Register to reply

Does a causal system have to be non-recursive?

by Bipolarity
Tags: causal, nonrecursive
Share this thread:
Bipolarity
#1
Mar13-14, 10:48 AM
P: 783
I have been trying to search for a clear definition of "discrete causal systems". The thing I want to know, which I've not been able to find, is whether non-recursiveness of the difference equation is part of the requirement for a causal discrete system?

Thanks!

BiP
Phys.Org News Partner Engineering news on Phys.org
Identifying long-distance threats: New 3D technology could improve CCTV images
Intelligent system that predicts when alarms might be triggered could greatly improve the management of industrial plant
3D printed nose wins design award
AlephZero
#2
Mar13-14, 01:57 PM
Engineering
Sci Advisor
HW Helper
Thanks
P: 7,157
A causal system is just one where the output at time ##T## only depends on the input at times ##t \le T##. In other words, the filter doesn't know anything about the future. That is a requirement for any filter that operates in real time (unless you want to change the laws of physics!) . If you are filtering data that has been acquired in the past, the filter doesn't have to be causal.

Recursiveness is irrelevant. That just says the output at time ##T## also depends on the output at times ##t \le T##, but those outputs ultimately depend on the inputs.

Recursiveness is useful in practice because you can design a filter that does a finite number of "operations" (either analog or digital) but the output depends on all the input from times ##-\infty < t \le T##. A simple example would be an digital "exponential smoothing" filter where the output at time ##T## is a weighted average of the input at time ##T##, and the output at the previous time ##T-\delta t##.


Register to reply

Related Discussions
Causal signals and causal system Electrical Engineering 2
How is dx(t)/dt system non-causal Engineering, Comp Sci, & Technology Homework 4
Causal System ? Engineering, Comp Sci, & Technology Homework 3
Causal system? Engineering, Comp Sci, & Technology Homework 0
Causal system Engineering, Comp Sci, & Technology Homework 0