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(Solved): Exercise 6 Consider the signal x(t)=cos(\pi t)+2cos(4\pi t) The signal is sampled to obtain the sign ...
Exercise 6 Consider the signal
x(t)=cos(\pi t)+2cos(4\pi t)The signal is sampled to obtain the signal
x[n]=x(nT)with Fourier transform
x(e^(j\omega )). a) (5 pt) What is the minimum sampling frequency
\omega _(s)=(2\pi )/(T)that can be used to avoid aliasing? In the following questions assume that the sampling frequency is
6\pi b) (10 pt) Sketch the Fourier transform
x(e^(j\omega ))of
x[n](or
x_(T)(\omega )). c) (10 pt) The signal, sampled with sampling frequency is
\omega _(s)=6\pi , is reconstructed with an ideal reconstruction filter with
H(j\omega )={(3,|\omega |<3\pi ),(0 otherwise ):}Find an expression for the output
y(t)of the filter.
