CE 40763 – Assignment 1
Problem 1
(a) Determine if the following system is linear: y(n) = Ax(n) + B
(b) Determine if the following system is causal: y(n) = ax(n)+ x(n2 )
(c) Determine if the following system is time-invariant: y(n) = sign[x(n)]
Problem 2
We know that for a system to be stable in BIBO sense, we shall have the following property:
If the system’s x(n) is bounded, then the output y(n) shall be bounded as well. In other words, there
exist constants M x and M y such that
x (n)  M x    y (n)  M y  
Show that for an LTI system, the above condition is simplified as an “absolute summability” condition on
the impulse response of the system, h(n) , i.e.,

 h(k )  
k  
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CE 40763 – Assignment 1
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