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How to change x(t) to x(λ)

I want to make hilbert of x(t)=(t^2)+1 (Or other)
And I know x^(t)=1/ [FONT="]π[/FONT] [FONT="]∫(x(λ)/t-λ)dλ
but I don't know how to change x(t) to x(λ)
if any one can help me tell me
[/FONT]

Replies

  • silverscorpion
    silverscorpion
    That's a silly doubt.. It's all about the integration variable. ie, X(t) or X(s) or X(m), it's one and the same.

    If X(t) = t^2, then X(s) will be equal to s^2, X(m) is m^2 and so on..

    So, hilbert transform X^(t) = integral( (m^2/(t-m)) dm)

    Clear??
  • Hamed
    Hamed
    Thanks, this happen because I think [FONT="]λ is wave lenght then I got confiused.
    [/FONT]
  • Hamed
    Hamed
    I try but I can not find hilbert of e^(-t)
    Can you help me?

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