6. Signal z(t) is a periodic CT signal with the Fourier series representation α(t) = Σαμecht k=0 where the Fourier serie

[answerhappygod]

1 (41.78 KiB) Viewed 45 times

6. Signal z(t) is a periodic CT signal with the Fourier series representation α(t) = Σαμecht k=0 where the Fourier series coefficients are given by 2 k=0 ax tka, otherwise 2 (a) Find and sketch the Fourier transform X(jw) for -4 <w < 4. (b) The signal x(t) is provided as input to an LTI system with the following impulse response h(t): sin(t) cos (41) h(t) = t Find the Fourier transform (w) of h(t). (Hint: You do not need to compute the FT integral here. Instead, express h(t) as the product of a sinc signal and cosine signal, then use the multiplication property of the Fourier transform.) (C) Let y(t) be the output of the LTI system when X(t) is provided as input. Use the relation Y (w) = X(w)(w) to find the spectrum Y(w) of the output. Also sketch the spectrum (d) By using your result in (c), find the time-domain representation y(t) = x(t)*h(t) of the output signal