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Least-squares method for multi-dimensional deconvolution

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2 Author(s)
Yanagida, M. ; Osaka University, Suita, Osaka, Japan ; Kakusho, O.

Least-squares method is applied to multi-dimensional deconvolution or estimation of input waveforms to a multi-input multi-output system given the transfer characteristics of the system. Suppose a system accepts n-dimensional input s(t) and it produces m-dimensional output f(t). Let hij(t) be the impulse response of the channel from jth input terminal to ith output terminal. Using an m × n matrix h(t) = [hij(t)], the input-output relation can be written as f(t) = h(t) o\ast s(t) , where o\ast denotes the matrix convolution introduced here. The minimum-norm least-squares estimate for s(t) is expressed as \hat{s}(t) = h^{\oplus}(t) o\ast f(t) , where ⊕ denotes the generalized convolutional inverse matrix. In the case of m > n, \hat{s}(t) yields the least-squares estimate for s(t). Efficient computation can be performed in the frequency domain. Practical applications are shown as source sound estimation in a multi-source multi-microphone configuration using sinusoidal waves and stationary vowels as source sounds.

Published in:

Acoustics, Speech, and Signal Processing, IEEE International Conference on ICASSP '82.  (Volume:7 )

Date of Conference:

May 1982