Xử lý tín hiệu số DSP (digital signal processing)

Xử lý tín hiệu số DSP (digital signal processing)Xử lý tín hiệu số DSP (digital signal processing)Xử lý tín hiệu số DSP (digital signal processing)Xử lý tín hiệu số DSP (digital signal processing)Xử lý tín hiệu số DSP (digital signal processing)Xử lý tín hiệu số DSP (digital signal processing)Xử lý tín hiệu số DSP (digital signal processing)Xử lý tín hiệu số DSP (digital signal processing)Xử lý tín hiệu số DSP (digital signal processing)Xử lý tín hiệu số DSP (digital signal processing)Xử lý tín hiệu số DSP (digital signal processing)Xử lý tín hiệu số DSP (digital signal processing)Xử lý tín hiệu số DSP (digital signal processing)

Chapter 1 INTRODUCTION TO DIGITAL SIGNAL

PROCESSING 1.1 Introduction 1.2 Signals 1.5 Signal Processing

Copyright c Victoria, BC, Canada Email: aantoniou@ieee.org

Frame # 2 Slide # 2 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

t With the invention of the digital computer and the rapidadvances in VLSI technology during the 1960s, a new way ofprocessing signals emerged: digital signal processing.

t This and the next two presentations provide a brief historicalsummary of the emergence of signal processing and its

applications

Frame # 2 Slide # 4 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

t This and the next two presentations provide a brief historicalsummary of the emergence of signal processing and its

applications

t To start with, a classification of the various types of signalsencountered in today’s technological world is provided

t With the invention of the digital computer and the rapidadvances in VLSI technology during the 1960s, a new way ofprocessing signals emerged: digital signal processing.

t This and the next two presentations provide a brief historicalsummary of the emergence of signal processing and its

applications

t To start with, a classification of the various types of signalsencountered in today’s technological world is provided

t Then the sampling processis described as a means of

converting analog into digital signals

Frame # 2 Slide # 6 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

t Typically one assumes that a signal is an electrical signal, forexample, a radio, radar, or TV signal

However, in DSP a signal is any quantity that depends on one

or more independent variables

Frame # 3 Slide # 8 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

t Typically one assumes that a signal is an electrical signal, forexample, a radio, radar, or TV signal

However, in DSP a signal is any quantity that depends on one

or more independent variables

A radio signal represents the strength of an electromagneticwave that depends on one independent variable, namely, time

may be any quantity other than time.

Frame # 4 Slide # 10 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Signals Cont’d

t In our generalized definition of a signal, there may be morethan one independent variable and the independent variablesmay be any quantity other than time

For example, a digitized image may be thought of as lightintensity that depends on two independent variables, thedistances along the x and y axes; as such a digitized image is,

in effect, a 2-dimensional signal

may be any quantity other than time.

For example, a digitized image may be thought of as lightintensity that depends on two independent variables, thedistances along the x and y axes; as such a digitized image is,

in effect, a 2-dimensional signal

A video signal is made up of a series of images which changewith time; thus a video signal is light intensity that depends

on the distances along the x and y axes and also on the time;

in effect, a video signal is a 3-dimensional signal

Frame # 4 Slide # 12 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Signals Cont’d

t In our generalized definition of a signal, there may be morethan one independent variable and the independent variablesmay be any quantity other than time

For example, a digitized image may be thought of as lightintensity that depends on two independent variables, thedistances along the x and y axes; as such a digitized image is,

in effect, a 2-dimensional signal

A video signal is made up of a series of images which changewith time; thus a video signal is light intensity that depends

on the distances along the x and y axes and also on the time;

in effect, a video signal is a 3-dimensional signal

Frame # 5 Slide # 14 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Signals Cont’d

Natural signals are found, for example, in:

t Acoustics, e.g., speech signals, sounds made by dolphins andwhales

t Astronomy, e.g., cosmic signals originating in galaxies andpulsars, astronomical images

t Astronomy, e.g., cosmic signals originating in galaxies andpulsars, astronomical images

t Biology, e.g., signals produced by the brain and heart

Frame # 5 Slide # 16 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Signals Cont’d

Natural signals are found, for example, in:

t Acoustics, e.g., speech signals, sounds made by dolphins andwhales

t Astronomy, e.g., cosmic signals originating in galaxies andpulsars, astronomical images

t Biology, e.g., signals produced by the brain and heart

t Seismology, e.g., signals produced by earthquakes andvolcanoes

t Astronomy, e.g., cosmic signals originating in galaxies andpulsars, astronomical images

t Biology, e.g., signals produced by the brain and heart

t Seismology, e.g., signals produced by earthquakes andvolcanoes

t Physical sciences, e.g., signals produced by lightnings, theroom temperature, the atmospheric pressure

