Fourier Series Steering Coefficient for Moving Sound Source
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Solution Overview
Problem
Existing acoustic signal processing devices face significant computational challenges when calculating steering vectors for moving sound sources and microphones, leading to inefficient calculation of signal waveforms in dynamic environments.
Innovation Solution
The use of N-order Fourier series expansion to model steering coefficients, reducing the amount of calculation required by selecting appropriate values for N, such as (M+K)(2N+1) < (M×K), allows for efficient calculation of signal waveforms received by microphones during movement.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If steering vectors are calculated for each discrete time when at least one of sound source and microphone is moving, then accurate signal waveform calculation is achieved, but calculation time and computational complexity increase significantly
Solution Approach 1:
The patent transforms the steering coefficient calculation from time-domain to frequency-domain using Fourier series expansion. By representing the steering coefficient g[k,m] as a sum of complex exponentials with frequencies proportional to the relative position, the calculation complexity is reduced from O(K×M) to O((K+M)×N), where N is the number of Fourier terms. This parameter transformation enables efficient calculation while maintaining accuracy for moving sound sources and microphones.
2Productivity
If steering vectors are pre-calculated and stored for each discrete time, then signal processing speed is improved, but data storage requirements increase
Solution Approach 1:
The patent segments the steering coefficient representation into a small number of Fourier series terms (typically N<<K and N<<M). Instead of storing all K×M steering coefficients, only the Fourier coefficients are stored, which can be compactly represented. This segmentation reduces the storage requirement from O(K×M) to O(N), enabling fast signal processing without excessive memory usage.
Data Source
AI summary
An acoustic signal processing device calculates a signal waveform that a microphone receives when at least one of a sound source and the microphone is moving. The acoustic signal processing device includes a coefficient calculation unit configured to model a steering coefficient gk,m representing how much an amplitude of a sound source signal emitted at an mth discrete time, where m is an integer between 1 and M and M is a length of the sound source signal, is transferred to an amplitude of a signal that the microphone receives at a kth discrete time, where k is an integer between 1 and K and K is a length of a recording signal, using N-order Fourier series expansion where N is an integer of 1 or more, and a recording signal calculation unit configured to calculate the signal waveform that the microphone receives using the modeled steering coefficient gk,m.