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MNP/CE00039-2/Signal Processing / Sem1 2008

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Faculty of Engineering & Advanced

Technology

Signal Processing

CE00039-2

LABORATORY ASSIGNMENT

Module Tutors:

Dr Alison Carrington & Dr Mohammad Patwary

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GENERAL INTRODUCTION

Introduction

Three laboratory assignments are presented in this document. These laboratory based

assignments are weighted as 50% of the overall mark for the module. The final examination

is weighted as 50%.

Module Learning Outcomes

Learning Outcome

1. Demonstrate fundamental understanding of Signal Processing.Knowledge &

Understanding

2. Apply appropriate analytical techniques to critically evaluate signals and

their processing

Analysis

Learning

3. Use simulation models and the key analytical skills to critically evaluate

results and relate them to theory.Application

4. Communicate Ideas Effectively. Communication

The laboratory based assignments will assess learning outcomes 3 and 4 and based on a

Formal Report including Background Research, Data Analysis, Discussion &

Recommendations, and Matlab model and simulation.

The criteria and formats are explained later in this document.

Marks allocation and feedback sheets are attached at the end of this document. Copies should

be attached to your work. Students are expected to present a detailed analysis of results and

comparison with theory.

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General Objective

The aim of this assignment is to allow the student to develop an in-depth understanding of the

technical components of a Analogue and Digital signal processing.

For guidance throughout the assignment, see your module tutor, Dr Alison Griffiths or Dr

Mohammad Patwary.

Assessment Criteria

Laboratory Log Book (optional)

Maintaining a useful laboratory log book is an important skill and should:

a) be an accurate record of the work done and the results;

b) give traceability for the work done;

c) form the basis of any report which may be written subsequently, ie it should be a clear,

stand alone record, with comments and a brief conclusion, from which any report could

easily be written without having to repeat any of the work;

d) be written up while you are in the laboratory, ie within the 3 hour session, not from bitsof paper after you have left the laboratory; this only wastes your time;

The laboratory log book should be a bound A4 notebook or a loose leaf binder. You are

expected to provide your own log book and graph paper etc.

The front page should show:

YOUR NAME

MODULE CODE and TITLE

LECTURER'S NAME

LABORATORY SUPERVISOR'S NAME

Each laboratory assignment should be headed with :

DATE - on which the work was done,

TITLE - of the assignment,

NAMES - your name and names of the people present in your sub-group for that

assignment.

Laboratory sheets should be inserted, stapled in if necessary. Log book entries should be

clear, concise and legible.

It will be useful if you store your exercise models, as they can be used in this assignment.

Handing-In Dates

Final submission deadlines are shown on the assignment front sheet attached to this

assignment. Laboratory sessions will be on a timetabled rota with all sessions completed by

the end of week 11 (normally). The majority of the log book record should be written up

while you are in the laboratory. The formal report may be handed-in as soon as you have

written it, along with the log book, but no later than the final submission deadlines given.

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Work handed in after the set deadlines is not acceptable and will be awarded zero marks. If

there is a valid reason for late submission, the procedure for extenuating circumstances must

be followed which includes the requirement for documentary evidence (eg a medical

certificate if illness was the reason). See your student handbook. Extenuating Circumstances

claim forms may be obtained from the Faculty Office. The work may be accepted if the

reason is considered to be sufficient justification.

Work submitted for assessment which is not your own work (i.e. copied) will be disqualified

and awarded zero marks.

Assignment Front Sheet

A standard assignment front sheet is attached, this must be attached to the front of your work

andmust be easily visible to the administration staff and the module tutors.

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Faculty of Computing, Engineering and Technology

Module Name: Signal Processing

Module Number : CE00039-2Title of Assignment : Analogue to Digital and Digital to Analogue conversion of signals

andMatlab SimulationModule Learning Outcomes for This Assignment

1. Demonstrate critical understanding of signal processing Knowledge andUnderstanding

2. Apply appropriate analytical techniques to critically evaluate signals andtheir processing

Analysis

3. Use equipment and simulation models and the analytic skills to criticallyevaluate results and relate them to theory.

Application

4. Communicate ideas effectively. Communication

Hand in deadline : 16th

December 2008

Assignment descriptionImplement your solution using MATLAB. A formal report should explain and justify your design and results

obtained. Include m-files as an appendix to the main report. Reference all information sources.

