UNIVERSITY OF SOUTH AFRICA

SCHOOL OF ENGINEERING

CONTINUOUS ASSESSMENT

Practical

.

Year Course

DSPPRA4

Digital Signal Processing IV (Practical)

Examiner: Mr. W.D Govender Moderator: Mr. W.D Govender

External Moderator: Mr. K. Naidoo Marks: 100

Weight of Assessment: 80%

INSTRUCTIONS TO ALL STUDENTS:

1. Plagiarism is the act of taking words, ideas and thoughts of others and presenting it as your own. It is a form of theft which involves a number of dishonest academic activities.

2. Your answer to each task attempted should commence on a new page, be spaced out adequately and be appropriately numbered.

3. Read the questions carefully.

4. Pay careful attention to the allocated marks.

5. Your practical report must be submitted to Turnitin. (The details for this will be posted on the course website)

6. After submitting this practical, there will be a short oral presentation where you will be asked questions about the practical and asked to demonstrate your working code. This presentation will be done using the Microsoft Teams where you will be able to share your screen. (You will have to book a timeslot which will be posted on your course website)

Welcome to the School of Engineering.

A Few Important Notes

For this practical, a personal computer is required as computer programs will have to be written. The computer language or simulation tools to use are solely the students choice.

The following list will give you an idea of what computer simulation tools are available on the market. Some of them are free and others are expensive.

Tools Type of license Platform

Matlab Commercial PC/Unix/M

ac -

Matlab (Student version) Commercial PC/Unix/M

ac Most Universities (±R300) (RAU)

Mathcad Commercial PC/Mac -

SciLab - matrixbased scientific software package GNU Unix Internet -

Octave - MATLAB lookalike GNU Unix Internet -

ftp.che.utexas.edu/pub/octave

R-Lab - MATLABlike matrixoriented programming language GNU Unix Internet -

evans.ee.adfa.oz.au /pub/RLaB

• SciLab, Octave and R-Lab are available on the internet for the Linux version of Unix.

• Normal C, Pascal or Basic could also be used.

I suggest that you use Octave for this practical, due to its similarity to Matlab and its builtin functions which can be easily utilised.

THE PRACTICAL

INTRODUCTION

This subject is at the B-Tech level. This assignment comprises of the practical work required for the subject Digital Signal Processing IV (Practical). Do not underestimate the amount of time you will need to spend absorbing the requirements and completing the practical work.

WHAT IS EXPECTED

This aim of this practical is to give you an opportunity to obtain a practical understanding of the theory learnt in DSP4701. This should be considered when attempting the practical.

Experience has shown that students often submit the minimum amount of work in these practical’s and obtain minimum marks. This is not an exam, but rather a practical assignment.

The following is what I expect to see in your report:

? Clear indication of the tasks you have chosen (numbered as the Tasks are).

? Structure according to the practical template given.

? A clear writing style that lays out your thoughts and understanding.

? Your thought process while doing the practical in the form of bullet points, algorithms, and/or flow diagrams.

? Calculations where necessary.

? Well commented code.

? Well labelled diagrams and waveforms.

? Screenshots of waveforms.

? Screenshots of results where applicable.

? Discussions of results obtained.

? A reference list (references according to the IEEE format)

Do not flood your report with endless, unnecessary theory. At this level, I expect your work to be well documented.

STRUCTURE

This assignment consists of eight tasks altogether. From these eight, you must choose four according to the following:

? For Task 1 you must choose between Task 1A and Task 1B

? For Task 2 you must choose between Task 2A and Task 2B

? For Task 3 you must choose between Task 3A and Task 3B

? For Task 4 you must choose between Task 4A and Task 4B

SUBMITTION OF WORK

Your practical must be submitted on the course website on or before the due date. The Turnitin report of your practical must be attached to your report and sent. Failure to do so will result in a zero mark.

OTHER IMPORTANT POINTS TO NOTE:

? Your code must be copied and pasted into your report. Your code must not be a screenshot or entered as a picture into the report.

? Plagiarism of any sort will automatically result in your practical being marked out of 50% of the total mark and you will face disciplinary action.

TASKS TO BE COMPLETED CAN BE FOUND ON THE FOLLOWING PAGES

• Task 1: Page 5 • Task 2: Page 6

• Task 3: Page 7

• Task 4: Page 8

Task 1

Task 1A - Find the DFT and IDFT of a given DT signal

1A.1.

