FIR PERFECT SIGNAL RECONSTRUCTION FROM MULTIPLE CONVOLUTIONS - MINIMUM DECONVOLVER ORDERS

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.