% of

mark

Criterion Unsatisfactory Threshold Good Excellent

25 Research ideas

and concepts

using a variety ofinformation

sources

Little relevant

research. Few

items referenced.Poor

understanding of

the topic

Research

information

related to theproblem domain

Research and

evaluate

informationrelated to the

problem domain

Initiate and

undertake searches

for informationrelated to the

problem domain,

evaluate it andrecommend

actions based on

the information

25 Design the

required solution

Incomplete

methodology.

Poor

understanding ofthe problem

Design using

routine

techniques

Design to fulfill

the specified

requirement

Innovative design

to fulfill the

specified

requirement

35 Use MATLAB to

implement the

solution

Poor or

inappropriate use

of MATLAB

Use MATLAB to

implement an

algorithmrelevant to theproblem

Use MATLAB to

implement the

design solution

Use MATLAB to

implement the

design solution,analyse andevaluate its use

15 Effective written

communication

Poor reporting,

unstructured, little

communication of

technicalinformation

Clear

communication of

technicalinformation

Coherent

communication

using technicallanguage

accurately

Professional

presentation using

technical languagefluently

Table 1- Assessment Criteria

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INTRODUCTION

This laboratory uses the simulation package, MatlabTM

and SimulinkTM

.

Quantizing a Signal

This section shows how theQuantizing Encoderand Quantizing Decoderblocks use the partition andcodebook parameters.

Scalar Quantization Example 1

The figure below shows how theQuantizing Encoderblock uses the partition and codebook asdefined above to map a real vector to a new vector whose entries are either -1, 0.5, 2, or 3. In theScope window, the bottom signal is the quantization of the (original) top signal.

To build the model, gather and configure these blocks:

Signal From Workspace,

in the Signal P rocessing Blockset DSP Sources library. The output signal samples obtained from theMATLAB workspace at successive sample times. A signal matrix is interpreted as having onechannel per column. Signal columns be buffered into frames by sepecfiying a number of sample perframe greater than 1.

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SetSignal to [-2.4,-1,-.2,0,.2,1,1.2,1.9,2,2.9,3,3.5]'.

Quantizing Encoder

The Quantizing Encoder block quantizes the input signal according to the Partition vector and

encodes the input signal according to the Codebook vector. The input signal can be either a scalar ora vector. This block processes each vector element independently.

The first output is the quantization index. The second output is the quantized signal. The values forthe quantized signal are taken from the Codebook vector.

The Quantization partition parameter, P, is a real vector of length n whose entries are in strictlyascending order.

The Quantization codebook parameter, whose length is n+1, prescribes a value for each partition inthe quantization. The first element of Quantization codebook is the value for the interval betweennegative infinity and the first element of P. The second output signal from this block contains thequantization of the input signal based on the quantization indices and prescribed values.

You can use the function lloyds in the Communications Toolbox with a representative sample of yourdata as training data, to obtain appropriate partition and codebook parameters

SetQuantization partition to [ 0, 1, 3] .

SetQuantization codebook to [ - 1, 0. 5, 2, 3] .

Terminator

In the Simulink Sinks library. The Terminator block can be used to cap blocks whose output ports arenot connected to other blocks. If you run a simulation with blocks having unconnected output ports,Simulink issues warning messages. Using Terminator blocks to cap those blocks avoids warningmessages

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Scope In the Simulink Sinks library

o After double-clicking the block to open it, click theParameters icon and setNumberof axes to 2.

Connect the blocks as shown in the figure. Also, from the model window's Simulation menu, chooseConfiguration parameters; then in the Configuration Parameters dialog box, set Stop time to 12.Running the model produces a scope image similar to the one above. (To make the axis ranges andtitle exactly match those in the figure, right-click each plot area in the scope and selectAxesproperties.)

Scalar Quantization Example 2

This example, shown in the figure below, illustrates the nature of scalar quantization more clearly. Itsamples and quantizes a sine wave and then plots the original (top) and quantized (bottom) signals.The plot contrasts the smooth sine curve with the polygonal curve of the quantized signal. The verticalcoordinate of each flat part of the polygonal curve is a value in theQuantization codebook vector.

To open the completed model, clickhere in the MATLAB Help browser. To build the model, gatherand configure these blocks:

Sine Wave, in the Simulink Sources library (not the Sine Wave block in the Signal ProcessingBlockset DSP Sources library)

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Zero-Order Hold, in the Simulink Discrete library.

The Zero-Order Hold block samples and holds its input for the specified sample period. Theblock accepts one input and generates one output, both of which can be scalar or vector. Ifthe input is a vector, all elements of the vector are held for the same sample period.

You specify the time between samples with the Sample time parameter. A setting of -1 meansthe Sample time is inherited.

