Computer Program 3 for Analog and Digital Communication | ECGR 4123 | Study Guides, Projects, Research Electrical and Electronics Engineering

ECGR 4123/5191

Computer Problem #3

Due 10/28/04

For the project an individual write-up is required for each student. NOTE: working together is encourage,

but each student must submit their own work. Use a word processor such as MS Word to develop the write

up. Matlab Command line script or script files should be provided in the write up as well as Matlab figures.

Examples of this are illustrated in this assignment. Straight forward method for doing this is to use

Cut/Paste feature, placing script file in a MS Word Text Box.

{For the following problems you will need to use the function dtft (discrete time Fourier

transform) which can be obtained from the class website, dtft.m}

1) Examine the effects of a LPF on a rectangular pulse. Modify ECGR4123_CP_3a.m to

examine

     

txthty 

where

 















t

recttx

and

 

is a LPF designed using

Matlab’s “butter” function. Butter.m generates filter coefficients based on Butterworth filter

design constraints. Important Matlab functions used in the script file are: butter and freqz.

a) First examine the frequency response of the filter. What is the 3dB bandwidth of the

filter, i.e., the frequency at which the filter response is 3dB down from its maximum?

b) Next examine

 

and

 

in both the time domain and the frequency domain for

   

trecttx 100

. What is the 95% essential bandwidth for

 

c) Repeat (b) for

   

trecttx 10

d) Repeat (b) for

   

trecttx 500

2) Examine the effects of linear distortion on the transmission of a signal. Let the transmitted

signal be

       

 2txtxtxtr

where

 















t

recttx

{ i.e., Matlab code: r =

rectpuls(t,tau)-rectpuls(t-tau,tau)+rectpuls(t-2*tau,tau)) }. Given the communication channel

is modeled with

 

(as in part (1)), then investigate the effect of the channel on the

received signal,

 

, for

5001,0101,101

Answer the following based on your observations. Provide sufficient number of graphs to

support your analysis:

a) Compare and contrast the received signal for the different values of



b) If the linear system was representative of a communication system where

 

was the

impulse response of the channel: discuss the implications for each of the three received

signals.

3) The following example examines filtering signals. The signal to be examined is a train

whistle. The signal is part of Matlab and can be load as follows:

load train

sound(y,Fs)

where sound(y,Fs) plays the signal y based on sampling frequency Fs.

a) Provide graphs of the train whistle in the time domain and frequency domain make sure

to scale the axes correctly. Based on the Fourier analysis, identify the frequency of the 4th

highest peak amplitude.

b) Design a LPF which will reduce the power in the 4th peak by 50%, while minimizing the

distortion of the power in the first three peaks.

c) Provide time and frequency graphs of the filtered signal.

d) If you have access to headset or speakers, briefly comment on the sound of the signal

before and after filtering.

Partial preview of the text

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ECGR 4123/

Computer Problem

Due 10/28/

For the project an individual write-up is required for each student. NOTE: working together is encourage, but each student must submit their own work. Use a word processor such as MS Word to develop the write up. Matlab Command line script or script files should be provided in the write up as well as Matlab figures. Examples of this are illustrated in this assignment. Straight forward method for doing this is to use Cut/Paste feature, placing script file in a MS Word Text Box. {For the following problems you will need to use the function dtft (discrete time Fourier transform) which can be obtained from the class website, dtft.m}

Examine the effects of a LPF on a rectangular pulse. Modify ECGR4123_CP_3a.m to

examine y ^^ t ^  h^ ^ t ^  x ^ t where ^ ^ 

x t rect and h  t  is a LPF designed using

Matlab’s “butter” function. Butter.m generates filter coefficients based on Butterworth filter design constraints. Important Matlab functions used in the script file are: butter and freqz. a) First examine the frequency response of the filter. What is the 3dB bandwidth of the filter, i.e., the frequency at which the filter response is 3dB down from its maximum?

b) Next examine x ^^ t  and y^ ^ t  in both the time domain and the frequency domain for

x  t   rect  100 t . What is the 95% essential bandwidth for x  t ?

c) Repeat (b) for x ^^ t ^  rect ^10 t 

d) Repeat (b) for x ^^ t ^  rect ^500 t 

Examine the effects of linear distortion on the transmission of a signal. Let the transmitted

signal be r^ ^ t ^ ^ x ^ t ^  x ^ t ^  x ^ t ^2 where ^ ^ 

t x t rect { i.e., Matlab code: r = rectpuls(t,tau)-rectpuls(t-tau,tau)+rectpuls(t-2*tau,tau)) }. Given the communication channel

is modeled with h ^^ t  (as in part (1)), then investigate the effect of the channel on the

received signal, y ^^ t , for ^ ^110 ,^1100 ,^1500.

Answer the following based on your observations. Provide sufficient number of graphs to support your analysis:

a) Compare and contrast the received signal for the different values of ^.

b) If the linear system was representative of a communication system where h ^^ t was the

impulse response of the channel: discuss the implications for each of the three received signals.

The following example examines filtering signals. The signal to be examined is a train whistle. The signal is part of Matlab and can be load as follows: load train sound(y,Fs) where sound(y,Fs) plays the signal y based on sampling frequency Fs. a) Provide graphs of the train whistle in the time domain and frequency domain make sure to scale the axes correctly. Based on the Fourier analysis, identify the frequency of the 4th highest peak amplitude. b) Design a LPF which will reduce the power in the 4th^ peak by 50%, while minimizing the distortion of the power in the first three peaks. c) Provide time and frequency graphs of the filtered signal. d) If you have access to headset or speakers, briefly comment on the sound of the signal before and after filtering.

Computer Program 3 for Analog and Digital Communication | ECGR 4123, Study Guides, Projects, Research of Electrical and Electronics Engineering

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Partial preview of the text

Download Computer Program 3 for Analog and Digital Communication | ECGR 4123 and more Study Guides, Projects, Research Electrical and Electronics Engineering in PDF only on Docsity!

ECGR 4123/

Computer Problem

Due 10/28/

examine y ^^ t ^  h^ ^ t ^  x ^ t where ^ ^ 

x t rect and h  t  is a LPF designed using

b) Next examine x ^^ t  and y^ ^ t  in both the time domain and the frequency domain for

x  t   rect  100 t . What is the 95% essential bandwidth for x  t ?

c) Repeat (b) for x ^^ t ^  rect ^10 t 

d) Repeat (b) for x ^^ t ^  rect ^500 t 

signal be r^ ^ t ^ ^ x ^ t ^  x ^ t ^  x ^ t ^2 where ^ ^ 

is modeled with h ^^ t  (as in part (1)), then investigate the effect of the channel on the

received signal, y ^^ t , for ^ ^110 ,^1100 ,^1500.

a) Compare and contrast the received signal for the different values of ^.

b) If the linear system was representative of a communication system where h ^^ t was the