Multi-Channel Complex Sampling for Bandpass Time-Delay Calculation
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Solution Overview
Problem
Existing digital signal processing methods face challenges in performing complex sampling using two or more sampling channels, particularly in handling signal bandwidths equal to or higher than the sampling frequency, and accurately calculating time delays between sampling channels, especially when signal frequency ranges contain whole multiples or half-multiples of the sampling frequency.
Innovation Solution
A system and method for complex sampling using multiple sampling channels, involving analog-to-digital converters, frequency-domain transformation units, delay units, and coefficient multiplication to generate a complex signal, along with a processing unit for calculating time delays, allowing for accurate time delay determination using phase and gain coefficients.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If uniform sampling is used according to Nyquist-Shannon theorem, then signal reconstruction is possible when sampling frequency exceeds 2B, but the theorem is invalid when signal frequency range contains whole multiples or half-multiples of the sampling rate
Solution Approach 1:
The patent divides the sampling process into multiple uniform sampling sequences that are interleaved to form a non-uniform sampling scheme. By segmenting the sampling into separate channels with different time delays, the system can handle bandpass signals whose frequency ranges contain multiples or half-multiples of the sampling rate, thus resolving the limitation of the Nyquist-Shannon theorem for such signals.
Solution Approach 2:
The patent changes the sampling parameters by introducing multiple sampling sequences with different time delays and interleaving them. This transforms the standard uniform sampling approach into a non-uniform sampling scheme that is specifically adapted for bandpass signals, allowing reliable reconstruction even when the signal frequency range contains multiples or half-multiples of the sampling rate.
2Productivity
If second order sampling is used for bandpass signals, then the theoretical minimal sampling rate of two-times bandwidth can be applied, but accurate time delay calculation becomes challenging when signal frequency contains multiples or half-multiples of sampling frequency
Solution Approach 1:
The patent employs feedback mechanisms in the form of interpolation filters that use the sampled sequences to reconstruct the original bandpass signal. The feedback loop allows for accurate time delay calculation by comparing the sampled sequences and adjusting the reconstruction process, even when the signal frequency contains multiples or half-multiples of the sampling rate, thus maintaining measurement precision while achieving efficient sampling.
Solution Approach 2:
The patent combines multiple uniform sampling sequences with different time delays into a composite non-uniform sampling scheme. This composite approach allows the system to achieve the theoretical minimal sampling rate of two-times bandwidth while maintaining accurate time delay calculation through the synergistic combination of multiple sampling channels and interpolation processing.
3Adaptability or versatility
If multiple sampling channels with time delays are used for complex sampling, then signal processing capability is improved, but system complexity increases
Solution Approach 1:
The patent designs the multiple sampling channels to perform multiple functions: each channel not only samples the signal with a specific time delay but also contributes to both real and imaginary components of the complex signal through the interpolation process. This multi-functionality reduces the need for additional dedicated components, thereby improving frequency range processing capability while limiting the increase in overall system complexity.
Data Source
AI summary
A method and system for performing complex sampling of signals using two or more sampling channels and calculating time delays between these channels. The system and method are operable to enable complex sampling of a signal in a frequency-domain by predefined-order sampling, including utilizing a sampling channel for converting an analog signal to a corresponding substantially non-delayed digital signal; and transforming the digital signal into a plurality of corresponding frequency-domain substantially non-delayed discrete components; providing additional sampling channels enabling to perform a predefined-order sampling, the predefined-order depending on a number of the additional sampling channels, each additional sampling channel configured to perform a number of stage, giving rise to the multiplied frequency-domain delayed discrete components; and combining the multiplied frequency-domain delayed discrete components with the corresponding frequency-domain substantially non-delayed discrete components, giving rise to an output frequency-domain complex signal.