Assume the following LTI system where the input signal is an impulse train (i. e.,x(t)=∑(t−nT0)[infinity]n=−[infin ity].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||<3020otherise, where 0=2πT0.c)Sketch the magnitude and phase spectra of the output(|Y()|and∡Y()) if the system is a high-pass filter with H()={1||>5020otherise, where 0=2πT0.d)Sketch the magnitude and phase spectra of the outputif the system is a filter with H()=11+j.