Could we assume the given inverse Fourier transform property on homeworks?
motoole2
I'm not positive if this is what you're asking, but let me give this a shot. If F(k) is the Fourier transform of f(x), you can assume that the inverse Fourier transform of F(k) is f(x).
friendlygrape
Maybe this was already covered, but why is the continuous fourier transform equation positive infty to negative infty and not the other way around?
motoole2
Oops---this is indeed a typo. Thanks for pointing this out! It should be an integral from negative infty to positive infty. That is
$F(k) = \int_{-\infty}^{\infty} f(x) e^{-j2\pi k x} dx$ (Fourier transform)
Could we assume the given inverse Fourier transform property on homeworks?
I'm not positive if this is what you're asking, but let me give this a shot. If F(k) is the Fourier transform of f(x), you can assume that the inverse Fourier transform of F(k) is f(x).
Maybe this was already covered, but why is the continuous fourier transform equation positive infty to negative infty and not the other way around?
Oops---this is indeed a typo. Thanks for pointing this out! It should be an integral from negative infty to positive infty. That is
$F(k) = \int_{-\infty}^{\infty} f(x) e^{-j2\pi k x} dx$ (Fourier transform)
and
$f(k) = \int_{-\infty}^{\infty} F(x) e^{j2\pi k x} dx$ (inverse Fourier transform)