Communication Systems
EE380 – Communication Systems Spring 2012-2013
Section 1 – SET 1
Quiz Number 1 – Solutions
Closed Book; Closed Notes Time Given=10 minutes (Feb 14, 2013) “I certify that I have neither received nor given unpermitted aid on this examination and that I have reported all such incidents observed by me in which unpermitted aid is given.” Signature Name Student ID
Question 1: [4 points] Consider a linear time-invariant (LTI) system with impulse response h(t) whose Fourier transform is H(f ) = ∧(f ). Recall that ∧(f ) is non-zero only from f = −1 to f = +1. Find the output of the system if the input is: (a) x(t) = sin 0.5πt Solution: ∧(0.25) sin 0.5πt = 0.75 sin 0.5πt (b) x(t) = cos 10πt Solution: ∧(5) cos 10πt = 0 Question 2: [6 points] An input signal x(t) = sinc (4t) is applied to to an LTI system with impulse response h(t) = sinc (6t). Let the output of the LTI system is y(t). (a) What type of signal is x(t) ? Energy-type or Power-type? Solution: Energy-type (b) Find the energy or power of the input signal x(t)? Solution:
∞ −∞ 1 4 2
⊓
f 4
df =
1 4
(c) Find the energy or power of the signal y(t)? Solution: Y (f ) = H(f )X(f ) =
1 24
⊓
f 4
. Thus, Py =
1 2 24
×4=
1 144
(d) What is the time domain expression of y(t)?
1 Solution: y(t) = 6 sinc (4t) Question 3: [3 points] Draw ⊓ t−2 4
. Label all important points.
Solution: Box with height 1 and width 4 (from t = 0 to t = 4).
EE380 – Communication Systems Spring 2012-2013
Section 1 – SET 2
Quiz Number 1 – Solutions
Closed Book; Closed Notes Time Given=10 minutes (Feb 14, 2013) “I certify that I have neither received nor given unpermitted aid on this examination and that I have reported all such incidents observed by me in which unpermitted aid is given.” Signature Name Student ID
Question 1: [4 points] Consider a linear time-invariant (LTI) system with impulse response h(t) whose Fourier transform is H(f ) = ∧(f ). Recall that ∧(f ) is non-zero only from
Section 1 – SET 1
Quiz Number 1 – Solutions
Closed Book; Closed Notes Time Given=10 minutes (Feb 14, 2013) “I certify that I have neither received nor given unpermitted aid on this examination and that I have reported all such incidents observed by me in which unpermitted aid is given.” Signature Name Student ID
Question 1: [4 points] Consider a linear time-invariant (LTI) system with impulse response h(t) whose Fourier transform is H(f ) = ∧(f ). Recall that ∧(f ) is non-zero only from f = −1 to f = +1. Find the output of the system if the input is: (a) x(t) = sin 0.5πt Solution: ∧(0.25) sin 0.5πt = 0.75 sin 0.5πt (b) x(t) = cos 10πt Solution: ∧(5) cos 10πt = 0 Question 2: [6 points] An input signal x(t) = sinc (4t) is applied to to an LTI system with impulse response h(t) = sinc (6t). Let the output of the LTI system is y(t). (a) What type of signal is x(t) ? Energy-type or Power-type? Solution: Energy-type (b) Find the energy or power of the input signal x(t)? Solution:
∞ −∞ 1 4 2
⊓
f 4
df =
1 4
(c) Find the energy or power of the signal y(t)? Solution: Y (f ) = H(f )X(f ) =
1 24
⊓
f 4
. Thus, Py =
1 2 24
×4=
1 144
(d) What is the time domain expression of y(t)?
1 Solution: y(t) = 6 sinc (4t) Question 3: [3 points] Draw ⊓ t−2 4
. Label all important points.
Solution: Box with height 1 and width 4 (from t = 0 to t = 4).
EE380 – Communication Systems Spring 2012-2013
Section 1 – SET 2
Quiz Number 1 – Solutions
Closed Book; Closed Notes Time Given=10 minutes (Feb 14, 2013) “I certify that I have neither received nor given unpermitted aid on this examination and that I have reported all such incidents observed by me in which unpermitted aid is given.” Signature Name Student ID
Question 1: [4 points] Consider a linear time-invariant (LTI) system with impulse response h(t) whose Fourier transform is H(f ) = ∧(f ). Recall that ∧(f ) is non-zero only from