Adaptive Digital Filter Coefficient Update Without Complex Division
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Solution Overview
Problem
Conventional adaptive digital filters have complex and large division circuits due to the coefficient renewal calculation formula, leading to long calculation times, which is inefficient for high-speed digital processing.
Innovation Solution
The adaptive digital filter employs a simplified coefficient renewal circuit using the formula a[n+1] = a[n] + β·e[n]·q[n]/2m, where 2m is greater than the conventional divisor, allowing for a simple logic circuit for division processing, and is implemented in both fixed-point and floating-point systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the coefficient renewal calculation is performed in accordance with Formula (1) using a divisor calculator and division circuit, then an accurate renewal value a[n+1] is calculated, but the arrangements of the division circuit become complex and large, and the calculation time becomes unduly long
Solution Approach 1:
The patent changes the denominator parameter from the complex expression (u[n]²+u[n-1]²) to a simplified form involving only u[n-1]², and introduces a new parameter γ (gamma) to replace the factor β. This parameter transformation allows the division circuit to be replaced by simpler multiplication and addition circuits, resolving the contradiction between accuracy and circuit complexity
Solution Approach 2:
The patent replaces the complex division circuit with simpler computational operations (multiplication and addition) that are computationally 'cheaper' and faster. The new formula uses operations that require less computational resources and time, effectively substituting the expensive division operation with more efficient alternatives
2Measurement precision
If the coefficient renewal calculation is performed in accordance with Formula (1), then an accurate renewal value is obtained, but the calculation time becomes unduly long
Solution Approach 1:
The patent substitutes the mechanical division operation with a different computational mechanism based on multiplication and addition. The new formula a[n+1] = a[n] + γ·u[n-1]·e[n]/(2·u[n-1]²) replaces the time-consuming division with operations that can be executed faster in digital systems, reducing calculation time while preserving accuracy
Solution Approach 2:
By transforming the mathematical parameters and reformulating the coefficient renewal equation, the patent eliminates the need for division operations that consume excessive time. The introduction of parameter γ and the restructured formula enable faster computation through multiplication and addition only
3Productivity
If a different formula is used to replace Formula (1) for simple and high-speed digital processing, then a simple and high-speed coefficient renewal circuit can be produced, but the accuracy of coefficient renewal may be affected
Solution Approach 1:
The patent incorporates feedback mechanisms where the error signal e[n] is used to adjust the coefficient a[n] iteratively. The new formula maintains this feedback loop while using simplified operations, ensuring that the coefficient converges to the correct value through repeated adjustments, thus preserving accuracy despite the simplified computation
Data Source
AI summary
An adaptive digital filter includes a filtering circuit and a coefficient renewal circuit. The filtering circuit has a coefficient a defined by a fundamental formula: a[n+1]=a[n]+β·e[n]·q[n]/p[n]. β is a number greater than 0 and smaller than 2, e[n] is a difference between the input and the output of the filter, and q[n] and p[n] are formulas. The renewal circuit calculates a renewal value of the coefficient a. The coefficient renewal circuit calculates 2m (m is an integer) greater than p[n] in the fundamental formula, and also calculates the renewal value of the coefficient a in accordance with an execution formula: a[n+1]=a[n]+β·e[n]·q[n]/2m in place of the fundamental formula.