jk89
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Hello there! This is my first post, and I've got to say what a great forum you run here. Its helped me out many times before and for that I'm really grateful.
I have a problem with one of the Maths homeworks I've been set. The question has two parts the first part being:
If we have a function f(x) which is defined to be:
-e^(ax) for x<0
e^(-ax) for x>=0
Find its Fourier transformation with
f~(p) = (1/root(2*pi))*integral(f(x)*e^(-ipx)dx) in the limits of infinity and -infinity.
This part i think I've cracked, my answer is:
f~(p)=-(1/root(2*pi))*(2ip/(p^2+a^2)
Now then next step is a bit tricker:
2) Use the theory of Fourier transformations and your answer to the first part to determine the function g(x):
where g(x) is defined to be:
g(x) = integral((p*e^(ipx))/(p^2+a^2)dp) in the limits of infinity and -infinity.
By inspecting the integral i know that the Fourier transform of g(x) is:
g~(x) = p/(p^2+a^2)
However i can't seem to work it back from there any tips would be greatly appreciated but i don't want the full answer(spoils the fun!
)
Cheers!
I have a problem with one of the Maths homeworks I've been set. The question has two parts the first part being:
If we have a function f(x) which is defined to be:
-e^(ax) for x<0
e^(-ax) for x>=0
Find its Fourier transformation with
f~(p) = (1/root(2*pi))*integral(f(x)*e^(-ipx)dx) in the limits of infinity and -infinity.
This part i think I've cracked, my answer is:
f~(p)=-(1/root(2*pi))*(2ip/(p^2+a^2)
Now then next step is a bit tricker:
2) Use the theory of Fourier transformations and your answer to the first part to determine the function g(x):
where g(x) is defined to be:
g(x) = integral((p*e^(ipx))/(p^2+a^2)dp) in the limits of infinity and -infinity.
By inspecting the integral i know that the Fourier transform of g(x) is:
g~(x) = p/(p^2+a^2)
However i can't seem to work it back from there any tips would be greatly appreciated but i don't want the full answer(spoils the fun!
)Cheers!