G. Harikumar et Y. Bresler, FIR PERFECT SIGNAL RECONSTRUCTION FROM MULTIPLE CONVOLUTIONS - MINIMUM DECONVOLVER ORDERS, IEEE transactions on signal processing, 46(1), 1998, pp. 215-218
Given p co-prime finite impulse response (FIR) filters h(i) is an elem
ent of R-mh, it well known that there exist q(i) is an element of R-mq
such that Sigma(i) h(i)q(i) = delta. Importantly, this enables signa
l recovery from its convolutions with p greater than or equal to 2 co-
prime FIR filters by FIR filtering, We show that such q(i) exist almos
t surely if and only if m(q) greater than or equal to [(m(h) - 1)/(p -
1)], where [x] is the smallest integer greater than or equal to x. Th
e results also provide conditions for full rank of certain key matrice
s arising in the blind multichannel deconvolution problem.