Multi-Block FIR Filtering for Low-Latency Frequency-Domain Convolution
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Solution Overview
Problem
Existing digital FIR filters face challenges in achieving real-time processing due to high computational costs and latency in convolution techniques, making them unsuitable for fast and complex digital signal processing in audio and video applications.
Innovation Solution
A novel multi-block convolution method is introduced, where the impulse response coefficients are segmented into time domain filter blocks, transformed into frequency domain blocks using DFT, and processed with a single delay line for frequency domain sample blocks, reducing computational time and latency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If direct time domain convolution is used, then manufacturing precision is maintained, but productivity deteriorates due to high computational cost increasing linearly with filter length
Solution Approach 1:
The filter impulse response is divided into multiple blocks, and the convolution operation is performed in blocks rather than processing the entire filter at once. This segmentation reduces the computational complexity from linear O(N) to logarithmic O(log N) by using frequency domain processing for each block, while maintaining filtering accuracy through proper block overlap handling.
Solution Approach 2:
The patent replaces direct time-domain mechanical convolution with frequency-domain convolution using FFT algorithms. This substitution transforms the computational mechanism from linear time-domain operations to logarithmic frequency-domain operations, dramatically improving computational efficiency while preserving the filtering effect through the Fourier transform relationship.
2Productivity
If single-block convolution is used, then productivity is improved with logarithmic computational cost, but loss of time increases due to inherent latency equal to block length
Solution Approach 1:
The patent divides the single-block convolution into multiple smaller blocks with overlap. By processing the filter impulse response in segmented blocks and using overlap-add or overlap-save methods, the system reduces the latency per block while maintaining the logarithmic computational efficiency of frequency-domain processing.
Solution Approach 2:
The patent pre-computes and stores the frequency domain representation of the filter blocks before actual filtering operations. This preliminary action allows the filtering process to directly use pre-computed data, reducing the real-time processing latency while maintaining computational efficiency during the actual filtering operation.
3Loss of time
If multi-block convolution is used, then loss of time is reduced with shorter block latency, but device complexity increases due to multiple frequency domain blocks
Solution Approach 1:
The patent designs the multi-block convolution system with a universal processing framework where the same frequency-domain processing pipeline handles all blocks. This multi-functionality allows the system to process multiple blocks through a single unified algorithm, reducing the effective complexity despite handling multiple blocks, as the same FFT-based machinery serves all segmentation purposes.
Solution Approach 2:
The patent implements a nested structure where smaller filter blocks are nested within the overall multi-block filtering framework. Each block is processed independently through frequency domain operations, but they are coordinated through a unified overlap-add or overlap-save structure, creating a nested organizational pattern that manages complexity through hierarchical organization.
4Productivity
If frequency-domain delay line convolution is used, then productivity is improved, but loss of substance increases due to higher memory requirements
Solution Approach 1:
The patent extracts only the essential frequency domain representations of the filter blocks that are needed for processing, rather than storing complete time-domain impulse responses or all intermediate processing data. This extraction approach reduces memory requirements by keeping only the minimal necessary data in frequency domain form for the multi-block convolution operations.
Solution Approach 2:
The patent pre-computes and stores the frequency domain representations of filter blocks in advance, before actual filtering operations begin. This preliminary computation allows the system to use compact frequency domain data during real-time processing rather than storing large amounts of time-domain data, reducing memory usage during the critical filtering operation while maintaining computational efficiency.
Data Source
AI summary
A method for finite impulse response (FIR) digital filtering is provided that includes generating a frequency domain sample block from an input sample block of length L, adding the computed frequency domain sample block to a reverse time-ordered set of previously generated frequency domain sample blocks as a newest frequency domain sample block, computing a spectral multiplication of each of K newest frequency domain sample blocks in the reverse time-ordered set with a corresponding frequency domain filter block in a time-ordered set of K frequency domain filter blocks of a FIR filter, adding the K results of the K spectral multiplications to generate an output spectral block, inverse transforming the output spectral block to generate a time domain output block, and outputting L filtered output samples from the time domain output block.