ECE 561 Digital Communications Systems Homework #1 1. For the signal: x(t ) = Ae at u (t ), a > 0 a. Is x(t) an energy or power signal? Why? b. Find the energy or power for x(t). c. Find the energy or power spectral density for x(t) 2. For the signal: x(t
ECE 561 Digital Communications Systems MATLAB Tutorial #3 In this tutorial we will simulate a detector for a binary symbol set. We will start with a signal set for which a 1 is represented by a positive one volt pulse and a 0 is represented by a negative
ECE 561 Digital Communications Systems MATLAB Tutorial #4 In this tutorial we will: Generate Raised Cosine Pulses Generate Duobinary Pulses Create Eye Diagrams
Raised Cosine Pulses Construct the Simulink model shown below. The Raised Cosine Transmit Filte
ECE 561 Digital Communications Systems
Homework #7
1. A 16-ary PSK system has symbol error probability, PE = 10-5. Assume a Gray code is used
for the symbol to bit assignment.
a. What is the approximate bit error probability, PB? [Answer: PB = 2.5 10 6 ]
ECE 561 Digital Communications Systems
Homework #3
1. A random variable, X, is defined by the probability density function:
f X (x) = 2e2 x , x 0
a. What is the mean of X? [answer: ]
b. What is the cumulative distribution function FX(x)? [answer: 1 e2 x ]
ECE 561 Digital Communications Systems
Homework #8
1. For a noncoherently detected orthogonal FSK system, with a symbol duration of 1ms, what is
the minimum 90% power bandwidth for:
a. M = 2
b. M = 8
c. M = 16
2. For the coherent detection of a 100 bps BF
ECE 561 Digital Communications Systems
Homework #10
1. A 100Kbps data stream is to be transmitted on a 3 KHz bandwidth telephone line. Is it
possible to approach error free transmission with an Eb/No of 10dB?
2. What value of Eb/No (in dB) is required for
ECE 561 Digital Communications Systems
Homework #5
1. An analog signal is sampled, quantized, and transmitted over a channel with a maximum
bandwidth of 100 KHz using binary PCM.
a. If a rolloff factor of r = 0.6 is used, what is the maximum data rate in
ECE 561 Digital Communications Systems
Homework #1
1. For the signal: x(t) = Ae at u(t), a > 0
a. Is x(t) an energy or power signal? Why? [answer: energy signal]
b. Find the energy or power for x(t). [answer:
A2
]
2a
c. Find the energy or power spectral d
ECE 561 Digital Communications Systems
Homework #9
1. A transmitter has an output of 2W at 2GHz. Assume the transmitter and receiver antennas
are parabolic dishes 1 meter in diameter with efficiencies of 0.55.
a. Find the antenna gain in dB.
b. Calculate
ECE 561 Digital Communications Systems
Homework #4
1.
For the orthogonal signal set:
s1(t)
s2(t)
A
A
t
T/2
T/2
t
T
a. If s1 is applied to the correlator shown below, sketch the outputs r1 and r2 for 0 t
T.
s1
x
!0t
x
!0t
si
r1
r2
s2
r1(t)
A2T/2
Answer: r
ECE 561 Digital Communications Systems
Homework #6
1. A coherent ASK system is transmitting at 100K bps. The power spectral density of the
AWGN at the receiver is No/2 = 2.5 x 10-7 W/Hz. The amplitude of the received carrier (for
a 1) is 0.75V and the car
ECE 561 Digital Communications Systems MATLAB Tutorial #2 This tutorial describes the blocks in the Communications Blockset that are used for quantization and pulse modulation. In the first example we will simulate a uniform quantizer that has a range of
ECE 561 Digital Communications Systems MATLAB Tutorial #1 Assignments in this course contain problems that must be completed using MATLAB. A minimal knowledge of MATLAB is required to get started. Advanced MATLAB features will be introduced in tutorials p
ECE 561 Digital Communications Systems Homework #2 1. An information source has a 100 character alpha numeric message to transmit in 2 seconds using 7-bit ASCII coding with an eighth bit added for error detection. Calculate the bit rate and symbol rate fo
ECE 561 Digital Communications Systems Homework #3 1. A random variable, X, is defined by the probability density function:
f X ( x ) = 2 e2 x , x 0
a. What is the mean of X? b. What is the cumulative distribution function FX(x)? c. What is the probabilit
ECE 561 Digital Communications Systems Homework #4 1. An analog signal is sampled, quantized, and transmitted over a channel with a maximum bandwidth of 100 KHz using binary PCM. a. If a rolloff factor of r = 0.6 is used, what is the maximum data rate in
ECE 561 Digital Communications Systems Solutions for Homework #1 1. a. x 2 (t ) = A 2 e2 at u (t ) A 2 e2 at dt < energy signal
0
b. =
0
A 2 e2 at dt =
A2 2a A A2 2 x ( f ) = X( f ) = 2 a + j 2 f a + 4 2 f 2
c. From the table, X ( f ) =
2. a. b. Power si
ECE 561 Digital Communications Systems Solutions for Homework #2 1. 100 char * 8 bits/char = 800 bits bit rate = 800/2 = 400 bps in all cases a. 400bps/(1bit/sym) = 400 sym/sec b. 400bps/(2bit/sym) = 200 sym/sec c. 400bps/(3bit/sym) = 133.3 sym/sec d. 400
ECE 561 Digital Communications Systems Solutions for Homework #3 1. a. = b. FX ( x ) =
0
x 2 e2 x dx = . = 1 / 2
x
0
2 e2 x dx = . = 1 e2 x
c. P(0 x 1) = FX (1) = 1 e2 = 0.865 d. P(1 x 2 ) = FX (2 ) FX (1) = 1 e4 1 e2 = 0.117
(
)
2. From the given form of
ECE 561 Digital Communications Systems MATLAB Assignment #1 Turn in all commands, models, results, and output graphs for the problems below. 1. For the waveform, x(t) given in problem 2 of homework #1, use MATLAB from the Command Window to do the followi
ECE 561 Digital Communications Systems MATLAB Assignment #2 Turn in all commands, models, results, and output graphs for the problems below. 1. Create a Simulink model consisting of a Sine Wave (from the Signal Processing Blockset Sources), a Time Scope
ECE 561 Digital Communications Systems MATLAB Assignment #3 Part 1. Create a Simulink model similar to the one described in MATLAB Tutorial #3 to generate and detect 1Kbps information represented by the unipolar binary signal set:
s1 (t ) = 1; 0 t 1ms s2
ECE 561 Digital Communications Systems MATLAB Assignment #4 Part 1. Create a Simulink model that will generate a raised cosine waveform for a binary data stream. a. Generate a waveform for 20 randomly generated bipolar binary values with a data rate of 10
ECE 561 Digital Communications Systems Solution to MATLAB Assignment #1 1. a. > t=0:.01:3-.01; > x=cos(2*pi*t)+5*cos(4*pi*t); > plot(t,x)
b. > power=sum(x.^2)/length(x) power = 13.0000 c. > X=fft(x); > fs=1/.01; > deltaf=fs/length(x); > N=length(x); > p
ECE 561 Digital Communications Systems Solutions to MATLAB Assignment #2 1. a. On the Configuration parameters, set the Stop time to 1024*4/2200, Discrete, Fixed time step.
b.Change the Stop time to 1024*4/1500.
2. a.partition=[2:1:2]codebook=[2,1.5:1:1
ECE 561 Digital Communications Systems
Homework #2
1. An information source has a 100 character alpha numeric message to transmit in 2 seconds
using 7-bit ASCII coding with an eighth bit added for error detection. Calculate the bit rate
and symbol rate fo