Register to reply

Properties of Systems Memoryless, Causal, time invariant, linear

by itsdinamo
Tags: signals and systems
Share this thread:
itsdinamo
#1
Aug20-11, 07:43 PM
P: 1
Hi, I need a hand with my reasoning on the following question.
I have answered all the questions, but not too sure weather they are correct.
Please guide me or point me on the right direction if they are not correct.
Regards

1. A system defined by the following equation y(t)=[x(t-2)]^2
Is the system Memoryless, Causal, Time Invariant, linear

The attempt at a solution

Memoryless ?

y(t)=x(t-2) has memory, the output is equal to the input two seconds ago.
y(t)=[x(t)]^2 = memoryless, the output at time t0 depends only on the input value at time t0.

Now, y(t)=[x(t-2)]^2 can be thought as y(t)=[x(t-2)*x(t-2)] right?, if so, my best guess would be that the system y(t)=[x(t-2)]^2 has memory.

Causal?
by definition; A system is causal if the output at any time t0 is dependent on the input only for t<=t0.
y(t)=[x(t-2)]^2 = causal

Time Invariant?
by definition if
x(t)--->y(t), then
x(t-t0)--->y(t-t0)
so;
x(t-t0)--->[x((t-t0)-2)]^2
y(t-t0)=[x((t-t0)-2)]^2,
Therefore, y(t)=[x(t-2)]^2 is time invariant.

linear ?
A system is linear if it is homogeneous and additive.
Homogeneous Property
if x(t)--->y(t), then
ax(t)--->ay(t) a= alpha
Additive Property
if x1(t)--->y1(t), and x2(t)--->y2(t), then
x1(t)+x2(t)--->y1(t)+y2(t),

x(t)--->y(t)=[x(t-2)]^2
multiply input by alpha a, then
ax(t)--->[ax(t-2)]^2
ay(t)--->a[(x(t-2))^2]
system y(t)=[x(t-2)]^2 is not homogeneous, thus not linear.
Phys.Org News Partner Science news on Phys.org
'Smart material' chin strap harvests energy from chewing
King Richard III died painfully on battlefield
Capturing ancient Maya sites from both a rat's and a 'bat's eye view'

Register to reply

Related Discussions
Linear and time-invariant system Engineering, Comp Sci, & Technology Homework 2
Linear time invariant(LTI) systems Engineering, Comp Sci, & Technology Homework 2
Linear Time Invariant System Engineering, Comp Sci, & Technology Homework 1
Properties of systems of linear equations Linear & Abstract Algebra 2
Linear Time Invariant System Response Engineering, Comp Sci, & Technology Homework 0