Wavelet Bandpass Sampling for Sparse Signal Recovery Without Aliasing
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing compressed sensing methods face challenges in efficiently sampling sparse multi-band signals at low rates, particularly due to aliasing issues and high power consumption, especially when dealing with wideband signals and interference outside the signal's support.
Innovation Solution
A non-uniform wavelet bandpass sampling method that projects signals onto waveforms from a Gabor or wavelet frame at a lower bandpass sampling rate, followed by non-uniform sampling, which reduces the sampling rate while minimizing aliasing and noise interference by selecting waveforms based on the signal's bandwidth characteristics.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If non-uniform sampling is used to reduce sampling rate, then power consumption is reduced and sampling rate approaches information rate, but aliasing occurs and signal recovery is impeded
Solution Approach 1:
The signal is pre-processed through projection onto waveforms from a Gabor or wavelet frame before sampling. This preliminary transformation concentrates the signal energy into a fewer number of coefficients, creating a sparse representation that can be sampled at lower rates without losing critical information, thus preventing aliasing while enabling reduced sampling rates
Solution Approach 2:
The patent changes the representation parameters of the signal by transforming it from the time domain to a time-frequency domain using wavelet or Gabor frames. This parameter transformation allows the signal to be represented in a sparse form where only a few coefficients carry significant information, enabling sub-Nyquist sampling while maintaining signal recovery accuracy
2Reliability
If wideband signal sampling is performed at Nyquist rate, then complete signal capture is achieved, but power consumption increases
Solution Approach 1:
The patent transforms the sampling approach by changing from uniform time-domain sampling to non-uniform sampling in the time-frequency domain. By projecting the wideband signal onto wavelet or Gabor frames, the signal representation is changed to a sparse form where only essential frequency components need to be captured, reducing the effective sampling rate and thus power consumption while maintaining complete signal capture
Solution Approach 2:
Before sampling, the signal undergoes preliminary projection onto a dictionary of waveforms. This pre-processing step identifies and concentrates the essential signal energy into specific time-frequency atoms, allowing the system to focus sampling resources only on the relevant signal components rather than uniformly sampling the entire wideband spectrum, thereby reducing power consumption
3Use of energy by moving object
If sampling rate is reduced below Nyquist frequency, then power consumption is reduced, but aliasing occurs
Solution Approach 1:
The patent changes the sampling parameters by moving from uniform time-domain sampling to non-uniform sampling in the time-frequency domain. The projection onto wavelet or Gabor frames transforms the signal into a representation where aliasing is minimized because the sampling occurs in a transformed domain that better preserves signal structure even at reduced rates
Solution Approach 2:
The signal is pre-transformed into a sparse representation before sampling. This preliminary action of projection onto a dictionary concentrates signal energy into fewer coefficients, creating a representation that is more robust to undersampling. The sparsity induced by the transformation prevents aliasing because the essential signal information is concentrated in specific coefficients that can be captured even at sub-Nyquist rates
4Productivity
If non-uniform sampling is used, then sampling rate is reduced, but timing jitter sensitivity increases
Solution Approach 1:
The patent changes from time-domain sampling parameters to time-frequency domain sampling parameters. By projecting the signal onto wavelet or Gabor frames with specific time-frequency localization properties, the sampling becomes less sensitive to timing jitter because the waveforms provide inherent time-frequency resolution that can tolerate small timing variations without significant loss of measurement accuracy
Data Source
Figure 1
Figure 2
Figure 3
AI summary
The invention relates to a compressed sensing method based on non-uniform wavelet bandpass sampling. A K-sparse signal of interest is projected onto a sequence of waveforms succeeding one another at the bandpass sampling rate, the waveforms belonging to an overcomplete dictionary, the parameters of the waveforms depending on the characteristics of the bands of the signal. The correlation values are then non-uniformly sampled to provide a compressed representation of the signal.