Polyphase High-Pass Filter Coefficients for Accurate Interpolation
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Solution Overview
Problem
Existing high-pass filter modules achieve insufficient interpolation accuracy for high-precision applications when determining filter coefficients from the impulse response of a time-continuous ideal high-pass filter.
Innovation Solution
A high-pass filter module incorporating a polyphase filter with filter coefficients based on the inverse of an autocorrelation matrix, where each element includes a sign-alternating factor, minimizing interpolation error and achieving a high-pass characteristic.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If filter coefficients are determined by sampling the impulse response of a time-continuous ideal high-pass filter, then the high-pass characteristic is achieved, but the interpolation accuracy is insufficient for high-precision applications
Solution Approach 1:
The patent changes the parameter used for determining filter coefficients from simple impulse response sampling to a polyphase filter structure with coefficients derived from the inverse of an autocorrelation matrix. This parameter change transforms the coefficient determination method to achieve both high-pass characteristic and high interpolation accuracy simultaneously.
Solution Approach 2:
The patent employs a composite filter structure combining polyphase filter theory with autocorrelation matrix inversion. The filter coefficients are constructed as a composite of multiple components: the polyphase decomposition structure and the weighted autocorrelation matrix elements, creating a hybrid approach that resolves the contradiction between high-pass characteristic and interpolation accuracy.
2Measurement precision
If the polyphase filter uses filter coefficients based on the inverse of an autocorrelation matrix with sign-alternating factors, then the high-pass characteristic is maintained, but the device complexity increases
Solution Approach 1:
The patent applies segmentation by dividing the filter into multiple polyphase components. The autocorrelation matrix is constructed from segmented signal samples, and the filter coefficients are derived from the inverse of this segmented matrix structure. This segmentation approach manages the complexity by organizing the calculation in a structured manner while maintaining high interpolation accuracy.
Solution Approach 2:
The patent performs preliminary calculation of the autocorrelation matrix and its inverse before actual filtering operations. By pre-computing these complex matrix operations, the system reduces the real-time computational burden during signal processing, thereby managing device complexity while achieving high interpolation accuracy.
Data Source
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AI summary
A high-pass filter module (10) is described. The high-pass filter module (10) comprises a signal input (12), a signal output (14), and a polyphase filter (16). The polyphase filter (16) is connected to both the signal input (12) and the signal output (14). The signal input (12) is configured to receive an input signal that comprises a set of input signal samples. The polyphase filter (16) is configured to determine additional samples based on the input signal samples, thereby obtaining an output signal comprising an augmented set of input signal samples. Filter coefficients of the polyphase filter (16) depend on an inverse of an autocorrelation matrix of the input signal. Each element of the autocorrelation matrix comprises a respective weighting factor, wherein the weighting factors each comprise a sign-alternating factor, wherein the sign-altering factor alters its sign between neighboring input signal samples. Further, a method for determining filter coefficients of a high-pass filter module (10) is described.