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EEM-306 Communication Systems
HW #1
(5 Questions)
1) Determine whether the following are “energy” or “power” signals. Accordingly, determine their energy or power values.
a. ()0001,220,TtTtwtTelse−<<=Π=
b. ()()00costwttTω=Π
c. ()()20coswttω=
d. ()23,10,twttelse>=

2) If a periodic signal is odd-symmetric (()()vtvt=−−), then its F.S. coefficients can be obtained as
()()020002sin2TncvtntTTπ=∫ dt
Use this expression to evaluate when nc()vtA= for 002tT<< and ()vtA=−
for 02Tt<0 T is the period. Evaluate the first few coefficients nc − < 0, where
(as magnitudes, and phases).
3) Given the signal ()()0512coswttω=+, where 0022f 0 ωπ π ==, obtain the autocorrelation ()wRτ and the spectral density ()wSf .
4) For a power signal, the time average operator is denoted and defined by
()()/2/21limTTTxtxT−→∞=∫ t dt
Consequently, the power is defined as
()2xPxt��
If powers of ()ut and ()vt are uP and , then Schwartz’s equality states that vP
()()2*vwvtwtPP≤ Eq. 1
We have already seen that
Eq. Q ()()0vvRRτ≤
Derive Eq. Q, starting from Eq. 1, by substituting ()()wtvtτ=−.

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