Digital Filter Coefficient Alternation for Low-Complexity Cutoff Control
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Solution Overview
Problem
Existing digital filters require dedicated logic or calculation power for multiplication operations, which can be resource-intensive, especially when dealing with coefficients that have multiple decimal places.
Innovation Solution
Approximating multiplication operations using sums and shifts with coefficients as negative powers of two, allowing for alternative sets of coefficients to approximate the original coefficients, thereby reducing the need for multiplier circuit blocks and enabling a wider range of cutoff frequencies.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If multiplication operations are performed using dedicated multiplier circuit blocks or CPU multiplication instructions, then the filtering precision is maintained with exact coefficients, but the hardware complexity and calculation power requirements increase significantly
Solution Approach 1:
The patent replaces the mechanical multiplication operation with a digital bit-shifting operation. Instead of using multiplier circuit blocks or CPU multiplication instructions, the invention uses left-shifting operations (multiplication by powers of 2) to achieve the same filtering effect with significantly reduced hardware complexity and computational overhead
Solution Approach 2:
The patent changes the representation of filter coefficients from arbitrary decimal values to powers of 2 (specifically 2^n where n is an integer). This parameter transformation allows the use of efficient bit-shifting operations instead of complex multiplication, resolving the contradiction between precision and hardware complexity
2Productivity
If approximation coefficients are used to reduce multiplication operations, then the resource requirements decrease, but the cutoff frequency precision deteriorates
Solution Approach 1:
The patent transforms the coefficient representation to powers of 2, which enables efficient bit-shifting operations while maintaining sufficient filtering precision for practical applications. This parameter change achieves both high processing efficiency and acceptable frequency precision
Solution Approach 2:
The patent uses approximation coefficients that are powers of 2, which are not exactly equal to the ideal filter coefficients but provide sufficient accuracy for practical purposes. This partial approximation achieves the desired balance between processing efficiency and filtering performance
Data Source
AI summary
A method includes receiving an input digital signal and applying the input digital signal to digital filter processing with a corner frequency to produce a filtered output digital signal. The digital filter processing includes a set of multiplication operations using a set of filter multiplication coefficients. The set of multiplication operations is performed by alternately using a first set of approximate multiplication coefficients and a second set of approximate multiplication coefficients different from the first set of approximate multiplication coefficients. The approximate multiplication coefficients in the first set of approximate multiplication coefficients and the second set of approximate multiplication coefficients approximate multiplication coefficients in the set of filter multiplication coefficients as a function of negative power-of-two values. The alternating of multiplication operations results in digital filter processing with average corner frequency approximating the corner frequency.