# Math Help - Determine the signals

1. ## 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]= $\sum_{k=-infinty}^{n}x[k]$
Ans: Time Invariant,Linear and BIBO stable

c) y[n]= $\sum_{k=n-2}^{n+2} x[k]$
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

2. ## Re: Determine the signals

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?

3. ## Re: Determine the signals

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]= $\sum_{k=-infinty}^{n}x[k]$
Ans: Time Invariant,Linear and BIBO stable

c) y[n]= $\sum_{k=n-2}^{n+2} x[k]$
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