1A.2.

Write a computer program to determine the DFT and IDFT of a signal. The following sequence must be used when writing your program:

Given the DT sequence: x = [1 2 3 4 5]

The DFT result to be obtained: X = 15, -2.50+3.44i, -2.50+0.81i, -2.49-0.81i, -2.493.44i

The following must be included as part of your results:

? A labelled plot of the input sequence

? Labelled plots of the magnitude and phase response of your filter

? A plot of the IDFT of the sequence

? A short discussion of your results

Use your code from 1A.1. to determine the 8-point the DFT and IDFT of the signal:

x = [1 2 3 4 4 3 2 1]

(Submit a screenshot of the answer obtained) [20]

[5]

[25]

Task 1B - Find the FFT and IFFT of a given sequence

1B.1.

1B.2.

Write a computer program to determine the FFT and IFFT of a signal. The following sequence must be used when writing your program:

Given the sequence: x = [1 2 3 4 5]

The FFT result to be obtained: X = 15, -2.50+3.44i, -2.50+0.81i, -2.49-0.81i, -2.493.44i

The following must be included as part of your results:

? A labelled plot of the input sequence

? Labelled plots of the magnitude and phase response of your filter

? A plot of the IFFT of the sequence

? A screenshot of the FFT result obtained

? A short discussion of your results

Use your code from 1B.1. to determine the 8-point DFT of the signal:

x = [1 2 1 2 3 4 4 3]

(Submit a screenshot of the answer obtained)

[20]

[5]

[25]

Task 2

Task 2A - Linear Convolution of Two Sequences

2A.1. Write a computer program to determine the Linear Convolution of two finite length

sequences. The following sequence must be used when writing your program: Given the sequences: ??1 = [1 2 3 4 5] and ??2 = [5 8 3 5 4 6] The linear convolution that should be obtained is: ?? = [5 18 34 55 80 81 59 59 44 30]

The following must be included as part of your results: ? A screenshot of the answer you have obtained

? Labelled plots of the waveforms for ??1, ??2 and ??

? A discussion of your results [20]

2A.2.

Find the linear convolution of ??1 = [7 5 4 0] and ??2 = [0 3 6 2 9] (Submit a screenshot of the answer obtained) [5]

[25]

Task 2B – Auto Correlation of Two Sequences

2B.1.

Write a computer program to determine the Auto Correlation between two sequences. The following sequence must be used when writing your program:

Given the sequence: ?? = [1 2 3 4]

The answer that should be obtained is: ?? = [3.99, 11, 20, 30, 20, 11, 3.99]

The following must be included as part of your results: ? A screenshot of the answer you have obtained

? Labelled plots of the waveforms for ?? ?????? ??

? A discussion of your results

[20]

2B.2. Find the auto correlation function of a parabolic sequence for 0 = ?? = 5. [5]

[25]

Task 3

Task 3A – Implementation of LP FIR Filter

Design a LP FIR Filter and implement your design by writing a computer program.

Your design must have the following specifications:

? Use the Window method

? You may choose any of the Window functions – Refer to Annexure B for the data of different window functions

? Length of window (N) = 20

? Pass-band frequency = 200

? Stop-band frequency =300

? Sampling frequency = 1000

The following must be included as part of your results:

? Labelled plots of the magnitude and phase response of your filter

? A discussion of your results

[25]

Task 3B – Implementation of HP FIR Filter

Design a HP FIR Filter and implement your design by writing a computer program.

Your design must have the following specifications:

? Use the Window method

? You may choose any of the Window functions – Refer to Annexure B for the data of different window functions

? Length of window (N) = 20

? Pass-band frequency = 300

? Stop-band frequency =200

? Sampling frequency = 1000

The following must be included as part of your results:

? Labelled plots of the magnitude and phase response of your filter

? A discussion of your results

[25]

Task 4

Task 4A – Implementation of LP IIR Filter

Design a LP IIR Filter and implement your design by writing a computer program.

Your design must have the following specifications:

? Passband ripple = 15

? Stopband ripple = 60

? Passband frequency = 1500

? Stopband frequency = 3000

? Sampling frequency = 7000

The following must be included as part of your results:

? Labelled plots of the magnitude and phase response of your filter

? A discussion of your results

[25]

Task 4B – Implementation of HP IIR Filter

Design a HP IIR Filter and implement your design by writing a computer program.

