Fixed-Partition Audio Convolution With Low-Latency Fixed-Point FFT
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing frequency domain convolution techniques for audio signals with impulse response functions suffer from high computational cost and latency, particularly when dealing with long impulse responses, making them unsuitable for real-time applications.
Innovation Solution
Implementing convolution operations using fixed-point arithmetic, such as 16-bit integer numbers, to reduce memory resources and latency, while employing scaling techniques to minimize precision loss and truncation noise, and using frequency domain block processing to partition the impulse response function into smaller blocks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If direct convolution in the time domain is used, then the convolution operation is simple to implement, but the computational cost is very high and computation time increases linearly with filter length
Solution Approach 1:
The impulse response function is divided into multiple segments or partitions, allowing the convolution operation to be performed in smaller blocks. This segmentation enables parallel processing and reduces the computational burden of processing the entire long impulse response at once, thereby improving computational efficiency while maintaining implementation simplicity.
Solution Approach 2:
The patent transitions from time-domain convolution to frequency-domain convolution using FFT. This dimensional change from time domain to frequency domain transforms the convolution operation into point-wise multiplication, dramatically reducing computational complexity from O(N²) to O(N log N) and solving the efficiency problem while keeping the implementation straightforward.
2Productivity
If frequency domain convolution techniques are used, then computational cost is reduced with logarithmic scaling, but inherent latency is introduced due to buffering requirements
Solution Approach 1:
The impulse response is partitioned into smaller blocks that can be processed independently or with minimal overlap. This block-based approach in the frequency domain reduces the buffering requirements and latency compared to processing the entire impulse response at once, while still maintaining the computational efficiency benefits of frequency domain convolution.
3Loss of time
If traditional partitioned frequency domain methods are used, then latency is addressed by blocking, but performance remains slow and memory resources are not optimized
Solution Approach 1:
The patent changes the data representation parameter from floating-point to fixed-point arithmetic. This parameter change reduces memory bandwidth requirements and allows for more efficient processing, improving processing speed while the block-based frequency domain approach continues to handle latency effectively.
4Measurement precision
If floating point arithmetic is used for convolution operations, then precision is maintained, but memory resources and processing speed are not optimized
Solution Approach 1:
The patent changes the numerical representation from floating-point to fixed-point arithmetic. This parameter change trades some of the dynamic range of floating-point for the memory efficiency and processing speed advantages of fixed-point, while scaling techniques are applied to minimize precision loss and truncation noise, achieving both speed and acceptable precision.
Data Source
AI summary
A method for convolving an input signal with an impulse response function, the impulse response function being partitioned into a plurality of time segments of equal size, the method including transforming a segment of an input signal into the frequency domain to generate a frequency spectrum of the segment of the input signal; multiplying the frequency spectrum of the segment of the input signal with a frequency spectrum of each of the segments of the impulse response function; scaling the results from the multiplication of frequency spectra; accumulating the scaled results; and performing an inverse transform on the accumulated signals to generate a desired convolved signal in the time domain. The scaling includes performing a bitwise shift operation on the multiplication results, and performing the bitwise shift operation includes adding a bit to the multiplication results before the bitwise shift operation. Fast convolution of uniformly partitioned impulse response functions can be achieved by performing scaling of input signals, multiplication, and accumulation using fixed-point arithmetic.