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  1. Which one is a linear system?

    2. A.
    y[n] = x[n] x x[n - 1]
    B.
    y[n] = x[n] + x[n - 10]
    C.
    y[n] = x2[n]
    D.
    (a) and (c)

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    Answer : Option B

    Explanation :

    For linearity

    y1[n] = x1[n] + x2[n - 10] ...(1)

    y2 = x2[n] + x2[n - 10] ...(2)

    y1[n] = x1[n] + x2[n] + x2[n - 10] + x2[n - 10] ...(3)

    Now find y1[n] + y2[n]

    Corresponding to x1[n] + x2[n]

    It is same as equation (3) hence linear.

    But in part (c) y[n] = x2[n]

    ⇒ y1[n] = x21[n], y2[n] = x22[n]⇒ y1[n] + y2[n] = x22[n]...3

    But y1[n] + y2[n]

    Corresponing x1[n] + x2[n] is y1[n] + y2[n] = {x1[n] + x2[n]}2

    = x12[n] + x22[n] + 2x1[n] x2[n]....4

    Equations (3) and (4) are not same hence not linear.

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