Parallel Data Filtering via Sumdiff Segmentation and Frequency Domain Transform
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Solution Overview
Problem
Data convolution or filtering in the time domain is computationally intensive, and while parallel computing can reduce computation time, high data movement between processors can negate speed increases, necessitating a method to enhance filtering and convolution efficiency.
Innovation Solution
The method involves separating input data into parallel streams, transforming them into the frequency domain using FFTpc and pDCTs algorithms, filtering in the frequency domain, and then transforming back into the time domain using reverse FFTpc and reverse pDCTs algorithms, with the sumdiff function facilitating efficient data processing and reduction of data size for parallel processing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If parallel computing is used to reduce computation time, then processing speed improves, but data movement between processors increases which negates the speed increase
Solution Approach 1:
The patent segments the input data into multiple smaller streams that are distributed across parallel processors. Each processor works on a subset of the data independently, reducing the amount of data that needs to be moved between processors while maintaining parallel processing benefits. This segmentation of data is achieved through the sumdiff function that divides the data into streams of size n/p where p is the number of processors.
2Loss of time
If data is separated into parallel streams for concurrent processing, then computation time is reduced, but the complexity of the processing system increases
Solution Approach 1:
The patent implements a universal sumdiff function that handles multiple operations through a single algorithmic structure. This function can separate data into parallel streams, perform the necessary transformations, and combine results, thereby reducing the need for multiple separate complex functions and simplifying the overall system architecture while achieving parallel processing.
3Quantity of substance
If the sumdiff function is applied iteratively to reduce data size, then data is optimized for parallel processing, but additional computation steps are required
Solution Approach 1:
The patent applies the sumdiff function iteratively as a preliminary step to transform and reduce the input data into an optimized format suitable for parallel processing. By performing this data preparation in advance, the subsequent parallel processing steps can proceed more efficiently with smaller, pre-processed data streams, achieving better overall processing efficiency despite the additional computation steps.
Data Source
AI summary
A method for processing data in parallel includes the steps of: (a) separating input data into a plurality of streams using the sumdiff function; (b) transforming the plurality of streams from step (a) into frequency domain in parallel using the FFTpc algorithm and the pDCTs algorithm; (c) transforming the frequency-domain plurality of streams from step (b) into time domain in parallel using the reverse FFTpc algorithm and the reverse pDCTs algorithm; and (d) combining the plurality of streams from step (c) into output data using the sumdiff function.