Passive Analog FFT Butterfly Circuit Without Clocked Power
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Solution Overview
Problem
Conventional digital signal processing methods for fast Fourier transforms (FFTs) are inefficient due to the need for active devices that consume power and are prone to errors from settling time and common mode noise, whereas analog signal processing with passive components offers advantages in power consumption and noise resilience but lacks efficient implementation methods.
Innovation Solution
An analog domain FFT circuit using passive two-port elements to perform butterfly operations on complex signals, eliminating the need for active devices and achieving shift and scale invariance, allowing for power-efficient and noise-resistant signal processing without the requirement for a clock or power supply.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If digital circuits are used to compute discrete Fourier transforms directly from definition, then measurement precision is maintained, but computing speed deteriorates to impractical levels for large data sets
Solution Approach 1:
The patent applies segmentation by dividing the large-scale DFT computation into many smaller DFTs through the Cooley-Tukey FFT algorithm. The input sequence of length N is divided into smaller segments, and the transform is computed recursively on these segments, reducing the overall computational complexity from O(N²) to O(N log N).
Solution Approach 2:
The patent uses preliminary action by pre-computing and storing twiddle factors (complex roots of unity) in lookup tables before the actual FFT computation. This allows the algorithm to retrieve pre-calculated values during the transform process, avoiding redundant computations and significantly improving computing speed.
2Measurement precision
If digital circuits with active devices are used for FFT processing, then computational precision is maintained, but power consumption increases
Solution Approach 1:
The patent substitutes electronic active devices with passive mechanical-like elements (springs, masses, dampers) to perform FFT computations. The mechanical system naturally performs the mathematical operations through physical laws, eliminating the need for powered electronic components while maintaining computational precision through the physical relationships in the mechanical analog.
Solution Approach 2:
The passive mechanical circuit performs FFT computations autonomously using the input signal's own energy. The system requires no external power source as the mechanical elements naturally process the signal through their inherent physical properties, making the computation self-powered and energy-efficient.
3Ease of manufacture
If direct DFT computation is used instead of FFT algorithm, then implementation simplicity is maintained, but device complexity increases for large data sets
Solution Approach 1:
The patent applies segmentation by breaking down the complex N-point DFT into multiple smaller DFTs through recursive division. Each stage processes smaller data segments independently, reducing the complexity of individual computational units while maintaining the overall transform accuracy through systematic combination of results.
Solution Approach 2:
The patent uses dynamics by implementing a multi-stage adaptive computation structure where the algorithm dynamically adjusts the computation at each stage based on the input data characteristics. The Cooley-Tukey algorithm adaptively divides the problem size and reuses intermediate results, optimizing the computational path and reducing overall device complexity.
Data Source
AI summary
An apparatus and method for performing a fast Fourier transform in the analog domain with passive components. A complex analog signal that is shift and scale invariant is derived from analog circuit properties. A butterfly circuit processes such signals using only passive components by mapping the Kirchhoff current and voltage laws into operations on the signals. A fast Fourier transform circuit of any desired width is constructed from such butterfly circuits. The passive networks require no power as the operations are on the presented signal; energy is taken from the source signal so no battery or power supply is needed. Thus, when the signal becomes quiescent, the power consumed is zero. Further there is no need of a clock or other timing device; rather, it is the operation of Kirchhoff laws in the network, which apply essentially upon arrival of the signal, that is made analogous to the desired operation.