Frame # 5 Slide # 18 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Signals Cont’d

Man-made signals are found in:

t Audio systems, e.g., music signals

Communications, e.g., radio, telephone, TV signals

Frame # 6 Slide # 20 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Signals Cont’d

Man-made signals are found in:

t Audio systems, e.g., music signals

t Communications, e.g., radio, telephone, TV signals

t Telemetry, e.g., signals originating from weather stations andsatellites

Communications, e.g., radio, telephone, TV signals

t Telemetry, e.g., signals originating from weather stations andsatellites

t Control systems, e.g., feedback control signals

Frame # 6 Slide # 22 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Signals Cont’d

Man-made signals are found in:

t Audio systems, e.g., music signals

t Communications, e.g., radio, telephone, TV signals

t Telemetry, e.g., signals originating from weather stations andsatellites

t Control systems, e.g., feedback control signals

t Medicine, e.g., electrocardiographs, X-rays, magnetic

resonance imaging

Communications, e.g., radio, telephone, TV signals

t Telemetry, e.g., signals originating from weather stations andsatellites

t Control systems, e.g., feedback control signals

t Medicine, e.g., electrocardiographs, X-rays, magnetic

resonance imaging

t Space technology, e.g., the velocity of a space craft

Frame # 6 Slide # 24 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Signals Cont’d

Man-made signals are found in:

t Audio systems, e.g., music signals

t Communications, e.g., radio, telephone, TV signals

t Telemetry, e.g., signals originating from weather stations andsatellites

t Control systems, e.g., feedback control signals

t Medicine, e.g., electrocardiographs, X-rays, magnetic

resonance imaging

t Space technology, e.g., the velocity of a space craft

t Politics, e.g., the popularity ratings of a political party

Communications, e.g., radio, telephone, TV signals

t Telemetry, e.g., signals originating from weather stations andsatellites

t Control systems, e.g., feedback control signals

t Medicine, e.g., electrocardiographs, X-rays, magnetic

resonance imaging

t Space technology, e.g., the velocity of a space craft

t Politics, e.g., the popularity ratings of a political party

t Economics, e.g., the price of a stock at the TSX, the TSXindex, the gross national product

Frame # 6 Slide # 26 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Signals Cont’d

Two general classes of signals can be identified:

t Continuous-time signals

t Discrete-time signals

Frame # 8 Slide # 28 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

t Typical examples are:

– An electromagnetic wave originating from a distant galaxy

Frame # 8 Slide # 30 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Continuous-Time Signals

t A continuous-time signalis a signal that is defined at eachand every instant of time

t Typical examples are:

– An electromagnetic wave originating from a distant galaxy

t Typical examples are:

– An electromagnetic wave originating from a distant galaxy

Frame # 8 Slide # 32 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Continuous-Time Signals

t A continuous-time signalis a signal that is defined at eachand every instant of time

t Typical examples are:

– An electromagnetic wave originating from a distant galaxy

– The light intensity along the x and y axes in a photograph

t Typical examples are:

– An electromagnetic wave originating from a distant galaxy

– The light intensity along the x and y axes in a photograph

t A continuous-time signal can be represented by a function

x(t) where −∞ < t < ∞

Frame # 8 Slide # 34 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Continuous-Time Signals Cont’d

x (t)

t

Frame # 10 Slide # 36 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

t Typical examples are:

– The closing price of a particular commodity on the stock exchange

Frame # 10 Slide # 38 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Discrete-Time Signals

t A discrete-time signalis a signal that is defined at discreteinstants of time

t Typical examples are:

– The closing price of a particular commodity on the stock exchange

– The daily precipitation

t Typical examples are:

– The closing price of a particular commodity on the stock exchange

– The daily precipitation

– The daily temperature of a patient as recorded by a nurse

Frame # 10 Slide # 40 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Discrete-Time Signals Cont’d

t A discrete-time signal can be represented as a function

and T is a constant.

and T is a constant.

t The quantity x(nT ) can represent a voltage or current level or

any other quantity

Frame # 11 Slide # 42 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Discrete-Time Signals Cont’d

t A discrete-time signal can be represented as a function

and T is a constant.

t The quantity x(nT ) can represent a voltage or current level or

any other quantity

t In DSP, x(nT ) always represents a series of numbers.

and T is a constant.

t The quantity x(nT ) can represent a voltage or current level or

any other quantity

t In DSP, x(nT ) always represents a series of numbers.

t Constant T usually represents time but it could be any other

physical quantity depending on the application

Frame # 11 Slide # 44 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Discrete-Time Signals Cont’d

x (nT)

nT

Frame # 13 Slide # 46 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Discrete-Time Signals Cont’d

They are plotted as if they were continuous-time signals for thesake of convenience.

