How to calculate the STFT (by hand) of $$u(n)\cos(0.2\pi n)$$ for a rectangular window of a length 20, positioned at $n = 5$.
I know that to use STFT I need to divide longer signal to a shorter parts and than calculate Fourier Transform on each part. Also doing it from the definition is very long and I assume that there is a more efficient way to do it on paper.
I don't know how to start with the question so any materials on this topic are appreciated.
I came up with this idea:
First picture is just a rectangular window of length 20 and position 5. Second picture is how I see the STFT of it. Now to calculate STFT should I provide some coefficients like mainlobe width and highest sidelobe? How I can calculate them from my data?
Are my pictures good?