DFT from Fourier transform I always studied the DFT starting from his formula, but for some reasons I need to do comparison between the FT and the DFT. I found the pdf in this link very useful http://www.robots.ox.ac.uk/~sjrob/Teaching/SP/l7.pdf because it explains how the DFT can be obtained starting from the FT.
After the first formula it says " We could regard each sample f[k] as an impulse having area f[k]". What I don't understand is how it possible that the sample, being an impulse, has an area f[k]. Shouldn't t have an area f[k] multiplied by a very low number? This passage for me is crucial because I cannot understand why, passing from the FT to the DFT, the time increment disappears.
The area under an impulse function is one. So if you multiply a continuous time waveform with an impulse, the result will be a weighted impulse with the area equal to whatever the waveform was at that moment in time.