The Fourier transform of a triangular window function Windowing functions are explained on Wikipedia and they include plots of the Fourier transform for several windowing functions. For the triangle window  they provide

The above Fourier transform plot has a horizontal axis that goes from -40 bins to +40 bins, so this seems to be a discrete Fourier transform. However, I don't get a plot like that when I apply an FFT to 80 samples of a triangular window. I am further confused in that the graphic of the Fourier transform looks like a continuous plot rather than 80 discrete samples.

My questions are:
How does one create the plot for the Fourier transform of a triangular window?
Is the plot for a continuous Fourier transform or discrete Fourier transform?
Not the perfect fit, but a quick-and-dirty base to play on:

%nBin = 81;
nBin = 2049;

y=(20*log(fftshift(abs(fft(triang(81),nBin)))))';
x = linspace(-40,40,length(y));
basey = min(0,min(y));
ShadingColor = [0 0 1];
h = fill([x x(end) x(1)], [y basey basey], ShadingColor); 
set(h, 'EdgeColor','none', 'FaceAlpha', 0.5);