Properties of Systems Memoryless, Causal, time invariant, linear
Tags: signals and systems
Aug20-11, 07:43 PM
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.
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
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.
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
by definition if
Therefore, y(t)=[x(t-2)]^2 is time invariant.
A system is linear if it is homogeneous and additive.
if x(t)--->y(t), then
ax(t)--->ay(t) a= alpha
if x1(t)--->y1(t), and x2(t)--->y2(t), then
multiply input by alpha a, then
system y(t)=[x(t-2)]^2 is not homogeneous, thus not linear.
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