Frame # 15 Slide # 48 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Nonquantized and Quantized Signals

t Signals can also be classified as:

t A nonquantized signalis a signal that can assume any valuewithin a given range, e.g., the ambient temperature.

Frame # 16 Slide # 50 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Nonquantized and Quantized Signals

t Signals can also be classified as:

Frame # 17 Slide # 52 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Alternative Notation

t A discrete-time signal x(nT ) is often represented in terms of

the alternative notations

x(n) and xn

t In the early presentations, x(nT ) will be used most of the

time to emphasize the fact that a discrete-time signal is

typically generated by sampling a continuous-time signal x(t)

at instant t = nT

Frame # 18 Slide # 54 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Alternative Notation

t A discrete-time signal x(nT ) is often represented in terms of

the alternative notations

t In the early presentations, x(nT ) will be used most of the

time to emphasize the fact that a discrete-time signal is

typically generated by sampling a continuous-time signal x(t)

at instant t = nT

t In later presentations, the more economical notation x(n) will

be used where appropriate

discrete-time signal.

Frame # 19 Slide # 56 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Sampling Process

To be able to process a nonquantized continuous-time signal

by a digital system, we must first sample it to generate adiscrete-time signal

We must then quantize it to get a quantized discrete-timesignal

Sampling Process Cont’d

A sampling system comprises three essential components:– sampler

– quantizer

– encoder

Sampling Process Cont’d

A samplerin its bare essentials is a switch controlled by a

clock signal which closes momentarily every T seconds thereby transmitting the level of the input signal x(t) at instant nT , i.e., x(nT ), to its output.

Encoder

x(t)

Quantizer Sampler

x q ' (nT)

instant nT , i.e., x(nT ), to its output.

Parameter T is called the sampling period

Sampling Process Cont’d

A quantizeris a device that will sense the level of its input

and produce as output the nearest available level, say, xq(nT ),

from a set of allowed levels, i.e., a quantizer will produce aquantized continuous-time signal

a quantized continuous-time signal into a correspondingdiscrete-time signal in binary form.

Sampling Process Cont’d

The sampling system described is essentially an

analog-to-digital converter and its implementation can assumenumerous forms

Encoder

x(t)

Quantizer Sampler

x q ' (nT)

These devices go by the acronym of A/D converter or ADCand are available in VLSI chip form as off-the-shelf devices.

Sampling Process Cont’d

A quantized discrete-time signal produced by an A/Dconverter is, of course, an approximation of the originalnonquantized continuous-time signal

nonquantized continuous-time signal.

The accuracy of the representation can be improved byincreasing

– the sampling rate, and/or

– the number of allowable quantization levels in the quantizer

Frame # 26 Slide # 68 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Sampling Process Cont’d

A quantized discrete-time signal produced by an A/D

converter is, of course, an approximation of the originalnonquantized continuous-time signal

The accuracy of the representation can be improved byincreasing

– the sampling rate, and/or

– the number of allowable quantization levels in the quantizer

The sampling rate is simply 1/T = fs in Hz or 2π/T = ωs inradians per second (rad/s)

required processing can be performed by a digital system.

Frame # 27 Slide # 70 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Sampling Process Cont’d

Once a discrete-time signal is generated which is an accuraterepresentation of the original continuous-time signal, anyrequired processing can be performed by a digital system

If the processed discrete-time signal is intended for a person,e.g., a music signal, then it must be converted back into acontinuous-time signal

required processing can be performed by a digital system.

If the processed discrete-time signal is intended for a person,e.g., a music signal, then it must be converted back into acontinuous-time signal

Just like the sampling process, the conversion from a

discrete-to a continuous-signal requires a suitabledigital-to-analog interface

Frame # 27 Slide # 72 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5

Sampling Process Cont’d

Typically, the digital-to-analog interface requires a series oftwo cascaded modules, a digital-to-analog (or D/A) converter

and a smoothing device:

Smoothing device

y(nT)

y′(nT)

D/A

in Fig (b).

The stair-like nature of the quantized signal is, of course,undesirable and a D/A converter is normally followed by sometype of smoothing device, typically a lowpass filter, that willeliminate the uneveness in the signal

y'(t)

(a) nT y(nT)

(b)

t

Frame # 29 Slide # 74 A Antoniou Digital Filters – Secs 1.1, 1.2, 1.5