Factorization Permutations for Multi-Rate Filter Design
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Solution Overview
Problem
Designing multi-rate, multi-stage filters is challenging due to the difficulty in identifying and assessing various circuit architectures, each with different stages and sampling rate reductions, making it hard to select the optimal circuit design for a given application.
Innovation Solution
A method is developed to determine factorization permutations of natural numbers, which are used to explore and evaluate circuit designs. This involves storing canonical prime factor vectors and basis vectors to derive count sequences, outputting second and third basis vectors, and determining unique factorization permutations that define circuit designs, allowing for the assessment and selection of optimal circuit architectures.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If multiple circuit architectures are considered for multi-rate, multi-stage filter design, then design options and versatility improve, but design complexity and difficulty of assessment increase
Solution Approach 1:
The patent segments the complex design space by decomposing the overall filtering function into multiple stages, where each stage has a specific sampling rate reduction factor. This segmentation allows systematic exploration of architectures by independently selecting factors for each stage, rather than evaluating all possible architectures as a monolithic problem.
Solution Approach 2:
The patent systematically varies key parameters including the number of stages, sampling rate reduction factors at each stage, and circuit implementation choices. By parameterizing the design space and exploring different parameter combinations, the method enables comprehensive assessment of multiple architectures while maintaining systematic control over the complexity.
2Manufacturing precision
If comprehensive circuit design exploration is performed, then design quality and optimization improve, but computational resources and time increase
Solution Approach 1:
The patent performs preliminary analysis by pre-calculating and storing performance metrics for different stage configurations and sampling rate reductions. This preliminary action creates a database of pre-evaluated options that can be quickly referenced during design exploration, avoiding redundant computations and reducing overall design time while maintaining comprehensive evaluation.
Solution Approach 2:
The patent implements a hierarchical exploration strategy that focuses computational resources on the most promising design regions. Rather than exhaustively evaluating every possible architecture, the method performs partial exploration by prioritizing configurations that show potential based on preliminary metrics, thus achieving good optimization quality with reduced computational effort.
3Measurement precision
If detailed assessment of each circuit architecture is performed, then design selection accuracy improves, but processing complexity increases
Solution Approach 1:
The patent applies different levels of assessment detail to different parts of the design space. Rather than uniformly applying complex evaluation metrics to all architectures, the method uses local quality assessment by tailoring the depth and type of analysis to specific architectural features and their potential performance impact, thus achieving accurate assessment without unnecessary complexity.
Solution Approach 2:
The patent introduces intermediary metrics and intermediate evaluation steps that bridge the gap between simple architecture description and detailed performance analysis. These intermediary assessments include preliminary performance estimates, resource requirement calculations, and compatibility checks that simplify the overall assessment process while maintaining sufficient accuracy for design selection.
Data Source
AI summary
A method of determining a factorization permutation for a natural number can include storing a canonical prime factor vector within memory of a system and storing a first basis vector within the memory. The method can include deriving a first count sequence, including a plurality of counts, from the first basis vector, wherein each count of the first count sequence is a child of the first basis vector. For each count of the first count sequence, a second basis vector can be output that is a child of the count, wherein each count of the first count sequence and child second basis vector specifies a factorization permutation of the natural number.