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Math Help - Convolution operator

  1. #1
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    Convolution operator

    Give:
    f: Z --> R
    f(0) = -3
    f(1) = f(-1) = 2
    f(x) = 0, other wises.
    And the kernel K (1/4, 1/2, 1/4).
    How can we calculate f*K, where "*" is the convolution operator?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by le_su14 View Post
    Give:
    f: Z --> R
    f(0) = -3
    f(1) = f(-1) = 2
    f(x) = 0, other wises.
    And the kernel K (1/4, 1/2, 1/4).
    How can we calculate f*K, where "*" is the convolution operator?
    Take the definition of discrete convolution and plug in your values, there are
    at most 5 non zero values to be computed.

    RonL
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  3. #3
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    So:
    The first value: 0*1/4 + 0*1/2 + 2*1/4 = 1/2
    The second one: 0*1/4 + 2*1/2 + (-3)*1/4 = 1/4
    The third one: 2*1/4 + (-3)*1/2 + 2*1/4 = -1/2
    The 4th one: 0*1/4 + 2*1/2 + (-3)*1/4 = 1/4
    The last one: 2*1/4 + 0*1/4 + 0*1/2 = 1/2
    Is it right?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by le_su14 View Post
    So:
    The first value: 0*1/4 + 0*1/2 + 2*1/4 = 1/2
    The second one: 0*1/4 + 2*1/2 + (-3)*1/4 = 1/4
    The third one: 2*1/4 + (-3)*1/2 + 2*1/4 = -1/2
    The 4th one: 0*1/4 + 2*1/2 + (-3)*1/4 = 1/4
    The last one: 2*1/4 + 0*1/4 + 0*1/2 = 1/2
    Is it right?
    Looks OK to me (which means someone will come along and point out some
    minor error )

    RonL
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