Your design must have the following specifications:

? Passband ripple = 15

? Stopband ripple = 60

? Passband frequency = 1500

? Stopband frequency = 3000

? Sampling frequency = 7000

The following must be included as part of your results:

? Labelled plots of the magnitude and phase response of your filter

? A discussion of your results

[25]

ANNEXURE A

1. POLICY FOR PRACTICAL ASSIGNMENTS

a) All experiments must be performed.

b) To receive a pass mark, the student needs to receive a sub-minimum of 50%.

c) All students must have their own practical guide and components.

d) Every student must do his/her own practical, however students are allowed to receive help in a constructive manner.

e) Practical experiments must be built by the student himself/herself and the relevant answers supplied on the respective answer sheet for that experiment.

f) Use standard symbols and notation, as used in the theoretical notes and practical guide, on the answer sheet.

g) Where applicable, the construction of your practical assignment will be evaluated on the following criteria: I. neatness.

II. correct layout of components.

III. correct wiring techniques.

IV. correct operation of circuit.

V. students knowledge of the circuit; and VI. insight into the practical work.

h) All the experiments need to be certified by the students mentor (see the form attached), as the students own work. Refer to paragraph 3 for the very important information regarding the appointment of your mentor.

i) Students need to take every safety precaution (especially where the experiment involves 220V and 380-V alternating current). UNISA cannot be held responsible for any damage to equipment or harm to any person. In cases where the student is in doubt about any safety aspect, contact Unisa for assistance.

2. INTERACTION WITH THEORETICAL WORK

You are advised to conduct the experiments only after the relevant theory has been covered.

3. APPOINTMENT OF MENTOR

Your mentor plays a very important role in the successful completion of your assignment. The functions of your mentor are the following:

o help you in a constructive manner and o verify that it is your own work.

Your mentor should thus be appointed in order to fulfil the above-mentioned task.

Your mentor must preferably be professionally registered with ECSA (Engineering Counsel of South Africa) for us to accredit his authorisation of your work. If the person acting as your mentor is not registered with ECSA, then someone who is professionally registered with ECSA, should also authorise your assignment. The mentor must supply his particulars as requested on the authorisation form attached to each experiment, for us to accept his authorisation.

ANNEXURE B

Figure 1: Showing data for window functions

| P a g e

SCHOOL OF ENGINEERING

CONTINUOUS ASSESSMENT

Practical

.

Year Course

DSPPRA4

Digital Signal Processing IV (Practical)

Examiner: Mr. W.D Govender Moderator: Mr. W.D Govender

External Moderator: Mr. K. Naidoo Marks: 100

Weight of Assessment: 80%

INSTRUCTIONS TO ALL STUDENTS:

1. Plagiarism is the act of taking words, ideas and thoughts of others and presenting it as your own. It is a form of theft which involves a number of dishonest academic activities.

2. Your answer to each task attempted should commence on a new page, be spaced out adequately and be appropriately numbered.

3. Read the questions carefully.

4. Pay careful attention to the allocated marks.

5. Your practical report must be submitted to Turnitin. (The details for this will be posted on the course website)

6. After submitting this practical, there will be a short oral presentation where you will be asked questions about the practical and asked to demonstrate your working code. This presentation will be done using the Microsoft Teams where you will be able to share your screen. (You will have to book a timeslot which will be posted on your course website)

Welcome to the School of Engineering.

A Few Important Notes

For this practical, a personal computer is required as computer programs will have to be written. The computer language or simulation tools to use are solely the students choice.

The following list will give you an idea of what computer simulation tools are available on the market. Some of them are free and others are expensive.

Tools Type of license Platform

Matlab Commercial PC/Unix/M

ac -

Matlab (Student version) Commercial PC/Unix/M

ac Most Universities (±R300) (RAU)

Mathcad Commercial PC/Mac -

SciLab - matrixbased scientific software package GNU Unix Internet -

Octave - MATLAB lookalike GNU Unix Internet -

ftp.che.utexas.edu/pub/octave

R-Lab - MATLABlike matrixoriented programming language GNU Unix Internet -

evans.ee.adfa.oz.au /pub/RLaB

• SciLab, Octave and R-Lab are available on the internet for the Linux version of Unix.

• Normal C, Pascal or Basic could also be used.

I suggest that you use Octave for this practical, due to its similarity to Matlab and its builtin functions which can be easily utilised.

