Dsp 2 - Signals in Matlab

8/2/2019 Dsp 2 - Signals in Matlab

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Fundamentals of Signals

Practical Signal Processing Conceptsand Algorithms using MATLAB


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Fundamental of Signals


What is signal Processing?

The scope of signal processing has grown so broad as toobviate a perfect and precise definition of what is entailed in it

Traditionally, signal processing includes the materials thought inDSP courses but now signal processing has greater reach

because of its influence on related disciplines such as controls,communications theory and also digital communication.

Thus, signal processing can be defined as that area of appliedmathematics that deals with operations on or analysis of signals,in either discrete or continuous time, to perform usefuloperations on those signals.


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Digital signal processing is the process of extracting usefulinformation from an incoming set of signal (sampled at regularinterval, Ts)

When you speak,your voice ispicked up by ananalog sensor inthe cell phonesmicrophone

An analog-to-

digital converterchip convertsyour voice(analog) intodigital signals,representing 1sand 0s

The Digital SignalProcessor (DSP)compresses thedigital signals andremove anynoise.

In the receivers

cell phone, adigital-to-analogconverter chipchanges thedigital signalback to ananalog voice

signal

Your voice exitsthe phonethrough thespeaker


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What is Signal Processing Toolbox?

The Signal Processing Toolbox is a collection oftools built on the MATLABnumeric computingenvironment.

The toolbox supports a wide range of signalprocessing operations, from waveformgeneration to filter design and implementation,parametric modeling, and spectral analysis.

The toolbox provides two categories of tools.


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Section Outline

Creating and importing signals

Sampling and re-sampling

Signal visualization

Modeling noise

Modulation


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Discrete Signals

Time base: t = [0.0 0.1 0.2 0.3];

Signal data: x = [1.0 3.2 2.0 8.5];

Creating vectors in MATLAB:

>> t = [0.0 0.1 0.2 0.3];

>> t = 0:0.1:0.3;

>> t = linspace(0, 0.3, 4);


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Sampling Signals

Analog signal sources

Electromagnetic, audio, sonar, biomedical

Sampling

)()( sa nTxnx

discretesignal

analogsignal

sampletime


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Aliasing

Ms ff 2Shannon Sampling Theorem:

Ms ff 2 Ms ff 2

Original signal and sampled

signal have same frequency

Sampled signal is aliased to

half the original frequency


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Signal Visualization

View signal amplitude vs. time index

Functions

plot, stem, stairs, strips

Listen to datasound


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Signal Processing Tool

>> sptool


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Importing a Signal

Choose Import under the File menu


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Since MATLAB is a programming language, an endless variety of differentsignals is possible. Here are some statements that generate severalcommonly used sequences, including the unit impulse, unit step, and unit

ramp functions:

>> t = (0:0.01:1);

>> y = ones(101); % step

>> y = [1; zeros(100,1)]; % impulse

>> y = t ; % ramp>> y = t.^2; % exponential

>> y = square(2*pi*4*t); % generates a square wave every 0.25secs.

Signal Processing BasicsCommon Sequences


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Waveform generation

>> y = sin(2*pi*50*t) + 2*sin(2*pi*120*t); %two sinusoids,%one at 50 Hz%and one at%120Hz with%twice the amplitude

>> plot(t,y) %plot y versus time

>> plot(t(1:50),y(1:50)) %display only the first%50 points(zoom!)


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Signal Browser


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Changing Sample Rates

To change the sample rate ofa signal in SPTool,

1. Click one signal in the

signals column of SPTool.2. Select Sampling Frequencyin the Edit menu.

3. Enter the desired samplingfrequency and click OK.


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Signal GenerationSignal Generation

Signals

Create a time base vector

>> t = [0:0.1:2];

Signal as function of time>> x = sin(pi*t/2);

Useful MATLAB Functions

Nonperiodic functions

ones, zeros, step

Periodic functions

sin, cos, square, sawtooth


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Non-periodic Signals

>> t = linspace(0,1,11)

Step

>> y = ones(11,1);

Impulse

>> y = [1;zeros(10,1)];

Ramp

>> y = 2*t;


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Sine Waves

Parameters

AmplitudeA

Frequencyf

Phase shift

Vertical offsetB

General form

BtfABftAy ))(2sin()2sin(


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Square Waves

>> sqw1 = square(2*pi*4*t);

>> sqw2 = square(2*pi*4*t,75);

Duty cycle is 50% (default)

Frequency is 4 Hz

Duty cycle is 75%

Frequency is 4 Hz


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Sawtooth Waves

>> saw1 = sawtooth(2*pi*3*t);

>> saw2 = sawtooth(2*pi*3*t,1/2);

Peak at end of cycle (default)

Frequency is 3 Hz

Peak halfway through cycle

Frequency is 3 Hz


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Complex Signals

x(t) = e j2ft= cos(2ft) +j sin(2ft) = cos(t) +j sin(t)

>> x = exp(2*pi*j*f*t);

Useful MATLAB Functions: real, imag, abs, angle

z-plane: ej Time domain: sin(t)

Fs/2 0,Fs


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textread

xlsread

imreadimportdata wavread

uiimport

input

Importing Data


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Modeling Noise with Random Data

>> un = -5+10*rand(1,1e6);

>> hist(un,100)

>> gn = 10+5*randn(1,1e6);

>> hist(gn,100)

Uniform Gaussian


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Adding Noise to a Signal

noisy signal = signal + noise

>> y1 = x + rand(size(x)) uniform noise

>> y2 = x + randn(size(x)) Gaussian noise


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Pseudorandomness

0.95012928514718

This is the first number produced by the MATLAB uniform randomnumber generator with its default settings. Is it random?

A random sequence is a vague notion ... in which each term isunpredictable to the uninitiated and whose digits pass a certain numberof tests traditional with statisticians ...

- D.H. Lehmer

>> rand('state',s) Sets the state to s.

>> rand('state',0) Resets the generator to its initial state.

>> rand('state',sum(100*clock)) New state each time.


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Resampling

Useful MATLAB functions

downsample, upsample, resample, interp, decimate


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Modulation and Demodulation

y = modulate(x,fc,fs,'fm')

x = demod(y,fc,fs,'fm')

Dsp 2 - Signals in Matlab

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