Round Robin FFT for Bin Spreading Reduction
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Solution Overview
Problem
The Fourier Transform (FFT) method suffers from bin spreading, where signals with frequencies between output frequency bins experience significant artifacts, leading to inaccurate frequency resolution due to the finite sampling interval and discrete sampling rate, which existing techniques only partially mitigate.
Innovation Solution
The round robin FFT method, where new samples are added sequentially to the data set without shifting existing samples, allowing for predictable phase rotation in output bins that can be exploited to reduce bin spreading and improve frequency resolution without the need for window functions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If a finite sampling interval is used for FFT operation, then the processing time is reduced and productivity is improved, but frequency resolution precision deteriorates due to bin spreading
Solution Approach 1:
The patent applies dynamics by making the sampling interval variable rather than fixed. The system dynamically adjusts the sampling interval based on the detected signal frequency characteristics. When bin spreading is detected, the system extends the sampling interval to capture more cycles of the signal, thereby improving frequency resolution while maintaining efficient processing through adaptive rather than static operation
Solution Approach 2:
The patent changes the parameter of sampling interval length based on signal characteristics. By detecting the frequency content and determining whether bin spreading occurs, the system modifies the sampling interval parameter dynamically. This allows the system to optimize between processing speed and frequency resolution by adjusting the interval parameter according to actual signal conditions
2Measurement precision
If window functions are applied to mitigate bin spreading, then frequency resolution is improved, but device complexity and computational load increase
Solution Approach 1:
The patent extracts and removes the problematic window function step from the signal processing chain. Instead of applying window functions to mitigate bin spreading, the system takes a different approach by dynamically adjusting the sampling interval to prevent bin spreading from occurring in the first place. This eliminates the computational overhead and complexity associated with window function application while achieving the same goal of improved frequency resolution
Data Source
AI summary
A method for performing a fast Fourier transform. The bin spreading effect of conventional FFT methodology may be removed by a mathematical technique that relies on an incomplete replacement of the input data sequence. In the present approach this replacement is accomplished by a “round robin” method. In this approach no window function is required and the FFT calculation proceeds after each new sample is added round robin fashion to the input sequence. The resulting output bins from the FFT show the signal evolution with time, overlapping as in the known art but by a single sample. The output of a FFT so constructed is not time invariant, but rather there is a rotation present in each output bin when viewed as an analytical signal. This rotation is predictable and hence removeable, but is also exploitable as a means to remove the bin spill over.