FIR Filter Cascade Using Piecewise Polynomial Impulse Scaling
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional FIR filters require a large number of multipliers and delay elements to achieve steep attenuation characteristics, leading to increased complexity and cost, particularly in multimedia applications where high noise elimination and steep frequency characteristics are necessary.
Innovation Solution
The use of an FIR filter with an impulse response function expressed as an n-th degree piecewise polynomial, allowing for a reduced number of taps and delay circuits, and employing a cascade connection of scaled filters to achieve steep attenuation characteristics with fewer multipliers, thereby improving noise elimination and reducing costs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If high-order transfer characteristics are used to obtain steeper attenuation characteristics, then the attenuation characteristics are improved, but the number of multipliers and delay elements increases
Solution Approach 1:
The filter is divided into multiple first-order sections that are connected in cascade. Each section contributes to the overall attenuation characteristics, and by segmenting the filter into these smaller units, the design achieves steep attenuation without requiring a single high-order section with excessive multipliers and delay elements.
Solution Approach 2:
The invention changes the parameter of using piecewise polynomial functions (specifically cubic polynomials) to define the impulse response, rather than traditional windowing methods. This parameter change allows the filter to achieve the desired attenuation characteristics with fewer taps by optimizing the shape of the impulse response function in different frequency regions.
2Manufacturing precision
If a very high degree of transfer characteristics is required to create a pass-band filter with a very narrow band, then the filter selectivity is improved, but the number of multipliers increases
Solution Approach 1:
The narrow pass-band filter is constructed by cascading multiple first-order sections, each with a simple multiplier structure. This segmentation allows the achievement of high selectivity through the cumulative effect of multiple sections rather than requiring a single high-order section with many multipliers.
Solution Approach 2:
Multiple first-order filter sections are combined in cascade to achieve the overall narrow pass-band characteristic. By merging these simple sections, the filter achieves high selectivity while keeping the multiplier count manageable, as each section shares common delay elements.
Data Source
AI summary
Provided is an FIR filter capable of obtaining predetermined characteristics with a small number of input taps, delay circuits, and multipliers and achieving an improved response and low cost. In a low-pass filter, a band-pass filter, and a high-pass filter based on an FIR filter, a basic filter is configured that gives a basic impulse response function and has a filter coefficient determined from the impulse response function. Filters having different frequency characteristics are configured by changing the time scale or frequency scale of the basic filter. These filters having different frequency characteristics are combined in a cascade form or a step form, thereby constructing an FIR filter having a small number of taps.