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Fast Convolution Technique Using a Nonuniform Sampling Scheme: Algorithm and Applications in Audio Signal Processing
Convolution is one of the key operations in signal processing and control. Despite its importance, convolution is also known to be a computationally expensive process such that direct implementation in the time domain becomes prohibitive for various real-time applications. To overcome the difficulties encountered in convolution using long filters, an efficient method based on a nonuniform sampling scheme is proposed. This method exploits the proportional-band property of human hearing and seeks an optimal design of an exponentially sampled finite impulse response (FIR) filter, in accord with a proportional-band frequency domain template. To justify the proposed technique, experiments were carried out for two audio signal processing applications: head-related transfer functions (HRTFs) and reverberators. Using the proposed method, the memory requirement as well as the computation loading can be reduced drastically without any significant degradation in performance. Although the implementations using the proposed fast convolution technique are distinguishable from direct convolution, the listening tests reveal satisfactory and pleasant impressions.
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