How to change x(t) to x(λ)

Hamed

Hamed

@hamed-CMHhnw • Oct 22, 2024

I want to make hilbert of x(t)=(t^2)+1 (Or other)
And I know x^(t)=1/ [FONT=&quot]π[/FONT] [FONT=&quot]∫(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]

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  • silverscorpion

    silverscorpion

    @silverscorpion-iJKtdQ • May 21, 2009

    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??

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  • Hamed

    Hamed

    @hamed-CMHhnw • May 21, 2009

    Thanks, this happen because I think [FONT=&quot]λ is wave lenght then I got confiused.
    [/FONT]

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  • Hamed

    Hamed

    @hamed-CMHhnw • May 23, 2009

    I try but I can not find hilbert of e^(-t)
    Can you help me?

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