In-Place DFT Computation Without Output Reordering
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Solution Overview
Problem
Existing DFT, FFT, and DCT computations on processing units face complexity issues due to the need for extra storage or location switching to reorder elements, which increases overall complexity and computation costs.
Innovation Solution
The implementation absorbs the matrix transposing operation into other functions, allowing for in-place DFT, FFT, and DCT computations on modern CPU vector processing units without reordering or shuffling output data, reducing processing cycles and energy consumption.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If extra storage or location switching is used to reorder output elements, then the output elements are properly ordered, but the overall complexity and computation costs increase
Solution Approach 1:
The patent combines the reordering operation with the DFT computation itself by using in-place computation and carefully designed data flow. The output elements are generated and stored in their final positions directly during the computation process, merging what would traditionally be separate operations (computation + reordering) into a single integrated process.
Solution Approach 2:
The patent applies preliminary reordering to the input data before computation using bit-reversal permutation. By pre-ordering the input elements according to the required output sequence, the computation can proceed without additional reordering steps, as the data is already in the correct positional relationship for the algorithm.
2Ease of operation
If extra storage is allocated for reordering operations, then output elements can be properly arranged, but memory usage and computation costs increase
Solution Approach 1:
The patent implements in-place computation where the algorithm uses the input array itself as the output array. The computation overwrites input elements with output elements directly in their final positions, eliminating the need for separate output storage. The data structure serves itself by being both input and output medium.
Solution Approach 2:
The patent merges the input and output storage spaces into a single array. By using in-place computation with carefully managed data flow and temporary variables, the algorithm performs both reading input and writing output in the same memory location, eliminating the need for duplicate storage allocation.
3Ease of operation
If location switching functions are used to reorder elements, then output data is properly ordered, but processing time and computation costs increase
Solution Approach 1:
The patent merges the reordering operation with the computational operation by using in-place computation. The same computational passes that transform the data also position it correctly in the output array, eliminating separate reordering passes and reducing total processing cycles.
Solution Approach 2:
The patent performs preliminary bit-reversal permutation on input data before the main computation. This pre-ordering of input elements ensures that subsequent computational steps produce output in the correct order without requiring additional reordering operations, saving processing time.
Data Source
AI summary
In one embodiment, a computer-implemented method of discrete Fourier transform (DPT), FFT, or DCT computations on a system comprising a processor is described herein. In one example, the method includes receiving, with the processor, input complex samples from memory of the system, determining input vectors based on the received input complex samples, determining a DFT radix p of p macro blocks based on the input vectors, determining p independent DFT-L vectors based on the p macro blocks with L being based on p, and generating p DFT-N output vectors without reordering or shuffling output data based on the p independent DFT-L vectors.