Electronic – calculate FFT based on an oscillogram

fftfourieroscilloscoperectifier

derrzet
derrzet

Hi,

I'd like to understand the context in between an oscillogramm and the resulting FFT. My example is a full-wave rectifier and I am try to calculate some harmonics.

Because the function is symmetric I only need to calculate the an-values:
$$
A_n = a_n = \frac{2}{\pi}\int_0^{2\pi} \! f(t) * cos(nt) \, \mathrm{d}t \\
a_n = \frac{2}{\pi}\int_0^{2\pi} \! |sin(t)| * cos(nt) \, \mathrm{d}t
$$
dividing up for integrating
$$
a_n = \frac{2}{\pi} \left( \int_0^{\pi} \! sin(t) * cos(nt) \, \mathrm{d}t + \int_{\pi}^{2\pi} \! (-sin(t)) * cos(nt) \, \mathrm{d}t \right) \\
$$
result of the integral
$$
a_n = \frac{2}{\pi} \left( -\frac{cos(\pi n) + 1}{n^2 – 1} – \frac{cos(2\pi n) + cos(\pi n)}{n^2 – 1} \right)
$$
My question is whether my way was right up to here and how I have to transfer this into the fft?

Best Answer

If it helps, you have a sine wave multiplied by a square wave added to a phase shifted sine wave multiplied by another phase shifted square wave.

Addition translates to addition in fourier space, multiplication maps to convolution.

So what you're going to get is the FT of a square wave shifted along the w axis and with an imaginary component, I think.