Sub-Nyquist Signal Reconstruction Using Delayed Dual Sampling
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Solution Overview
Problem
Conventional digital samplers require a sampling rate at least twice the highest frequency of the signal (Nyquist rate) to avoid aliasing and accurately represent analog signals, limiting the applicability and efficiency of signal reconstruction.
Innovation Solution
Recover an original signal from two under-sampled versions using samplers operating below the Nyquist rate by applying a delay to one of the samplers and performing Fourier transforms to de-alias the spectral components, allowing reconstruction through inverse Fourier transforms.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If a conventional sampler operates below the Nyquist rate, then the sampling cost and complexity are reduced, but the original signal cannot be recovered due to aliasing
Solution Approach 1:
The patent divides the signal recovery process into multiple segments by using multiple samplers operating at different time offsets. Instead of requiring a single high-speed sampler, the system segments the sampling process across multiple lower-speed samplers, each capturing aliased versions of the signal. These segments are then processed through Fourier transforms and combined to reconstruct the original signal, resolving the contradiction between using simpler samplers and maintaining recovery accuracy.
Solution Approach 2:
The patent introduces Fourier transforms as an intermediary processing step between sampling and signal reconstruction. The Fourier transform acts as a mediator that separates the aliased spectral components introduced by below-Nyquist sampling, allowing the original signal to be recovered through inverse Fourier transforms. This intermediary mathematical operation enables accurate signal recovery despite using lower-cost sub-Nyquist samplers.
2Measurement precision
If the sampling rate is increased to meet the Nyquist criterion, then signal fidelity is maintained, but the sampling system becomes more expensive and less efficient
Solution Approach 1:
The patent changes the sampling parameters by operating multiple samplers at rates below the Nyquist rate, with each sampler using a different time offset parameter. This parameter change approach allows the system to achieve the same effective sampling resolution as a single high-rate sampler would provide, but using multiple lower-cost components. The Fourier transform processing compensates for the lower individual sampling rates, maintaining overall signal fidelity while reducing component costs.
3Reliability
If multiple samplers are used to capture signal information, then signal reconstruction accuracy improves, but the system complexity increases
Solution Approach 1:
The patent makes each sampler multi-functional by having them perform the same basic sampling operation but at different time offsets. This universality allows the system to use identical, standardized sampler components rather than requiring different specialized components, reducing overall system complexity despite using multiple samplers. The shared processing pipeline (Fourier transforms and inverse transforms) further reduces complexity by providing a unified processing framework for all sampler outputs.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Enables faithful signal reconstruction using slower and less expensive samplers, extending the range of high-speed signal capture and measurement, reducing costs, and maintaining signal fidelity across applications like digital audio and high-speed communication systems.
Implementation Method 1
performing a Fourier transform of the first sampled signal to provide a first signal spectral component and performing a Fourier transform of the second sampled signal to provide a second signal spectral component
Implementation Method 2
providing a delayed input signal by delaying the input signal for a predetermined time
Data Source
AI summary
A method of reconstructing an input signal includes providing (104) a first sampled signal (110) by sampling an input signal (102) at a sampling rate fs, the sampling rate being less than a Nyquist sampling rate for the input signal, providing a delayed input signal (107), sampling (108) the delayed input signal at the sampling rate to provide a second sampled signal (112), performing (114) a Fourier transform of the first sampled signal and the second sampled signal to provide a first signal spectral component (118) and a second signal spectral component (120), respectively, combining (122) the first signal spectral component and the second signal spectral component to provide a first de-aliased spectral component (124A) and a second de-aliased spectral component (124B), and performing (126) an inverse Fourier Transform on the first de-aliased spectral component and the second de-aliased spectral component to provide a reconstructed signal (128).