FIR Filter Coefficient Setting for Flat Passbands and Narrow Transitions
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Solution Overview
Problem
Existing FIR digital filters face challenges in independently controlling passband and stopband characteristics, leading to wider transition bandwidths and signal noise, with methods like windowing and Parks-McClellan exhibiting limitations such as equiripple artifacts and convergence issues.
Innovation Solution
A method that modifies the windowing impulse response by summing an auxiliary impulse response to achieve a compensated impulse response, allowing for flatter passbands and improved transition bandwidths, with discrete time modulation and specific auxiliary impulse responses designed to enhance amplitude responses and reduce stopband ripples.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Stability of the object's composition
If the windowing method is used to design FIR filters, then the passband is flat, but the transition bandwidth becomes wider and stopband attenuation is insufficient
Solution Approach 1:
The patent merges the windowing method with the Parks-McClellan method by combining their respective impulse responses. Specifically, it uses a window function to generate a first impulse response and the Remez exchange algorithm to generate a second impulse response, then combines them to create a hybrid filter that achieves both flat passband and narrow transition bandwidth
Solution Approach 2:
The patent creates a composite impulse response by combining elements from two different design methods. The hybrid impulse response integrates the flat passband characteristics from the windowing method with the narrow transition bandwidth characteristics from the Parks-McClellan method, achieving properties superior to either individual method
2Manufacturing precision
If the Parks-McClellan method is used to minimize transition bandwidth, then the transition bandwidth is reduced, but equiripple artifacts appear in the passband
Solution Approach 1:
The patent extracts and removes the harmful equiripple artifacts from the filter response by applying a window function to the Parks-McClellan impulse response. The windowing process suppresses the oscillations in the passband while preserving the narrow transition bandwidth achieved by the Remez exchange algorithm
Solution Approach 2:
The patent converts the harmful equiripple behavior into a benefit by using it to define the second impulse response through the Remez algorithm, then combining it with the windowing approach. The equiripple characteristics are intentionally generated and then controlled through the hybrid combination to achieve desired stopband attenuation while maintaining passband flatness
3Manufacturing precision
If the number of filter taps is increased to reduce transition bandwidth, then the transition bandwidth is reduced, but the filter complexity and computational load increase
Solution Approach 1:
The patent changes the approach from increasing filter order to optimizing the combination of two impulse responses. By adjusting the window function parameters and the Remez algorithm parameters, the method achieves narrow transition bandwidth with moderate filter order, reducing the number of required taps compared to traditional approaches
Data Source
AI summary
The present invention discloses a method for determining FIR digital filter coefficients providing a compensated amplitude response of a conventional windowing filter. The compensation allows independent control of passband and stopband specifications, while narrowing the transition bandwidths. The method comprises the steps of summing an auxiliary impulse response to a windowing impulse response, wherein the auxiliary impulse response has a phase response identical to that of the windowing impulse response, and an amplitude response comprising frequency shifted pulses positioned to induce the required compensation. The summing is followed by a modulation with a discrete time function to obtain the filter impulse response. The invention discloses a characterization of the pulse compensation on the amplitude response, a filter design method and computer program based on this characterization. The invention discloses an FIR filter device with coefficients set by this method.