I have seen many times that people gets the frequency response function using DTFT. Can I use the Fourier series, and when I do that?
Examining a physical phenomena (expressed as a mathematical function) in the frequency domain can be very fruitful sometimes. In case you are capable to perfectly express your function mathematically, i.e. by writing down an analytical function, you can manually use a Fourier series to find the amplitudes of any specific frequency. However, this is a mathematical approach which is quite irrelevant to the most of engineering tasks. Since you probably do not know exactly what you are looking for, trying to analyze what is going on will be very tedious this way. More often, you find yourself with a lot of recorded digital data you would like to analyze. You will be interested to find the dominant frequencies (by which the amplitude is the largest) and will be glad to obtain a plot showing you all the data arrange along the frequency axis. This is exactly what DFT (or FFT and etc,,) does.