By Topic

Discrete-Time LTI Systems Beyond Convolution

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
Vogel, P. ; Dept. of Medientechnik, Univ. of Appl. Sci., Dusseldorf, Germany

Examples for LTI systems are found in the literature that cannot be represented as a convolution. Their outputs can be approximated by outputs of FIR filters and considered as generalized convolution systems. These examples illustrate that impulse and frequency response provide no complete description of the system. In this paper, a general theory for discrete-time LTI systems is represented. LTI systems are defined on a signal space, which is a vector space, closed with respect to a shift operation. Signals are not necessarily bounded and need not belong to a normed vector space. Vector space concepts like dependent and independent vectors are transferred to signal spaces in order to define arbitrary LTI systems. A first method, defining LTI systems by independent input signals, shows that impulse and frequency response can be defined independently from each other. According to another method, the signal space is extended by a new input. An equation is given describing all possible outputs belonging to the new input. Extending the signal space to all discrete-time signals reveals universal LTI systems, which are not even generalized convolution systems.

Published in:

Signal Processing, IEEE Transactions on  (Volume:60 ,  Issue: 8 )