Wavelet Bandpass Sampling for Sparse Signal Aliasing Control
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
The method employs a non-uniform wavelet bandpass sampling approach, projecting signals onto waveforms from a Gabor or wavelet frame at a bandpass sampling rate, followed by non-uniform sampling, which reduces the sampling rate while minimizing aliasing and noise interference, using an overcomplete dictionary to spread measurements efficiently across the spectral support.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Use of energy by stationary object
If non-uniform sampling is used to reduce sampling rate, then power consumption is reduced, but aliasing and noise interference increase
Solution Approach 1:
The patent applies preliminary action by projecting the signal onto wavelet basis functions before sampling. This preprocessing step transforms the signal into a representation where the subsequent non-uniform sampling produces beneficial aliasing patterns that can be reversed during reconstruction, rather than harmful aliasing that loses information.
Solution Approach 2:
The patent changes the parameter of sampling rate from a fixed Nyquist rate to a variable non-uniform rate. By using different sampling intervals adapted to the signal's time-frequency characteristics, the system achieves lower average power consumption while maintaining reconstruction quality through the wavelet transform's ability to handle the resulting aliasing.
2Quantity of substance
If sampling rate is reduced below Nyquist frequency, then data stream size is reduced, but aliasing occurs
Solution Approach 1:
The signal is pre-processed by projection onto wavelet basis functions before downsampling. This preliminary transformation ensures that when aliasing occurs during non-uniform sampling, it occurs in a controlled manner in the wavelet coefficient domain, preserving the essential signal information for later reconstruction.
Solution Approach 2:
The wavelet transform acts as an intermediary between the original signal and the downsampled measurements. By transforming the signal into the wavelet domain first, the system creates an intermediate representation that is more robust to aliasing, allowing information to be preserved even at reduced sampling rates.
3Measurement precision
If ADC operates at Nyquist rate to capture wideband signal, then signal accuracy is maintained, but power consumption increases
Solution Approach 1:
The patent segments the wideband signal into multiple frequency bands using wavelet decomposition. Each band can then be sampled at a lower rate appropriate to its bandwidth, rather than sampling the entire wideband signal at the highest required rate, thereby reducing overall power consumption while maintaining accuracy for each frequency component.
Solution Approach 2:
The system dynamically adjusts the sampling rate based on the signal's time-frequency characteristics. By using wavelet projection, the system identifies when signal energy is concentrated in specific frequency bands and adapts the sampling rate accordingly, maintaining measurement precision when needed while reducing power consumption during low-activity periods.
Data Source
AI summary
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.