Thread: Determine the signals

Determine if each of the following systems is (i) memoryless (ii) invertible, (iii)
linear, (iv) time-invariant, (v) causal, and (iv) BIBO-Stable
a)y[n]=x[2n]
Ans:Invertible,Time Invariant,BIBO stable, Linear

b) y[n]=
Ans: Time Invariant,Linear and BIBO stable

c) y[n]=
Ans:TIme Invariant,Linear and BIBO stable.

I got the answers I think but I dont know how to explain. Can someone help for the explanation.

Thank you & regards

given y[n]=x[2n]

the value of y[n] does not depend upon the values of x[k] for k<n hence it is memoryless
x[n]=y[n/2] since x[n] can be expressed in terms of y[n] it is INVERTIBLE

for a function x1[n] the output is y1[n]=x1[2n]

for a function x2[n] the output is y2[n]=x2[2n]

consider a function x3[n]=x1[n]+x2[n]
the output is y3[n]=x3[2n] = x1[2n]+x2[2n] = y1[n]+y2[n]
since for a function x1[n]+x2[n] the output is y1[n]+y2[n] it is LINEAR

for a function x[n] the output is y[n]=x[2n]
consider function x1[n]=x[n-t] the output y1[n]=x[2(n-t)]
if u delay the function y[n] by t u get x[2n-t] since they both are not equal it is NOT TIME INVARIANT

since the value of y[n] depends upon the future values of x[n] it is NOT CASUAL

if we give a bounded input x[n] for all values of n then x[2n] is also bounded so is y[n] hence it is BIBO STABLE


Is this corrct for question a?

Originally Posted by jonbrutal

Determine if each of the following systems is (i) memoryless (ii) invertible, (iii)
linear, (iv) time-invariant, (v) causal, and (iv) BIBO-Stable
a)y[n]=x[2n]
Ans:Invertible,Time Invariant,BIBO stable, Linear

b) y[n]=
Ans: Time Invariant,Linear and BIBO stable

c) y[n]=
Ans:TIme Invariant,Linear and BIBO stable.

I got the answers I think but I dont know how to explain. Can someone help for the explanation.

Thank you & regards

Posting multiple choice questions looks like posting assessed work.

CB