I'm new to the discrete Fourier Transform and have managed to do a few examples by hand, (for example the Fourier Transform of $\sin(x)$). I now want to try the transform on signals that are made up of more than one constituent frequency, for example: $\sin(x)+\sin(2x)$.
I understand the basics of the DFT but have never worked with signals made up of more than one frequency, so I'm not sure how to actually go about it. I have a code for an FFT that can do this for me, but I want to learn to do it manually as well.
Thanks in advance :)