Digital IIR Filter for NMR Gradient Distortion Compensation
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Solution Overview
Problem
Conventional methods for compensating distortions in magnetic field gradients during NMR measurements are inadequate, particularly for fast switching and oscillating distortions, and fail to consider correlations between magnetic field coils, leading to suboptimal measurement quality.
Innovation Solution
A method using a digital transfer function G(s) that can replicate both transient exponential and oscillating behaviors, allowing for effective compensation of complex time-dependent distortions, implemented using digital IIR filters to predistort input signals for magnetic field coils, considering interactions between coils.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional high-pass filtering methods are used to compensate for gradient field distortions, then exponential transient behavior can be corrected, but oscillating distortions and fast switching effects cannot be adequately compensated
Solution Approach 1:
The patent changes the mathematical parameters of the filter by using a second-order transfer function instead of first-order high-pass filters. This allows the system to model both exponential transients and oscillating behaviors through the characteristic equation s² + as + b = 0, where the coefficients a and b can be adjusted to match different distortion patterns including oscillations.
Solution Approach 2:
The invention introduces dynamic adaptability by allowing the filter coefficients to be optimized based on the specific switching conditions and distortion characteristics. The method dynamically adjusts the compensation strategy by selecting appropriate filter orders and coefficients that match the actual distortion behavior, whether exponential or oscillating.
2Measurement precision
If iterative optimization methods are used to determine filter parameters, then compensation can be optimized, but the process is time-consuming and cannot keep up with fast switching
Solution Approach 1:
The patent applies preliminary action by pre-calculating and storing optimized filter coefficients for different switching conditions and distortion scenarios. These pre-optimized parameters are then directly applied during fast switching without requiring time-consuming iterative optimization at the moment of switching, thus maintaining both precision and speed.
Solution Approach 2:
The invention replaces time-consuming iterative numerical optimization with direct analytical solutions or pre-computed lookup tables. Instead of iteratively adjusting parameters during switching, the system uses closed-form solutions or pre-stored optimal coefficients that can be instantly retrieved and applied.
3Measurement precision
If separate compensation methods are used for each magnetic field coil, then individual distortions can be addressed, but correlations between coils are not compensated
Solution Approach 1:
The patent merges the compensation approach by using a multi-channel transfer function that simultaneously processes multiple coil signals. The combined transfer function H(s) = (s² + a₁s + b₁)/(s² + a₂s + b2) applies unified compensation logic across all coils, allowing the system to account for correlations and interactions between different magnetic field coils while maintaining individual distortion compensation.
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
This approach significantly improves the compensation of magnetic field distortions, achieving a magnetic field profile that closely matches the desired profile, even during rapid switching and oscillations, thereby enhancing the quality of NMR measurements.
Implementation Method 1
pre-distortion is effected using a transfer function... implemented using digital IIR filters
Implementation Method 2
The inventive transfer function G(s) is designed such that it can easily replicate both transient exponential behavior and temporarily oscillating behavior
Implementation Method 3
replicate both transient exponential behavior and temporarily oscillating behavior
Implementation Method 4
Due to eddy currents which are induced in conducting parts of the gradient coil itself and in its surroundings during switching, the magnetic field is distorted directly following current switching
Data Source
AI summary
A method for driving a power supply (84) of a magnetic field coil (85) for generating a predetermined magnetic field profile B(r,t) in the volume under investigation of a nuclear magnetic resonance (=NMR) apparatus (81), wherein for compensation of distortions caused by the apparatus, an input signal i(t) is predistorted, that predetermines the time behavior of the magnetic field profile, wherein the power supply (84) is driven by the predistorted signal o(t), is characterized in that the predistortion is performed using a transfer function of the formG(s)=O(s)I(s)=∑n=0Nsnbn∑n=0Nsnan,with s=σ+jω, s εC, and with N≧2, wherein O(s) is the Laplace transform of o(t), and I(s) is the Laplace transform of i(t). This inventive method improves compensation of distortions of one or more gradient fields including their correlations during rapid switching.