FFT Signal Filtering Using Even-Odd Spectrum Channels
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Solution Overview
Problem
Existing signal filtering methods for radars with large impulse response lengths face significant computational challenges and inefficiencies due to the large number of operations required, particularly when using Fourier transforms, which result in half of the calculated points being lost and increased computational load.
Innovation Solution
A signal filtering method that transmits the input signal through two channels, applying discrete Fourier transforms and inverse discrete Fourier transforms to specific indices of the signal spectrum, allowing for the recombination of output signals to produce a filtered signal, thereby reducing memory requirements and computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If a Fourier transformation is applied to filter a signal with a very large impulse response, then the filter operation becomes multiplicative in the frequency domain, but half of the calculated points are lost and the computational load increases
Solution Approach 1:
The patent divides the frequency domain processing into two separate channels: an even channel that processes even-indexed frequency points and an odd channel that processes odd-indexed frequency points. This segmentation allows each channel to work with only the necessary points, avoiding the loss of computational points while maintaining the multiplicative advantage of frequency domain filtering. The input signal is split into even and odd components, processed separately through FFT-based filtering, and then recombined to produce the complete filtered output.
2Productivity
If the size of the Fourier transform is increased to obtain more usable points, then more signal points can be calculated, but the memory space requirements and computational complexity increase
Solution Approach 1:
The patent segments the frequency domain processing into even and odd channels, where each channel processes only its designated set of frequency points. This allows the system to achieve complete signal reconstruction without needing to compute twice as many points as the traditional single-channel approach. By processing even and odd points separately and recombining them, the patent reduces memory requirements while maintaining full productivity.
Solution Approach 2:
Instead of computing a full Fourier transform at a size that would produce excessive points (and thus excessive memory requirements), the patent applies partial action by computing only the necessary even or odd points in each channel. This partial processing approach achieves the required output with reduced computational and memory resources compared to a complete transform at larger dimensions.
Data Source
AI summary
A signal filtering method for filtering a numerical input signal that is sampled at a sampling frequency in order to obtain a filtered signal, the method including a first operation of application of a discrete Fourier transform to M points on a processed signal in order to obtain M points of the spectrum of the processed signal, each point of the spectrum of the processed signal corresponding to the even-numbered indices of a spectral analysis at 2*M points of the processed signal; and a second operation of application of a discrete Fourier transform to M points on the processed signal in order to obtain M points of the spectrum of the processed signal, each point of the spectrum of the processed signal corresponding to the odd-numbered indices of a spectral analysis at 2*M points of the processed signal.