THE PRACTICAL

INTRODUCTION

This subject is at the B-Tech level. This assignment comprises of the practical work required for the subject Digital Signal Processing IV (Practical). Do not underestimate the amount of time you will need to spend absorbing the requirements and completing the practical work.

WHAT IS EXPECTED

This aim of this practical is to give you an opportunity to obtain a practical understanding of the theory learnt in DSP4701. This should be considered when attempting the practical.

Experience has shown that students often submit the minimum amount of work in these practical’s and obtain minimum marks. This is not an exam, but rather a practical assignment.

The following is what I expect to see in your report:

? Clear indication of the tasks you have chosen (numbered as the Tasks are).

? Structure according to the practical template given.

? A clear writing style that lays out your thoughts and understanding.

? Your thought process while doing the practical in the form of bullet points, algorithms, and/or flow diagrams.

? Calculations where necessary.

? Well commented code.

? Well labelled diagrams and waveforms.

? Screenshots of waveforms.

? Screenshots of results where applicable.

? Discussions of results obtained.

? A reference list (references according to the IEEE format)

Do not flood your report with endless, unnecessary theory. At this level, I expect your work to be well documented.

STRUCTURE

This assignment consists of eight tasks altogether. From these eight, you must choose four according to the following:

? For Task 1 you must choose between Task 1A and Task 1B

? For Task 2 you must choose between Task 2A and Task 2B

? For Task 3 you must choose between Task 3A and Task 3B

? For Task 4 you must choose between Task 4A and Task 4B

SUBMITTION OF WORK

Your practical must be submitted on the course website on or before the due date. The Turnitin report of your practical must be attached to your report and sent. Failure to do so will result in a zero mark.

OTHER IMPORTANT POINTS TO NOTE:

? Your code must be copied and pasted into your report. Your code must not be a screenshot or entered as a picture into the report.

? Plagiarism of any sort will automatically result in your practical being marked out of 50% of the total mark and you will face disciplinary action.

TASKS TO BE COMPLETED CAN BE FOUND ON THE FOLLOWING PAGES

• Task 1: Page 5 • Task 2: Page 6

• Task 3: Page 7

• Task 4: Page 8

Task 1

Task 1A - Find the DFT and IDFT of a given DT signal

1A.1.

1A.2.

Write a computer program to determine the DFT and IDFT of a signal. The following sequence must be used when writing your program:

Given the DT sequence: x = [1 2 3 4 5]

The DFT result to be obtained: X = 15, -2.50+3.44i, -2.50+0.81i, -2.49-0.81i, -2.493.44i

The following must be included as part of your results:

? A labelled plot of the input sequence

? Labelled plots of the magnitude and phase response of your filter

? A plot of the IDFT of the sequence

? A short discussion of your results

Use your code from 1A.1. to determine the 8-point the DFT and IDFT of the signal:

x = [1 2 3 4 4 3 2 1]

(Submit a screenshot of the answer obtained) [20]

[5]

[25]

Task 1B - Find the FFT and IFFT of a given sequence

1B.1.

1B.2.

Write a computer program to determine the FFT and IFFT of a signal. The following sequence must be used when writing your program:

Given the sequence: x = [1 2 3 4 5]

The FFT result to be obtained: X = 15, -2.50+3.44i, -2.50+0.81i, -2.49-0.81i, -2.493.44i

The following must be included as part of your results:

? A labelled plot of the input sequence

? Labelled plots of the magnitude and phase response of your filter

? A plot of the IFFT of the sequence

? A screenshot of the FFT result obtained

? A short discussion of your results

Use your code from 1B.1. to determine the 8-point DFT of the signal:

x = [1 2 1 2 3 4 4 3]

(Submit a screenshot of the answer obtained)

[20]

[5]

[25]

Task 2

Task 2A - Linear Convolution of Two Sequences

2A.1. Write a computer program to determine the Linear Convolution of two finite length

sequences. The following sequence must be used when writing your program: Given the sequences: ??1 = [1 2 3 4 5] and ??2 = [5 8 3 5 4 6] The linear convolution that should be obtained is: ?? = [5 18 34 55 80 81 59 59 44 30]

The following must be included as part of your results: ? A screenshot of the answer you have obtained

? Labelled plots of the waveforms for ??1, ??2 and ??

? A discussion of your results [20]

2A.2.

Find the linear convolution of ??1 = [7 5 4 0] and ??2 = [0 3 6 2 9] (Submit a screenshot of the answer obtained) [5]

[25]

Task 2B – Auto Correlation of Two Sequences

2B.1.

