Zero-Latency FIR Filtering via Dual FFT Processing Channels
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Solution Overview
Problem
The performance of FIR filters in radars becomes problematic due to the large number of operations required for pulse compression, especially when the length of the impulse response is very large, leading to increased computational load and inefficiency.
Innovation Solution
A method for filtering numerical input signals involves transmitting the signal over two processing channels, applying discrete Fourier transforms and shifts, and combining the results to achieve efficient filtering with reduced computational resources.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the length of the impulse response of the filter is increased to achieve better pulse compression performance, then the filtering performance is improved, but the number of operations becomes very large making the filtering problematic or impossible
Solution Approach 1:
The patent divides the filtering operation into two separate processing channels. Each channel processes a portion of the impulse response (first channel processes h[0] to h[M-1], second channel processes h[M] to h[2M-1]). This segmentation reduces the computational complexity of each individual channel while maintaining the overall filtering performance through parallel processing and summation of results.
2Productivity
If Fourier transforms are used to reduce computational load, then the number of operations is reduced, but half of the calculated points are lost requiring the process to be doubled
Solution Approach 1:
The patent applies FFT to only M/2^p points in each processing channel instead of the full 2M points, significantly reducing the computational load. By segmenting the frequency domain processing and using the overlap-add method, the patent recovers all required frequency points without needing to double the process, thus maintaining computational efficiency while reducing implementation complexity.
Solution Approach 2:
The patent transforms the time-domain convolution problem into the frequency domain using FFT, where multiplication replaces convolution. This dimensional transformation from time domain to frequency domain enables efficient computation while the overlap-add method ensures all frequency points are properly recovered through careful arrangement of the frequency domain operations.
3Quantity of substance
If the size of the Fourier transform is increased to obtain more points, then more output points are available, but the computational load and implementation complexity increase
Solution Approach 1:
The patent processes the impulse response in segments of M points divided into two channels, with each channel applying FFT to M/2^p points. This segmentation strategy obtains all 2M required output points through parallel processing while keeping the FFT size manageable, thus increasing the quantity of output points without proportionally increasing computational load.
Data Source
AI summary
The invention relates to a method for filtering a numerical input signal sampled at a sampling frequency in order to obtain a filtered signal, the method including at least one step for:obtaining a first (respectively second) output signal by carrying out first (respectively second) operations on the first (respectively second) processing channel, the first (respectively second) operations including at least the application of a discrete Fourier transform to M/2p points on a signal coming from the input signal, the integer p being greater than or equal to 1,applying an inverse discrete Fourier transform to M/2p points on the first signal in order to obtain M points of the spectrum of the first signal, M being an integer strictly greater than 2, the application step being carried out by the addition of the results of two processing channels.