SIGNALS AND ACQUISITION

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What is “signal”? Patterns of variations that carry

information Financial data:

Change of $ against time

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What is “signal”? Patterns of variations that carry

information Variation (Earthquake)

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What is “signal”? Patterns of variations that carry

information Heart beat

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What is “signal”? Patterns of variations that carry

information Speech signal

Variations of air pressure in the vocal tract Signal representation: 1D x(t): function: varies with time

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What is “signal”? Patterns of variations that carry

information Image:

Change of color/intensity f(x,y) x, y: spatial coordinates Intensity changes with the spatial positions

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Signals and Electricity

wave

change of voltage

mic

Light

Lens

CCD

Object

change of voltage

Signals can convert to other physical form, e.g., electricity

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Microphones

Acoustic to electric transducer Sensor: converts sound into an electrical

signal Different types of microphone have

different ways of converting energy but they all share one thing in common: The diaphragm. a thin piece of material (such as paper, plastic or

aluminum) which vibrates when it is struck by sound waves.

In a typical hand-held mic, the diaphragm is located in the head of the microphone

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Microphone

When the diaphragm vibrates, it causes other components in the microphone to vibrate. These vibrations are converted into an electrical current which becomes the audio signal.

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diaphragm vibratesCoil move backward and forward past the magnetCreates a voltage

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1. Speak create sound waves (vibration in the air)

2. Inside the microphone: diaphragm: moves back and forth when the sound

waves hit it

3. Coil: attached to the diaphragm Moves back and forth

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4. magnet: produces a magnetic field.coil moves back and forth through the magnetic field an electric current flows

5. electric current flows out from the microphone

• To an amplifier / sound recording device

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Characteristics of signals

Speech signals Time variant Most signal structures change smoothly,

not abruptly Quasi-periodic in individual segments. In

other segments, has the temporal structure of noise

Pauses in the course of the speech signal

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Images

Image: variation of light intensity or rate of reflection as a function of position on a plane

Image capture: Convert info contained in an image to

corresponding signals that can be stored in a reproducible way

Sensor: conversion device Convert to electronic signals

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Images

Need a memory device to store the captured image data

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Case 3: Images

Sensors are produced on silicon wafers(30 to 50 units per wafer)

Let’s see how a pixel of image sensor looks like

Let’s see how a pixel of image sensor looks like

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15 cm

Zooming on the sensor makes the pixels visible

0.5 millimeters

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Working principle Photodiode

Works in much the same way as a solar cell

Uses two differently charged elements to chemically dope silicon wafers to create a N-type and P-type semiconductor

Light hits the semiconductor Allow free electrons to move from

N0Type to P-Type: create a current The strength of light determines

how much electricity is produced20

Color Images?

Sensor color: Color filter is put on the surface of every pixel Only the specific color of light can go thru the

filter

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Red color filter only passes red light

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Color images

Every photodiode: can only sense one color of a pixel

Need: Red, Green, Blue colors 4 photodiodes with different color filters

to compose one pixel Color Filter array (CFA)

Each two-by-two photodiodes contains 2 green, 1 blue and 1 red filter, each covering one pixel sensor

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Color images

The raw image data captured by sensor Convert to a full color image by a so-

called demosaicing algorithm

Bayer CFA

Color images

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Characteristics of signals Images

Two-dimensional Magnitude changing in spatial position Not periodic generally Abrupt changes + smooth regions

Edge -abrupt change in magnitude

Smooth region

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Summary

Different kinds of signals Speech, ECG, image

Natural signals – not artificially synthesized by human Acquire by different devices Speech (air pressure) – microphones

(electro-mechanical device) Image (light) – photodiodes

(optoelectronic device)

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Summary

Different signals Different characteristics Speech: quasi-periodic, noisy Image: 2D, smooth region + abrupt

changes region Need different tools for analyzing,

processing and recording these signals Mathematical Representation of Signals

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Signals

Speech: propagate with time varying magnitude

x(t)

x: a symbol represents this signal

t: a real number variable which refers to time

x(t) is the magnitude of the signal x received at time t, e.g. x(0) = 0; x(70.5) = -90.5; x(100.25) = 80

t = 100.25

t = 70.5t = 0

Sound: sum of sinusoidal waves at different frequencies

Water sound wave

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Why Sinusoids?

Interested in sinusoidal signals Signals that have their magnitude

changed according to a sine function In 1807, a famous mathematician, Joseph

Fourier, showed that

Almost all signals can be constructed by the summation of sinusoids of different frequencies, amplitudes and phase shifts

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Sinusoids almost all signals can be constructed

by sinusoidal signals of different magnitudes and frequencies (i.e. how fast the sinusoidal waves are changing)

The sum of sinusoidal waves of fundamental frequency fo and 3fo

The sum of sinusoidal waves of fo, 3fo, 5fo, and 7fo

The sum of sinusoidal waves of fo, 3fo, 5fo, 7fo, 9fo, 11fo, 13fo, 15fo, 17fo

Approximation to a square

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Sinusoids? Not just a mathematical function Are generated by real instrument Tuning fork

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Sinusoids: Clay whistle

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Sinusoids Basis of all signals A sinusoid is a signal that has its

magnitude changes in time according to a sine function sin()

sin

(in degree)

https://www.youtube.com/watch?v=pEXdTLsEAjk

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Sinusoids Radian

Standard unit of angular measure Equal to the length of the arc of a unit

circle 2/360

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Sinusoids Radian:

2/360

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Sinusoids sin() repeats itself for every 2 change in

A sin (2ft + )= A sin (t + )

amplitude frequency Phase shiftPeak = 1

sin(2t)

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Change of Amplitude

sin(x)

5 sin(x)

10 sin(x)

A sin (t + )How large the sine wave is

Change of Amplitude

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Frequency Number of cycles that a sine wave has

changed per second Unit: Hertz (Hz) Sine wave of f Hz:

Changes at a rate of f cycles per second or 2f radian per second

Takes 32 seconds to change one cycle, frequency = 1/32

32 sec32 secTime t (sec)

Frequency The smaller the frequency is,

the slower the change is

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60 sec60 secTime t (sec)

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Change of Frequencysin(x)

sin(2x)

Sin(3x)

A sin(t + )How fast the sine wave is changing

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Sinusoids Radian frequency, 0=2f0

Period = inverse of frequency Time that the signal repeats itself

T0= 1/f0

00

00

2and2T

T

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Example Sin(2 t)

Period =?, freq=?, radian freq=?

2and1,1

0 fT

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Example Sin(5 t)

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Phase angle The magnitude of a sine function must

start at 0 Some signals do not start at 0 A sin (t + )

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Change of Phase

10sin(2t+ 0.5)

10sin(2t + 1.5)

A sin (t + )

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Time shift and phase shift x(t) is the received signal If this signal is received t0 seconds

later x(t+ t0)

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Time shift and phase shift

A time shift of 15 seconds = a phase angle shift of /2

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Exercise

Sketch the waveform of the following sine wave signals

x(t) = 5sin(210t+1.5), for t from 0 to 200 msec

x(t) = 10sin(220t+1), for t from 0 to 200 msec

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Summary

Signal representation Sinusoids:

Model real signals Almost all signals can be constructed by

the summation sinusoids of different frequencies, amplitudes and phase shifts

Use of complex numbers to simplify operations in sinusoids

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References

M.J. Roberts, Fundamentals of Signals & Systems,McGraw-Hill, 2008. (Chapter 2)

James H. McClellan, Ronald W. Schafer and Mark A. Yoder, Signal Processing First, Prentice-Hall, 2003. (Chapter 2)