2
Given the Fourier series of a periodic discrete time sequence x[n] are
C<sub>k</sub> = cos(k?/4)+ sin(3k?/4), and the period of x[n] is 8, please compute x[n].
Sol: x[n]= 4?[n+1]+4?[n-1]-4j?[n+3]+4j?[n-3]
3
Given the input signal of a system is x[n] = \(\left(\frac{1}{2}\right)^{n-2}\)u[n-2], the unit sampling
response is h[n] = u[n+2], try to compute the response of the system by convolution
sum y[n].
Sol: y[n] = 2\left[1-\left(-\frac{1}{2}\right)^{n+1}\right]u[n]
4 Given a signal x(t) = \frac{sin 4?t}{?t}, -? < t < ?. Determine the maxim sampling period
for this signal T<sub>max</sub>.
Sol:
X(?) = \begin{cases} 1(\left|?\right| < 4?) \\ 0(\left|?\right| > 4?) \end{cases}
T<sub>max</sub> = \frac{?}{4?} = \frac{1}{4} (s)
