IIR Filter Structure Using First-Order Sections for Coefficient Stability
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Solution Overview
Problem
Infinite impulse response (IIR) filters are sensitive to numerical representation inaccuracies, leading to noisy or unstable outputs due to high sensitivity of high-order polynomials to coefficient errors, especially at low corner frequencies or small filter bandwidths.
Innovation Solution
The filter system employs a transfer function composed of cascaded first-order polynomial fractions with complex conjugate pairs, reducing sensitivity to coefficient inaccuracies and stabilizing the filter structure, which is further simplified by using separate multiplier elements for gain realization and eliminating numerator multipliers when zeros are -1 or 1.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If high-order polynomial transfer functions are used for IIR filters, then filter order and frequency selectivity are improved, but sensitivity to coefficient representation inaccuracies increases
Solution Approach 1:
The high-order polynomial transfer function is segmented into multiple first-order polynomial fractions. Each fraction operates independently with its own coefficient set, reducing the sensitivity to numerical inaccuracies. The overall transfer function is reconstructed by multiplying these first-order fractions, maintaining filter accuracy while improving stability.
2Productivity
If single precision floating-point format is used, then calculation speed and device complexity are improved, but coefficient representation accuracy deteriorates
Solution Approach 1:
The filter is segmented into first-order sections that are less sensitive to coefficient quantization errors. This segmentation allows the use of single precision floating-point format (7 digits accurate) without significant loss of filter performance, maintaining both calculation speed and acceptable accuracy.
Solution Approach 2:
The transfer function is transformed from a high-order polynomial form to a product of first-order polynomial fractions. This parameter change in the mathematical representation reduces the sensitivity to coefficient precision requirements, enabling effective use of single precision format.
Data Source
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AI summary
A filter system (201, 301, 401, 501, 601) with infinite impulse response shall be created that has a particularly low sensitivity in the numerical representation of filter coefficients. This is achieved through the transfer function of the filter system comprising at least one pair of first order polynomial fractions.