Fractional DSP Filtering with Altitude Exponent Response Control
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Solution Overview
Problem
Existing digital signal processing techniques are limited in accurately filtering and reconstructing systems due to artifacts such as ripples and wide transition bandwidths, which can obscure or alter relevant signals, leading to information loss.
Innovation Solution
A process involving a fractional order control system with filter components defined by Laplace functions and a variable fractional scaling exponent, adjusted by an altitude exponent to change the magnitude of the frequency response without altering the width of the transition band, allowing for precise amplification or attenuation of passbands and stopbands.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional digital signal processing techniques are used to filter signals, then filtering can be performed, but artifacts such as ripples and wide transition bandwidths occur which obscure relevant signals and cause information loss
Solution Approach 1:
The patent applies parameter changes by introducing a fractional scaling exponent (α) that modifies the magnitude of the frequency response. This exponent allows precise control over the filtering characteristics, enabling adjustment of passband and stopband magnitudes while maintaining transition band width, thereby reducing artifacts and information loss
Solution Approach 2:
The patent implements dynamics by making the filter characteristics adjustable through the fractional scaling exponent. This allows the filter to adapt its magnitude response dynamically while preserving the transition band properties, enabling optimization of signal fidelity without fixed limitations
2Measurement precision
If the magnitude of frequency response is changed to improve filtering accuracy, then signal fidelity improves, but the transition band width may be altered which affects filter performance
Solution Approach 1:
The patent uses parameter changes by introducing the fractional scaling exponent (α) as a control parameter. This single parameter enables adjustment of the magnitude response without affecting transition band width, simplifying the configuration process while improving filtering accuracy
Solution Approach 2:
The patent applies segmentation by separating the control of magnitude response from transition band characteristics. The fractional scaling exponent independently controls magnitude while transition band width remains determined by other parameters, allowing independent optimization of each aspect
Data Source
AI summary
A process for processing a digital signal comprises constructing a fractional order control system that models a desired frequency response by assembling filter components from a filter component library. The filter components are defined by Laplace functions that include a non-integer control order having a variable fractional scaling exponent. Then, the fractional order control system is adjusted by applying an altitude exponent to the fractional order control system, and the altitude exponent changes a magnitude of the frequency response without changing a width of a transition band of the frequency response. An input signal in the digital frequency domain is received and processed based upon the fractional order control system to generate a digital output that is conveyed.