Fixed-Point FFT Dynamic Range Expansion via Multi-Gain Reconstruction
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing fixed-point Fast Fourier Transform (FFT) algorithms face challenges in controlling stage growth, leading to potential overflow and saturation issues, which can degrade signal processing accuracy and require aggressive scaling that compromises resolution.
Innovation Solution
The implementation of a reconstruction method using two or more fixed-point FFT algorithms with different gain values, where the output of each algorithm is scaled to limit growth, and the final FFT values are reconstructed by comparing and selecting values to avoid saturation, combining the advantages of higher- and lower-gain FFTs while minimizing their disadvantages.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If aggressive scaling is applied to limit stage growth in fixed-point FFT algorithms, then overflow is avoided, but resolution is compromised
Solution Approach 1:
The FFT computation is divided into multiple stages, with scaling applied selectively at specific stage boundaries rather than uniformly throughout. This segmentation allows different parts of the computation to maintain different gain levels, avoiding unnecessary resolution loss while preventing overflow where it would occur.
Solution Approach 2:
Different scaling factors are applied to different stages based on their specific growth characteristics. Rather than applying a uniform aggressive scaling factor throughout, the algorithm uses locally optimized scaling at each stage boundary, matching the actual signal growth requirements of that particular stage while preserving resolution elsewhere.
2Measurement precision
If higher gain is used in FFT algorithms, then signal-to-noise ratio is improved, but saturation occurs more frequently
Solution Approach 1:
The algorithm dynamically adjusts the gain applied at each stage based on the actual signal characteristics and growth observed in that stage. Rather than using a static high gain throughout, the system adapts the scaling factor to match the local signal conditions, maintaining high SNR where needed while avoiding saturation where signal growth is limited.
Solution Approach 2:
The scaling parameters are changed at each stage boundary based on the specific growth factor observed in the preceding stage. This allows the algorithm to optimize the gain parameter locally for each stage, achieving high overall SNR while preventing saturation through stage-specific parameter adjustment.
3Device complexity
If uniform scaling is applied across all FFT stages, then implementation is simplified, but dynamic range is reduced
Solution Approach 1:
The uniform scaling approach is segmented into stage-specific scaling operations. Rather than applying a single scaling factor uniformly across all stages, the algorithm divides the computation into segments (stages) and applies appropriately optimized scaling to each, maintaining implementation simplicity while expanding the effective dynamic range.
Data Source
AI summary
A method for generating a Fast Fourier Transform (FFT) is disclosed. The method includes providing an input signal to two or more fixed-point FFT algorithms that apply different scaling to reduce growth of their output, resulting in each of the FFT algorithms yielding an array of FFT output values characterized by a different gain. The method further includes determining, on a per-FFT output value basis, whether an output value of an FFT algorithm with a relatively high gain was clipped due to saturation. If not, then the output value of that FFT algorithm is included in the final FFT. Otherwise, an output value of an FFT algorithm with a lower gain is included in the final FFT. Reconstructing the final FFT by such combination of values from different FFTs allows benefiting from the advantages of both higher- and lower-gain FFTs while avoiding or minimizing their disadvantages.