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Math Help - Determine the signals

  1. #1
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    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
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  2. #2
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    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?
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  3. #3
    Grand Panjandrum
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    Re: Determine the signals

    Quote Originally Posted by jonbrutal View Post
    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
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