Digital Filter Simplification Using Even-Odd FFT Channels
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Solution Overview
Problem
Current FIR filters used in radar applications face challenges with large impulse responses, leading to increased computational load and inefficiency due to the need for inverse Fast Fourier Transforms that result in half of the calculated points being lost, complicating the filtering process.
Innovation Solution
A method involving the application of discrete Fourier transforms and inverse discrete Fourier transforms on two processing channels with offset points, allowing for the calculation of all required spectrum points while reducing computational load by recombining the results, and optimizing the filter architecture to share resources between channels.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If a standard FFT-based filtering approach is used with filter length K, then the filtering operation can be performed in the frequency domain, but half of the calculated points are lost requiring doubling the process, which increases computational load and complicates implementation
Solution Approach 1:
The patent divides the frequency domain processing into two separate processing 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 M/2 points independently, avoiding the waste of calculating unnecessary points while ensuring all required spectrum points are obtained through recombination of both channels.
Solution Approach 2:
The patent introduces a new dimensional approach by separating the frequency domain into even and odd indices, effectively creating two parallel processing dimensions. This allows the system to calculate only the necessary M points by processing M/2 points in each dimension (channel), rather than calculating 2M points and discarding half of them as in the conventional approach.
2Reliability
If the impulse response length is very large as in radar impulse compression, then the filter can achieve the required filtering function, but the number of operations becomes very large making implementation problematic or impossible
Solution Approach 1:
The patent replaces the conventional time-domain mechanical filtering operation with a frequency-domain processing approach. By transforming the filtering operation into the frequency domain using FFT, the convolution operation in time domain is substituted with multiplication in frequency domain, significantly reducing the number of operations required for large impulse responses.
Solution Approach 2:
The patent changes the processing parameters by working with M/2 points in each channel instead of the full filter length K in a single channel. This parameter change reduces the computational burden while maintaining the required filtering accuracy through the recombination of even and odd channel results.
Data Source
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AI summary
The invention relates to a method for simplifying a sampled signal digital filter, the method comprising at least one step of: - to obtain a first intermediate filter, grouping the channels having discrete non-stationary operations on the same signal, the first channels having non-stationary operations on a first signal and the second channels having non-stationary operations on a second signal, - to obtain a second intermediate filter, on each of the first and second channels, switching the stationary operations with the non-stationary operations, to eliminate the redundant non-stationary operations, and - constructing the filter corresponding to the last intermediate filter obtained.