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ECE 461/561-001: Communication Systems Design: Min Max

This document is a midterm exam for an ECE 461/561 communication systems design course. It contains 6 questions testing concepts related to modulation techniques, Fourier analysis, and signal processing. Specifically, it asks students to analyze signals in the time and frequency domains, calculate Fourier transforms and Fourier series coefficients, determine modulation indices, and characterize amplitude modulated signals and their spectra. The exam is open book and must be submitted through the course's online learning platform by 3:30pm on January 28, 2021.

Uploaded by

Zhenyu Huo
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140 views5 pages

ECE 461/561-001: Communication Systems Design: Min Max

This document is a midterm exam for an ECE 461/561 communication systems design course. It contains 6 questions testing concepts related to modulation techniques, Fourier analysis, and signal processing. Specifically, it asks students to analyze signals in the time and frequency domains, calculate Fourier transforms and Fourier series coefficients, determine modulation indices, and characterize amplitude modulated signals and their spectra. The exam is open book and must be submitted through the course's online learning platform by 3:30pm on January 28, 2021.

Uploaded by

Zhenyu Huo
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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ECE 461/561-001: Communication Systems Design

Winter 2021 Midterm Exam 1

1/28/2021 14:00 – 15:15

D2L Dropbox close at 15:30

Name: PSU ID#:

1. (4pts) Please answer the following questions.

(a) Envelope detection is used in __________.


a: DSB-SC demodulation c: DSB-SC modulation
b: Conventional AM demodulation d: Conventional AM modulation

(b) The condition for Conventional AM modulation is ___________.

a: A  min s ( t ) c: modulation index ma  1

b: A  max s ( t ) d: modulation index ma  1

(c) Which statement is TRUE for Single Side-Band modulation?

a: SSB signal  ( t ) is complex c: SSB increases bandwidth efficiency

b: SSB decreases power efficiency d: SSB cannot be used for LC

(d) The advantage of DSB-SC AM over Conventional AM is __________.

a: Less bandwidth used in channel c: Less power consumed in the transmitter


b: Less complexity in receiver design d: None of above
2. (Impulse -- 2pts) Calculate the following expressions by using the properties of delta function:

a) 
−
cos( t ) (4t + 1)dt =

b) [e−t + cos(10 t )] (3t − 6) =

3. (Fourier Transform – 7pts) A signal x(t ) is given as:

sin( t )
x(t ) = sin c(t ) =
t

a) Please sketch x(t ) .

Sketch here: ________________________

b) Please calculate the Fourier transform X ( f ) of x(t ) .

X ( f ) = _______________________________________

c) Please sketch the magnitude spectrum of | X ( f ) | , and sketch line spectrum of phase spectrum of
X ( f ) .

_____________________________________ _____________________________________

| X( f )| X ( f )
d) If x1 (t ) = sin c(t − 1) , please calculate the Fourier transform X1 ( f ) of x1 (t )

X1 ( f ) = _______________________________________

e) Please sketch the magnitude spectrum of | X1 ( f ) | , and sketch line spectrum of phase spectrum of
X1 ( f ) .

_____________________________________ _____________________________________

| X1 ( f ) | X1 ( f )

4. (Fourier Series – 6pts) For a periodic signal x(t ) = 5sin(2 t ) + 3 , please

a) Find the period of the signal T ;

T=

b) Does this signal have DC energy? Yes: ___ No: ___

c)Find the Complex Exponential Fourier Series coefficients Cn of x(t ) (hint: may consider using Euler
identity).

1 T
T 0
d) Calculating the normalized power Px = | x(t ) |2 dt .

Px =
e) Please sketch the magnitude spectrum of | Cn | , and sketch line spectrum of phase spectrum of Cn .

_____________________________________ _____________________________________

| Cn | Cn

5. (Amplitude Modulation, 6 points) An USB-AM signal is generated by modulating a 2-kHz carrier


by the message signal 𝑠(𝑡) = 20𝑐𝑜𝑠(10𝜋𝑡) − 5 𝑐𝑜𝑠(6𝜋𝑡).The carrier power is 5 kW.

a) Determine 𝑠(𝑡) is energy signals, power signals, or neither. please show your brief proof.

b) Determine the signal sˆ(t ) .

c) Write an expression for the USB-AM signal.

d) Determine and sketch the amplitude spectrum of the USB-AM signal.


e) Compare the PEP and the normalized average power of the USB-AM signal

6. (0 pts) Comments:

Have Fun!

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