(800) 434-2582
Call Now!Franchise Info

Get Math Help

GET TUTORING NEAR ME!

By submitting the following form, you agree to Club Z!'s Terms of Use and Privacy Policy

    Home / Get Math Help

    Fourier Transform

    Result

    1/sqrt(2 π) integral_(-∞)^∞ (e^(-t^2) sin(t)) e^(i w t) dt = -1/2 i (e^(-1/4 (w + 1)^2)/sqrt(2) - e^(-1/4 (w - 1)^2)/sqrt(2))

    Plots

    Plots

    Plots

    Alternate forms

    (i e^(-1/4 (w + 1)^2) (e^w - 1))/(2 sqrt(2))

    -(i e^(-1/4 (w - 1)^2 - 1/4 (w + 1)^2) (e^(1/4 (w - 1)^2) - e^(1/4 (w + 1)^2)))/(2 sqrt(2))

    Expanded form

    (i e^(-1/4 (w - 1)^2))/(2 sqrt(2)) - (i e^(-1/4 (w + 1)^2))/(2 sqrt(2))

    Alternate form assuming w is real

    (i (1/(e^((w - 1)^2))^(1/4) - 1/(e^((w + 1)^2))^(1/4)))/(2 sqrt(2))

    Trigonometric transform

    ℱ_t[e^(-t^2) sin(t)](w) = i (ℱ_t^s[e^(-t^2) sin(t)](w))

    sqrt(2/π) integral_0^∞ (e^(-t^2) sin(t)) sin(w t) dt = (e^(-1/4 (w + 1)^2) (e^w - 1))/(2 sqrt(2))

    Find the right fit or it’s free.

    We guarantee you’ll find the right tutor, or we’ll cover the first hour of your lesson.