacturing precision
If wavelet sequence is modulated with CAZAC sequence to break phase coherence, then aliasing is reduced and reconstruction accuracy is improved, but system complexity increases
Solution Approach 1:
The CAZAC sequence provides a periodic modulation pattern that can be efficiently generated and applied to the wavelet sequence. This periodic structure allows the system to achieve the benefits of phase coherence breaking without requiring complex, non-repetitive modulation schemes. The periodic nature of the CAZAC sequence enables efficient implementation using standard signal processing techniques.
Data Source
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Figure 3A~3B
AI summary
The present invention relates to a low-aliasing wavelet bandpass sampling method and a corresponding device. The analog signal to be sampled is correlated with a wavelet sequence occurring at a rate fp, the positions of which in the sequence are time-modulated based on the arguments of a CAZAC sequence, in particular a Zadoff-Chu sequence. The correlation results are then sampled at a frequency fs ≤ fp and converted to digital to provide a compressed representation of the signal. The time modulation of the wavelet positions results in incoherent aliasing of the correlation signal within the sampling band, thus reducing aliasing.