IIR Filter Dithering Across Biquad Stages for Fixed-Point Stability

Resolve Bottlenecks,
Find Innovative SolutionsGenerate Solutions

Solution Overview

Problem

Infinite impulse response (IIR) filters are prone to inaccuracy and divergence, especially when implemented with fixed-point processors, due to their precision sensitivity, which can lead to self-oscillation and instability issues.

Innovation Solution

The implementation of dithering using a single random number generator circuit to apply random noise to the output of lower order filter stages before quantization, reducing correlation between signals and quantization errors, and stabilizing the IIR filters by decomposing higher order filters into biquad filters in cascade or parallel configurations.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Productivity

If IIR filters are implemented with fixed-point processors, then computational cost is reduced, but precision sensitivity causes inaccuracy and divergence

Engineering Contradiction:

Improvecomputational costVSAvoidfiltering accuracy

Core Design Contradiction:

ProductivityVSMeasurement precision

Solution Approach 1:

The higher-order IIR filter is decomposed into multiple lower-order filter stages (e.g., second-order sections). Each stage processes the signal independently with reduced precision requirements, eliminating the need for high-precision fixed-point arithmetic while maintaining overall filter accuracy.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

Dither noise is introduced as an intermediary signal between the filter computation and quantization. This random noise masks the correlation between quantization errors and signal components, preventing divergence while allowing the use of lower-precision fixed-point arithmetic.

Inventive Principle:

Principle #24Intermediary (Mediator)

2Reliability

If dithering is applied to reduce quantization error correlation, then stability improves, but computational complexity increases

Engineering Contradiction:

Improvefilter stabilityVSAvoidcomputational complexity

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The dithering operation is applied separately at each lower-order filter stage rather than at the final output only. This segmented approach uses simple random value addition at each stage, which is computationally cheaper than complex error feedback mechanisms while maintaining stability throughout the entire filter chain.

Inventive Principle:

Principle #1Segmentation

3Measurement precision

If higher order filters are decomposed into lower order stages, then precision sensitivity is reduced, but device structure becomes more complex

Engineering Contradiction:

Improveprecision sensitivityVSAvoidfilter structure

Core Design Contradiction:

Measurement precisionVSDevice complexity

Solution Approach 1:

Multiple lower-order filter stages are combined in a cascade configuration to reconstruct the overall higher-order filter response. Each stage uses simple second-order structure with minimal components, and their combined effect achieves the desired high-order filtering characteristics without requiring a complex monolithic high-order filter design.

Inventive Principle:

Principle #5Merging (Combining)

Data Source

PatentUS11804849B2Infinite impulse response filters with dithering and methods of operation thereof

Publication Date: 2023.10.31 STMICROELECTRONICS INT NV

AI summary

An infinite impulse response filter includes a plurality of lower order filter stages and a random number generator circuit. The plurality of lower order filter stages include a first filter stage coupled to a second filter stage. The random number generator circuit includes a first output coupled to the first filter stage and a second output coupled to the second filter stage. The random number generator circuit is configured to generate the same random value at both the first output and the second output. The infinite impulse response filter is an nth-order filter. The respective order of each of the lower order filter stages is less than n.