(Solved):   4. A signal \( x(t) \) with Fourier Series given by \[ \omega_{o x}=1, C_{o x}=1.5, C_{k x ...

 

4. A signal \( x(t) \) with Fourier Series given by \[ \omega_{o x}=1, C_{o x}=1.5, C_{k x}=\frac{3}{|k|}, \quad k=\pm 1, \pm 2, \pm 3, \cdots \] is input to the system with impulse response \[ h(t)=4 e^{-4 t} u(t) \] a) Plot the snectrum of the input signal. \( \left|C_{i x}\right| \) rs \( k \); b) Determine the frequency response of the system; \( H\left(j k \omega_{0}\right) \) : what type of filter is this (highpass, lowpass, bandpass)? Fxplain: c) Give the Fourier Series for the output signal \( y(t) \), i.e., find \( \omega_{0 y} \) and a formula for the general coetficient \( C_{k y} \). Show and explain all work.