Write a computer program to determine the Auto Correlation between two sequences. The following sequence must be used when writing your program:

Given the sequence: ?? = [1 2 3 4]

The answer that should be obtained is: ?? = [3.99, 11, 20, 30, 20, 11, 3.99]

The following must be included as part of your results: ? A screenshot of the answer you have obtained

? Labelled plots of the waveforms for ?? ?????? ??

? A discussion of your results

[20]

2B.2. Find the auto correlation function of a parabolic sequence for 0 = ?? = 5. [5]

[25]

Task 3

Task 3A – Implementation of LP FIR Filter

Design a LP FIR Filter and implement your design by writing a computer program.

Your design must have the following specifications:

? Use the Window method

? You may choose any of the Window functions – Refer to Annexure B for the data of different window functions

? Length of window (N) = 20

? Pass-band frequency = 200

? Stop-band frequency =300

? Sampling frequency = 1000

The following must be included as part of your results:

? Labelled plots of the magnitude and phase response of your filter

? A discussion of your results

[25]

Task 3B – Implementation of HP FIR Filter

Design a HP FIR Filter and implement your design by writing a computer program.

Your design must have the following specifications:

? Use the Window method

? You may choose any of the Window functions – Refer to Annexure B for the data of different window functions

? Length of window (N) = 20

? Pass-band frequency = 300

? Stop-band frequency =200

? Sampling frequency = 1000

The following must be included as part of your results:

? Labelled plots of the magnitude and phase response of your filter

? A discussion of your results

[25]

Task 4

Task 4A – Implementation of LP IIR Filter

Design a LP IIR Filter and implement your design by writing a computer program.

Your design must have the following specifications:

? Passband ripple = 15

? Stopband ripple = 60

? Passband frequency = 1500

? Stopband frequency = 3000

? Sampling frequency = 7000

The following must be included as part of your results:

? Labelled plots of the magnitude and phase response of your filter

? A discussion of your results

[25]

Task 4B – Implementation of HP IIR Filter

Design a HP IIR Filter and implement your design by writing a computer program.

Your design must have the following specifications:

? Passband ripple = 15

? Stopband ripple = 60

? Passband frequency = 1500

? Stopband frequency = 3000

? Sampling frequency = 7000

The following must be included as part of your results:

? Labelled plots of the magnitude and phase response of your filter

? A discussion of your results

[25]

ANNEXURE A

1. POLICY FOR PRACTICAL ASSIGNMENTS

a) All experiments must be performed.

b) To receive a pass mark, the student needs to receive a sub-minimum of 50%.

c) All students must have their own practical guide and components.

d) Every student must do his/her own practical, however students are allowed to receive help in a constructive manner.

e) Practical experiments must be built by the student himself/herself and the relevant answers supplied on the respective answer sheet for that experiment.

f) Use standard symbols and notation, as used in the theoretical notes and practical guide, on the answer sheet.

g) Where applicable, the construction of your practical assignment will be evaluated on the following criteria: I. neatness.

II. correct layout of components.

III. correct wiring techniques.

IV. correct operation of circuit.

V. students knowledge of the circuit; and VI. insight into the practical work.

h) All the experiments need to be certified by the students mentor (see the form attached), as the students own work. Refer to paragraph 3 for the very important information regarding the appointment of your mentor.

i) Students need to take every safety precaution (especially where the experiment involves 220V and 380-V alternating current). UNISA cannot be held responsible for any damage to equipment or harm to any person. In cases where the student is in doubt about any safety aspect, contact Unisa for assistance.

2. INTERACTION WITH THEORETICAL WORK

You are advised to conduct the experiments only after the relevant theory has been covered.

3. APPOINTMENT OF MENTOR

Your mentor plays a very important role in the successful completion of your assignment. The functions of your mentor are the following:

o help you in a constructive manner and o verify that it is your own work.

Your mentor should thus be appointed in order to fulfil the above-mentioned task.

Your mentor must preferably be professionally registered with ECSA (Engineering Counsel of South Africa) for us to accredit his authorisation of your work. If the person acting as your mentor is not registered with ECSA, then someone who is professionally registered with ECSA, should also authorise your assignment. The mentor must supply his particulars as requested on the authorisation form attached to each experiment, for us to accept his authorisation.

ANNEXURE B

Figure 1: Showing data for window functions

| P a g e

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