(10 points)\n(a) The output of an operator is y(t)=x(t)2cos(2\\pi f_(0)t), where x(t) is its input. y(t) is the input to a linear\ntime-invariant operator with impulse response h(t) and the output denoted as z(t). Write the expression\nfor the impulse response and evaluate the frequency-domain kernel function for the cascade of these two\noperators.\n(b) Find the Fourier spectrum of z(t),Z(f), if the Fourier spectrum of x(t) is x(f).\n(c) Let f_(0)=1000Hz,\nx(f)={(1-(|f|)/(100),|f|<100Hz),(0, otherwise ):}\nand\nH(f)=F{h(t)}={(1,|f-f_(0)|<50Hz),(1,|f+f_(0)|<50Hz),(0, otherwise. ):}\nFind and plot Z(f).
2. (10 points)
a) The output of an operator is y(t) = (t)2cos(2fot), where (t) is its input. y(t) is the input to a linear time-invariant operator with impulse response h(t) and the output denoted as z(t). Write the expression for the impulse response and evaluate the frequency-domain kernel function for the cascade of these two operators.
b) Find the Fourier spectrum of z(t), Z(f), if the Fourier spectrum of (t) is X(f)
c) Let fo =1000 Hz
Xf
0,
otherwise
and
1,|f-fo|<50 Hz 1. f+fo<50Hz otherwise.
Hf=F{ht}=
Find and plot Z(f)