Assume the following LTI system where the input signal is an impulse train (i. e. , x(t) = ∑ (t − nT0) [infinity] n=−[infinity] . a) Find the Fourier series coefficient of x(t). Then find its Fourier transform and sketch the magnitude and phase spectra.
b) Sketch the magnitude and phase spectra of the output (i. e., |Y()|and ∡Y()) if the system is a low-pass filter with H() = { 1 || < 30 2 0 otherise , where 0 = 2π T0 .
c) Sketch the magnitude and phase spectra of the output if the system is a high-pass filter with H() = { 1 || > 50 2 0 otherise , where 0 = 2π T0 .
d) Sketch the magnitude and phase spectra of the output if the system is a filter with H() = 1 1+j.