FFT/IFFT Processor Real-Complex Mapping Architecture
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Solution Overview
Problem
Existing FFT/IFFT processing methods are inefficient due to the increasing number of complex multiplications required as the number of data points increases, placing a burden on processing and storage requirements.
Innovation Solution
An FFT/IFFT processor that includes an even-odd data mapper to convert N real data values into N/2 mapped complex data values, and a separator-combiner to compute FFT or IFFT, reducing the number of complex multiplications needed by employing N/2 point FFT or IFFT structures.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If N-point FFT/IFFT processing is performed using conventional methods, then transformation accuracy is maintained, but the number of complex multiplications increases nonlinearily with N
Solution Approach 1:
The patent segments the N-point FFT/IFFT processing into two N/2-point processing operations. By dividing the input data into even and odd indexed elements and processing them separately through N/2-point transforms, the system reduces the computational complexity from O(N log N) to O((N/2) log (N/2)), thereby reducing the number of complex multiplications while maintaining transformation accuracy.
Solution Approach 2:
The patent introduces real-complex mapping as an intermediary mechanism that converts N real input values into N/2 complex values. This mapping serves as a mediator that enables the use of simpler N/2-point FFT/IFFT structures to achieve the same transformation effect as a full N-point transform, reducing computational burden while preserving accuracy.
2Adaptability or versatility
If the number of data points N increases, then transformation capability is enhanced, but processing requirements and storage needs increase
Solution Approach 1:
The patent applies segmentation by processing N data points through two separate N/2-point transforms rather than one N-point transform. This divides the processing workload and storage requirements into smaller, more manageable units, reducing the peak memory footprint and computational resources needed while maintaining the ability to handle N-point transformations.
Solution Approach 2:
The patent changes the parameter representation from N real values to N/2 complex values through real-complex mapping. This parameter transformation allows the system to maintain transformation capability for N points while using N/2 complex multiplications, effectively changing the computational parameters to reduce processing and storage requirements.
3Productivity
If conventional FFT algorithms are used, then computation speed is improved compared to direct DFT, but the number of complex multiplications still increases with N
Solution Approach 1:
The patent segments the FFT computation into two N/2-point FFT operations instead of one N-point FFT. Since the complexity of FFT scales with the number of points, this segmentation reduces the total number of complex multiplications required while maintaining the speed advantage of FFT over direct DFT computation.
Solution Approach 2:
The patent uses a copying approach by creating N/2 complex values from N real values through real-complex mapping. This copying process enables the system to reuse simpler N/2-point FFT structures multiple times, reducing the overall computational complexity while preserving the efficiency benefits of FFT algorithms.
Data Source
AI summary
The present invention provides an FFT/IFFT processor for use with N data values. In one embodiment, the FFT/IFFT processor includes an even-odd data mapper configured to provide a mapping of the N data values into N/2 mapped complex data values if the N data values are real. Additionally, the FFT/IFFT processor also includes a separator-combiner, coupled to the even-odd data mapper, configured to compute either an FFT based on the mapping or an IFFT based on the N data values if the N data values are complex.