This block provides a mechanism for discretizing one or more signals in time, or resamplingthe signal at a different rate. If your model contains multirate transitions, you must add Zero-Order Hold blocks between the fast-to-slow transitions. The sample rate of the Zero-OrderHold must be set to that of the slower block. For slow-to-fast transitions, use the Unit Delayblock. For more information about multirate transitions, refer to the Simulink or the Real-TimeWorkshop documentation.

o SetSample time to 0. 1.

Quantizing Encoder

o SetQuantization partition to [ - 1: . 2: 1] .

o SetQuantization codebook to [ - 1. 1: . 2: 1. 1] .

Terminator, in the Simulink Sinks library

Scope, in the Simulink Sinks library

o After double-clicking the block to open it, click theParameters icon and setNumberof axes to 2.

Connect the blocks as shown in the figure. Also, from the model window's Simulation menu, chooseConfiguration parameters; then in the Configuration Parameters dialog box, set Stop time to2*pi . Running the model produces the scope image as shown above. (To make the axis ranges andtitle exactly match those in the figure, right-click each plot area in the scope and selectAxesproperties.)

Determining Which Interval Each Input Is in

The Quantizing Encoder block also returns a signal, at the first output port, that tells which intervaleach input is in. For example, the model below shows that the input entries lie within the intervals

labeled 0, 6, and 5, respectively. Here, the 0th interval consists of real numbers less than or equal to3; the 6th interval consists of real numbers greater than 8 but less than or equal to 9; and the 5thinterval consists of real numbers greater than 7 but less than or equal to 8.

To open the completed model, click here in the MATLAB Help browser. To build the model, gatherand configure these blocks:

Constant, in the Simulink Sources library

o SetConstant value to [ 2, 9, 8] .

Quantizing Encoder

o SetQuantization partition to [ 3, 4, 5, 6, 7, 8, 9] .

o SetQuantization codebook to any vector whose length exceeds the length ofQuantization Partition by one.

Terminator, in the Simulink Sinks library

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Display, in the Simulink Sinks library

o Drag the bottom edge of the icon to make the display big enough for three entries.

Connect the blocks as shown above. Also, from the model window's Simulation menu, chooseConfiguration parameters; then in the Configuration Parameters dialog box, set Stop time to 10.Running the model produces the display numbers as shown in the figure.

You can continue this example by branching the first output of the Quantizing Encoder block,connecting one branch to the input port of theQuantizing Decoderblock, and connecting the output ofthe Quantizing Decoder block to another Display block. If the two source coding blocks'Quantizationcodebook parameters match, then the output of the Quantizing Decoder block will be the same asthe second output of the Quantizing Encoder block. Thus the Quantizing Decoder block partiallyduplicates the functionality of the Quantizing Encoder block, but requires different input data andfewer.

Assignment Problem set 1:

Construct the following model

Quantizing Encoder (8 levels):

o SetQuantization partition to [ 0. 5, 1. 5, 2. 5, 3. 5, 4. 5, 5. 5, 6. 5] .

o SetQuantization codebook to [ 0, 1, 2, 3, 4, 5, 6, 7] .

You are required to:

Develop the specified model Simulate the performance of the model in Matlab Simulink

Construct and analyze the model for different quantization levels (4, 8, and 16)

Plot the quantization error for different quantization levels Calculate the theoretical performance and compare

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Assignment Problem set 2:

An analogue cosine signal of frequency 50Hz is given by A=cos(2*3.14*50*t). Consider a

signal time span of 0.50sec and sampling frequency of 1000Hz during analogue to digital

conversion of the signal.

You are required to:

Generate the given analogue signal with Matlab script and plot it.

Using Matlab script, convert the discrete time signal into digital considering 8quantization levels.

Generate bar charts for all digitized bits within one figure window. ( plot MSB chartfirst).

Using Matlab script, reconstruct the analogue signal from the digital signals.

Using Matlab script, estimate the quantization error.

Generate a figure that will compare the given analogue signal, reconstructed signaland the quantization error.

Assignment Outcomes

Section 1:

Write a standard technical report (of around but not limited to 1500 words), to outline your

research findings and outline your recommendations.

Section 2:

Print out the complete Simulink model and Matlab code is to be electronically submitted, i.e.

on a CD.

Submission Format

The report structure is to include: Abstract, Contents, Introduction, Research, Theory,

Simulation, Results, Discussion, Conclusion and References. A second copy of the report is

to be electronically submitted on a CD.

Documents

CE00039_2_cwk_0809