FFT Accelerator Using Constant-Geometry and In-Place Butterflies
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Solution Overview
Problem
Existing FFT techniques require significant memory resources or complex hardware to implement efficient in-place transformations, lacking a simple routing scheme and additional memory usage.
Innovation Solution
The method employs a combination of constant-geometry and in-place butterflies to compute FFT, where constant-geometry butterflies process subsets of input points, transposing data, and subsequent in-place operations finalize the transformation, optimizing memory usage and routing complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If in-place FFT implementation is used to reduce memory usage, then memory requirements are reduced, but routing and control logic complexity increases
Solution Approach 1:
The patent divides the FFT computation into two distinct segments: constant-geometry butterfly operations that process data in a fixed pattern, and in-place butterfly operations that handle the remaining transformations. This segmentation allows each segment to be optimized independently, with the constant-geometry portion using simpler routing and the in-place portion utilizing already-computed addresses, thereby reducing overall routing complexity while maintaining memory efficiency.
Solution Approach 2:
The patent performs constant-geometry butterfly operations as a preliminary step before executing in-place FFT operations. By pre-processing the data with constant-geometry butterflies, the patent prepares the data in a format that simplifies subsequent in-place operations, allowing the in-place stage to use straightforward address computation without complex routing logic.
2Device complexity
If constant-geometry FFT is used to simplify routing, then routing complexity is reduced, but additional memory space is required
Solution Approach 1:
The patent merges constant-geometry FFT operations and in-place FFT operations into a unified hybrid architecture. The constant-geometry butterflies use simple fixed routing patterns, while the in-place butterflies compute addresses dynamically. By merging these two approaches, the patent achieves routing simplicity for the majority of operations while using additional memory only when necessary for the in-place stage, optimizing the trade-off between routing complexity and memory usage.
3Productivity
If radix-4 in-place FFT is used to process 1024 points, then computational efficiency is improved, but memory access patterns become complex requiring multiple memory banks
Solution Approach 1:
The patent segments the radix-4 FFT processing into constant-geometry stages that handle the majority of computations with simple memory access patterns, and in-place stages that handle the remaining transformations. This segmentation allows the system to achieve high computational efficiency through radix-4 operations while avoiding the need for complex multi-bank memory architectures, as the in-place stages can use straightforward address computation.
Data Source
AI summary
An FFT operation is performed by dividing n time-domain input points into a plurality of groups of m points, performing a plurality of constant-geometry butterfly operations on each of the groups of m points, and finally performing at least one in-place butterfly operation on the group of n points.