Recursive Difference Filter Coefficient Transformation
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Solution Overview
Problem
Existing digital filters, such as IIR, FIR, and ARMA filters, are complex in terms of hardware implementation and computational power due to the need for multiple multiplication operations, which increases power consumption and complexity.
Innovation Solution
The method involves computing a second set of coefficients as differences between successive coefficients of the first set, forming a difference filter, and adding a compensation factor to achieve identical performance with fewer coefficients, reducing the number of bits required and thus the complexity of multiplication.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional digital filters (IIR, FIR, ARMA) are implemented with standard coefficients, then filter performance is achieved, but hardware complexity and computational power requirements increase
Solution Approach 1:
The patent transforms the filter coefficients from their original form into a difference domain representation. By computing coefficients as differences between successive original coefficients (b1[l] = b0[l] - b0[l-1]), the parameter representation changes, enabling reduced bit-width implementation while maintaining filter performance characteristics.
Solution Approach 2:
The patent segments the coefficient representation into a difference domain form, separating the coefficient computation into original coefficients and their differences. This segmentation allows the filter to be implemented using fewer bits per coefficient, reducing overall hardware complexity while preserving the filtering function.
2Measurement precision
If conventional digital filters use full precision coefficients, then accurate filter performance is achieved, but the number of bits required for multiplication increases
Solution Approach 1:
The patent changes the parameter representation from absolute coefficient values to difference values. This transformation allows the same filter accuracy to be achieved with fewer bits, as the difference between successive coefficients typically requires less precision than the coefficients themselves, especially when coefficients vary smoothly.
3Productivity
If standard multiplication operations are used for filter coefficients, then filter operation is achieved, but computational power and power consumption increase
Solution Approach 1:
The patent substitutes the standard multiplication operation with a difference-domain multiplication approach. By representing coefficients as differences, the multiplication operations require fewer computational resources and less power, as the difference values have smaller magnitudes and can be represented with fewer bits, reducing the complexity of the multiplication hardware.
Data Source
AI summary
According to an aspect of the present disclosure, a method comprises computing first set of coefficients of a digital filter providing first filter performance, computing a second set of coefficients from the first set of coefficients, forming a difference digital filter with second set of coefficients to produce a difference filter output and adding a compensation factor to the difference filter output to achieve a second performance identical to the first filter performance. According to another aspect, the second set of coefficients are computed as difference between the successive first set of coefficients such that when the first set of coefficients comprises N number of coefficients, the second set of coefficients comprises N−1 number of coefficients. The method further comprises computing first set of coefficients according to a first relation, computing the second set of coefficients according to a second relation, generating the difference filter output in accordance with a third relation, computing a compensation factor in accordance with a fourth relation and generating a filtered output samples from a set of input samples in accordance with a fifth relation.