Selective Frequency-Bin Spectroscopy for Low-Complexity DFT Analysis
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Solution Overview
Problem
Spectroscopy methods, particularly those using Fourier transforms, face challenges with high computational complexity and memory usage due to the need to compute and store a large number of DFT values, especially in applications like electrochemical impedance spectroscopy.
Innovation Solution
Implementing a selective frequency bin DFT operation that reduces the number of frequency components computed by aligning excitation signals with specific frequency bins, using a controller to manage frequency bin selection and potentially correcting for frequency bin offsets caused by clock drift between excitation and sensing devices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a full N-point DFT is performed to analyze the response signal, then complete frequency domain information is obtained, but computational complexity and memory usage increase significantly
Solution Approach 1:
The patent extracts only the specific frequency bin corresponding to the excitation signal frequency from the complete N-point DFT spectrum. Instead of computing all N frequency bins, the system identifies and processes only the relevant bin (k = round(f_excitation * N / f_sampling)), thereby reducing computational complexity while maintaining measurement precision for the frequency of interest.
Solution Approach 2:
The patent applies local quality by focusing computational resources on a specific local region of the frequency spectrum - namely the frequency bin corresponding to the excitation signal. This localized approach computes only the necessary frequency component rather than the entire spectrum, optimizing the trade-off between accuracy and complexity for targeted frequency analysis.
2Measurement precision
If a full N-point DFT is performed to analyze the response signal, then complete frequency domain information is obtained, but memory usage increases to store all complex DFT values
Solution Approach 1:
The patent extracts only the specific frequency bin corresponding to the excitation signal frequency from the complete N-point DFT spectrum. Instead of computing all N frequency bins, the system identifies and processes only the relevant bin (k = round(f_excitation * N / f_sampling)), thereby reducing computational complexity while maintaining measurement precision for the frequency of interest.
3Measurement precision
If frequency bin offset correction is implemented to account for clock drift, then measurement accuracy is improved, but device complexity increases
Solution Approach 1:
The patent applies preliminary action by pre-calculating the frequency bin offset correction factor based on the ratio of actual excitation frequency to nominal excitation frequency. This correction factor is determined before the DFT operation and used to adjust the target frequency bin index, thereby compensating for clock drift without requiring complex real-time correction mechanisms during signal processing.
Data Source
AI summary
An apparatus includes an analog-to-digital converter (ADC) circuit having an analog input, and a digital output, the ADC circuit configured to sample a first signal at the analog input at a sampling frequency and provide a second signal representing samples of the first signal at the digital output. The apparatus further includes a processing circuit having a processing input, a frequency bin width input, a frequency bin index input, and a processing output, the processing input coupled to the digital output, and the processing circuit configured to provide a third signal as a Fourier transform representation of at least a part of the samples at the processing output based on states of the frequency bin width input and the frequency bin index input.