FIR Filter Coefficient Scaling to Reduce Quantization Error
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Solution Overview
Problem
Conventional FIR filters face issues with increased quantization noise and computation error, particularly when filter coefficients exceed the representation range, leading to insufficient reduction of computation error in existing techniques.
Innovation Solution
A filter device comprising delayers, multipliers, a coefficient adjuster, a signal converter, and a divider, where filter coefficients are adjusted by multiplying a design value with a factor and dividing by the maximum representation value to minimize computation error, and in stochastic computing, using stochastic representation to reduce errors associated with product-sum operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If filter coefficients are adjusted by multiplying with a large multiplying factor, then computation error is reduced, but the multiplication result exceeds the maximum value of the representation range
Solution Approach 1:
The patent divides the filter coefficient adjustment process into two separate stages: first multiplying the design value by the multiplying factor adjustment value, then dividing by the maximum value of the representation range. This segmentation allows the intermediate multiplication result to exceed the representation range without causing overflow errors, while still achieving the desired computation error reduction.
Solution Approach 2:
The patent introduces an intermediary variable (the quotient from dividing the multiplication result by the maximum value) that acts as a mediator between the multiplying factor adjustment and the final filter coefficient. This intermediary allows the system to handle values that would otherwise cause overflow while maintaining computational accuracy.
2Measurement precision
If the representation range of filter coefficients is increased, then computation error is reduced, but circuit scale and quantization bit rate increase
Solution Approach 1:
The patent changes the parameter of filter coefficient representation by allowing temporary exceedance of the maximum representation value during computation, then normalizing by dividing by the maximum value. This parameter change enables computation error reduction without permanently increasing the representation range or circuit scale.
3Reliability
If the length of the filter is increased, then filter characteristics are improved, but quantization noise increases
Solution Approach 1:
The patent applies preliminary action by adjusting the filter coefficients with a multiplying factor before the actual filtering operation. This preliminary adjustment compensates for the quantization noise that will occur during the filtering process, allowing longer filters to maintain better characteristics with reduced quantization noise.
Data Source
AI summary
A filter device includes: delay units serially connected to delay an input signal and output a delayed signal; multiplication units multiplying the delayed signal by a filter coefficient based on a predetermined value and a multiplying factor adjustment value; a coefficient adjustment unit that, when a multiplication result obtained by multiplying the predetermined value by the multiplying factor adjustment value exceeds a maximum value of a filter-coefficient representation range, divides the multiplication result exceeding the maximum value by the maximum value, and outputs a quotient of division as a coefficient adjustment value; a signal conversion unit outputting a signal obtained by adding after-filter-coefficient-multiplication signals outputted by the multiplication units and an adjusted signal obtained by adjusting a corresponding delayed signal using the coefficient adjustment value; and a division unit generating an output signal by dividing the signal outputted by the signal conversion unit by the multiplying factor adjustment value.