Multi-Channel Time-Delay Sampling for Sub-Nyquist Frequency Aliasing
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Solution Overview
Problem
Current sub-Nyquist sampling methods for multiple sinusoid signals face challenges such as inaccurate frequency estimation, hardware design difficulties, and high sample requirements, particularly for real-valued signals, and lack effective solutions for frequency aliasing and image frequency aliasing.
Innovation Solution
A multi-channel time delay sampling system that initializes multiple sinusoid signals across parallel channels with evenly spaced sampling points and a controlled time delay, constructs an autocorrelation matrix using ESPRIT, estimates signal parameters, and employs a closed-form robust Chinese remainder theorem to reconstruct frequency parameters, allowing for efficient sub-Nyquist sampling with reduced sampling points and improved accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If sub-Nyquist sampling is used to reduce sampling rate, then sampling pressure is reduced, but frequency aliasing and image frequency aliasing occur
Solution Approach 1:
The patent divides the sampling process into multiple parallel channels, each performing sub-Nyquist sampling independently. By segmenting the signal processing into L channels with different time delays, the system can resolve frequency aliasing through channel combination while maintaining low sampling rates in each channel
Solution Approach 2:
The patent introduces an autocorrelation matrix as an intermediary structure to process the sampled data from multiple channels. This matrix serves as a mediator that transforms the aliased frequency information into resolvable parameters through ESPRIT algorithm, enabling accurate frequency estimation despite sub-Nyquist sampling
2Measurement precision
If multiple sampling channels are used to resolve frequency aliasing, then frequency estimation accuracy is improved, but system complexity increases
Solution Approach 1:
The patent changes the sampling parameters (time delays) across different channels in a controlled manner. By setting specific time delay relationships between channels and using these known parameters in the ESPRIT algorithm, the system achieves accurate frequency estimation with a manageable number of channels rather than requiring excessive channels
3Measurement precision
If ESPRIT algorithm is used for parameter estimation, then frequency estimation accuracy is improved, but computational complexity increases
Solution Approach 1:
The patent performs preliminary construction of the autocorrelation matrix from the sampled data before applying the ESPRIT algorithm. This preprocessing step organizes the data in a form that enables the ESPRIT algorithm to work efficiently, reducing the computational burden during the actual frequency estimation phase
4Measurement precision
If Chinese remainder theorem is used to reconstruct frequencies, then aliasing resolution is improved, but method applicability is limited to complex signals
Solution Approach 1:
The patent dynamically adapts the Chinese remainder theorem approach by modifying it to work with the specific structure of multi-channel sub-Nyquist sampled data. The method dynamically determines the relationship between sampling rates and time delays, making the theorem applicable to real-valued signals rather than only complex signals
Data Source
AI summary
The disclosure discloses a multiple sinusoid signal sub-Nyquist sampling method based on a multi-channel time delay sampling system. The method includes step 1: initializing; step 2: enabling multiple sinusoid signals x(t) to respectively enter N′ parallel sampling channels after the multiple sinusoid signals are divided, wherein a sampling time delay of adjacent channels is τ, and the number of sampling points of each channel is N; step 3: combining sampled data of each sampling channel to construct an autocorrelation matrix Rxx, and estimating sampling signal parameters cm of each channel and a set of frequency parameters {circumflex over (f)}m by utilizing the ESPRIT method; step 4: estimating signal amplitudes αm and another set of frequency parameters fm′ through the estimated parameters cm and the sampling time delay τ of each channel by utilizing the ESPRIT method; and step S: reconstructing 2K frequency parameters {circumflex over (f)}m through the two sets of estimated minimum frequency parameters fm and fm′ by utilizing a closed-form robust Chinese remainder theorem, and screening out K correct frequency parameters {{circumflex over (f)}k}k=0K-1 through sampling rate parameters. The disclosure is configured to solve problems of frequency aliasing and image frequency aliasing occurring in real-valued multiple sinusoid signal sub-Nyquist sampling.