Constant Geometry Split Radix FFT Architecture
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Solution Overview
Problem
Conventional FFT architectures, including those using split radix algorithms, face limitations in throughput due to irregular scheduling and high latency issues caused by 'L-shaped' butterflies, making them unsuitable for high-speed applications.
Innovation Solution
A constant geometry architecture employing symmetrical butterflies with multiplexers and latches to selectively perform addition and subtraction operations, eliminating the need for complex multipliers and reducing latency, while using a reorder matrix and controller to manage data flow efficiently.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If conventional split radix architecture uses L-shaped butterflies, then the algorithm reduces non-trivial complex multiplications, but irregular scheduling and uneven latency between datapaths reduce throughput
Solution Approach 1:
The patent transforms the traditional L-shaped butterfly into a symmetrical butterfly structure where all four datapaths have equal length and symmetry. This symmetrization eliminates the irregular scheduling and uneven latency problems while preserving the reduced multiplication count advantage of split radix algorithms.
Solution Approach 2:
The patent introduces control signals that dynamically switch the operation mode of the symmetrical butterfly between different computational modes (e.g., radix-2 and radix-4 modes). This dynamic switching allows the architecture to adapt to different computational requirements while maintaining regular scheduling and uniform latency.
2Adaptability or versatility
If variable geometry architecture uses multiplexers to achieve Cooley-Tukey algorithm, then flexibility in computation is improved, but switching overhead reduces throughput
Solution Approach 1:
The patent segments the butterfly computation into separate real and imaginary datapaths with dedicated summing circuits for each. This segmentation eliminates the need for multiplexers to switch between different computational modes, as each datapath is dedicated to specific operations, thereby removing switching overhead while maintaining computational flexibility through control signals.
3Productivity
If constant geometry architecture uses fixed wires to avoid multiplexers, then switching overhead is reduced, but the architecture cannot efficiently implement split radix algorithm with irregular scheduling
Solution Approach 1:
The patent designs a universal symmetrical butterfly structure that can efficiently implement both radix-2 and radix-4 operations within the split radix algorithm. The constant geometry architecture achieves this universality through control signals that direct the fixed datapaths to perform different operations, eliminating the need for variable geometry while maintaining algorithm implementation efficiency.
Data Source
AI summary
An apparatus for performing a Fast Fourier Transform (FFT) is provided. The apparatus comprises a reorder matrix, symmetrical butterflies, and a memory. The reorder matrix is configured to have a constant geometry, and the butterflies are coupled in parallel to the reorder matrix. The memory is also coupled to the reorder matrix and each butterfly. The reorder matrix, the butterflies, and the memory can then execute a split radix algorithm.