Appendix D. Basic Definitions from Linear Systems Theory
D.1. Linear Time Invariant (LTI) Systems
A discrete linear time-invariant system is characterized uniquely by its impulse response sequence, b(n). This is the output of the system when its input is excited by the impulse sequence, δ(n), that is,(D.1)
When its input is excited by a sequence x(n), its output sequence is given by the convolution of x(n) with b(n), defined as(D.2)
For continuous time systems the convolution becomes an integral, that is,(D.3)where h(t) is the impulse response of ...
Get Pattern Recognition, 4th Edition now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
