Question

I’m suppose to do some work with Fourier transformations and I’m still really confused.

I’m given a signal (in this case it is f[t] = sin(2 pi s t / N) where s = 8 and N = 128)

And I’m suppose to find the Real, Imaginary, Phase, and Magnitude.

I understand how to get the Real and Imaginary, but the Phase and the Magnitude are beyond me…

the sudo code for getting the Real and the Imaginary is:

for u = 0 to M-1 do
F[u].real = 0
F[u].imag = 0
for x = 0 to M-1 do
    F[u].real += f[x] * cos(- 2 * pi * u * x / M)
    F[u].imag += f[x] * sin(- 2 * pi * u * x / M)
end do
F[u].real /= M
F[u].imag /= M
end do

Now somewhere in there is the phase and the magnitude, but where?!

Thanks!

Also, some programmer-equse explination of the basics of FTs would be wonderful as well!

Answer 1

If you think to real and imaginary components as coordinates in an XY plane then the phase is the angle between the vector and the X+ axis, and the magnitude is the length of the vector.
To compute then you just need

magnitude = sqrt(real*real + imag*imag)
phase = atan2(imag, real)