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In the system, the input signal is sampled by multiplying x(t) = cos(4000πt), s(t) = ∑ δ(t − k*Ts)(-∞ to +∞).
a. Calculate the Fourier transform X(jw) of the signal x(t).
b. By looking at X(jw), we can determine the sampling period Ts in the signal s(t) according to the Nyquist criterion.
c. Calculate the Fourier transform S(jw) of s(t).
d. Let z(t) = x(t). Calculate the Fourier transform Z(jw) of the signal z(t).
e. The z(t) signal is filtered using a low-pass filter with a cutoff frequency of 2000Ï€. Calculate the y(t) signal at the filter outlet.
f. The z(t) signal is filtered using a low-pass filter with a cutoff frequency of 4001Ï€. Then, the signal m(t) is obtained by multiplying it with the signal cos(2Ï€3000t). Calculate M(jw).
g. What is the bandwidth of M(jw)?