Recursive Discrete Fourier Transform Device Throughput Optimization
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Traditional recursive discrete Fourier transform (RDFT) devices have high time complexity and computation cycles, making them unsuitable for real-time processing in broadband communication systems like OFDM transmission systems.
Innovation Solution
The implementation of an RDFT device using input-decimation technology, where M pre-processors divide N input signals into M aggregated signals, reducing the number of inputs for a recursive-filter and minimizing computation cycles.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional recursive discrete Fourier transform is used, then the transform operation can be performed, but the computation cycle is long and time complexity is high
Solution Approach 1:
The patent applies segmentation by dividing the N-point input sequence into M separate subsequences, each containing N/M points. This allows the recursive filter to process M aggregated signals in parallel or with reduced sequential steps, reducing the computation cycle from O(N) to O(N/M) while maintaining the same transform functionality.
Solution Approach 2:
The patent implements preliminary action through pre-processing steps where M pre-processors compute aggregated signals from the input sequence before the main recursive filter operation. This pre-computation of aggregated signals reduces the workload during the main transform phase, thereby reducing the overall computation cycle and improving throughput.
2Adaptability or versatility
If traditional recursive discrete Fourier transform is used, then the transform operation can be performed, but the time complexity is high making it unsuitable for real-time processing
Solution Approach 1:
By segmenting the input sequence into M subsequences and processing them through M pre-processors followed by a recursive filter, the patent reduces the effective computation complexity from O(N²) to O(N·N/M) = O(N²/M). This segmentation enables real-time processing capability while managing device complexity through distributed computation.
Solution Approach 2:
The patent changes the processing parameter by introducing the decimation factor M, which transforms the computational approach from processing N individual points to processing N/M aggregated points. This parameter change reduces the time complexity and enables real-time processing adaptability without fundamentally changing the recursive filter structure.
Data Source
AI summary
A recursive discrete Fourier transform (RDFT) of this invention uses an input-decimation technique to reduce the number of input sequences for a recursive-filter so as to decrease the computation cycle of the recursive-filter. Therefore, the time complexity of the RDFT can be minimized, namely, increasing the throughput of the RDFT.