Abstract

Not every linear shift-invariant operator on two-sided sequences can be represented by a convolution. An operator defined on sequences that converge to zero in both directions is representable if and only if it is bounded in the sup norm. An operator defined on bounded sequences is representable if and only if it is semilocal in the sense that the error introduced by neglecting the tails of the input sequence can be made as small as desired. In either case, a representable operator has an absolutely summable impulse response.

Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call