Transcribed Text
6. Consider a discrete time linear timeinvariant system. The input to the system X [n] is
given by
n
x (n)=(2)nun) =
and the output of the system is ly[n] is given by
n

where u[n] is the unit step function.
a.
Determine the discrete time Fourier transform x(ejw) of the input x[n]
b. Determine the discrete time Fourier transform y(ejw) of the output y[n].
C. Determine a linear constant coefficient difference equation that describes this
system.
2. Consider the following signal X (t)
X (t) = 2 cos(6nt + 0) + 3 sin (8mt)
where 0 is a constant.
i.
Determine the fundamental period of x(t).
ii.
Express x (t) in the Fourier series representation of the form
8
x(>) E. = akelkwot
k=00
where wo is the fundamental frequency,
i.e., determine the Fourier series coefficients ak for all k.
3. Consider a discrete time periodic signal x[n] with period N = 4.
1,
n = 0,
X [n] =
1,
n = 1,
 1, n = 2,
1,
n = 3.
Determine the discrete time Fourier series coefficients for x[n]. Simplify your answer for
full score.
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