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))
Plot
Alternate form
(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 e^(-2 (w^2 + 1)) (e^((w + 1)^2) (e^((w - 1)^2))^(3/4) - e^((w - 1)^2) (e^((w + 1)^2))^(3/4)))/(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))