lecture1

Digital Signal Processing, © 2010 Robi Polikar, Rowan University

Lecture 1

Introduction

ECE 09.351.01

Digital Signal processing

Polikar

© 2010, All Rights Reserved, Robi Polikar.

No part of this presentation may be used without explicit written permission. Such permission will be given – upon request – for noncommercial educational purposes only. Limited permission is hereby granted, however, to post or distribute this presentation if you agree to all of the following:

1. you do so for noncommercial educational purposes;2. the entire presentation is kept together as a whole,

including this entire notice.3. you include the following link/reference on your site:

Robi Polikar, http://engineering.rowan.edu/~polikar.

http://users.rowan.edu/~polikar/CLASSES/ECE351

http://engineering.rowan.edu/

http://users.rowan.edu/~polikar/RESEARCH


Digital Signal Processing

This week in DSP

Getting to know each other

Introduction

What is DSP?

Signals

Is this yet another class testing our endurance on abstract math? (…Yes!)

What good is this miserable subject? Why do I care?

• Real world applications

Components of a typical DSP system

A practical exercise

DSP Spring’10 at a glance

On Friday prerequisite review for take home due Monday

M

RP Robi Polikar – All Rights Reserved © 2004 – 2010.

S.K. Mitra Digital Signal Processing, Wiley, © 2006.

Photo / diagram credits





What is DSP?

Digital Signal Processing:

Mathematical and algorithmic manipulation of discretized and

quantized or naturally digital signals in order to extract the most

relevant and pertinent information that is carried by the signal.

DSP SystemSignal to be

processed

Processed

signal

• What is a signal?

• What is a system?

• What is processing?





Signals

M

RP

RP

RP





Signals

Signals can be characterized in several ways: Continuous time signals vs. discrete time signals

• Temperature in this class at any given time – financial market data

Continuous valued signals vs. digital signals• Amount of current drawn by a device – average SAT scores of a school over years

– Continuous time and continuous valued : Analog signal

– Continuous time and discrete valued: Quantized signal

– Discrete time and continuous valued: Sampled signal

– Discrete time and discrete values: Digital signal

Real valued signals vs. complex valued signals• Resident use electric power – industrial use reactive power

Single channel signals vs. multichannel signals• Blood pressure signal – 128 channel EEG

Deterministic vs. random signal: • Test signals, power line – Recorded audio or noise (corrupted signal)

One-dimensional vs. two dimensional vs. multidimensional signals• Speech – image – video

(temperature)

(population)(daily aver. wind speed)

(CD audio, annual enrollment)





Signals

Analog Digital

Sampled QuantizedM





Signals

Formally speaking, any physical quantity that is represented as a

function of an independent variable is called a signal.

Independent variable can be time, frequency, space, etc.

Every signal carries information. However, not all of that information

is typically of interest to the end-user. The goal of signal processing is

to extract the useful information from the signal.

The part of the signal that is not useful is called noise.

Noise need not be “noisy.” Any part of the signal we are not interested is by

definition noise.

• If you are listening to a recording of two people talking, and you are really interested in

what only one of them saying, the other person’s speech is – as far as you are

concerned – noise!

• Though, often, noise is noisy! 60 Hz noise is very common (though not very

interesting, nor very challenging to clean)





Signal Processing

200 400 600 800 1000 1200 1400 1600 1800-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Noisy signal

500 1000 1500 2000

-0.2

0

0.2

0.4

0.6

0.8

Cleaned signal

Time, ms

RP





Signals & Sinusoids

Formally speaking, any physical quantity that is represented as a

function of an independent variable is called a signal.

Independent variable can be time, frequency, space, etc.

Sinusoids play a very important role in signal processing, because

They are easy to generate

They are easy to work with – their mathematical properties are well known

Most importantly: All signals can be represented as a sum of sinusoids

• Fourier transforms – more about this later.

In continuous time:

)sin()( tAty

Amplitude Angular frequency

(radians/sec)

Phase

(radians)





A continuous time domain sinusoid is a periodic signal

Angular frequency: A different measure of rate of change in the signal, easier to use with sinusoidal signals, represented in radians/second.

Analog frequency (f – measured in Hertz, 1/sec), the period T (measured in seconds), and the angular frequency Ω are related to each other by

Phase: The number of degrees –in radians – the sinusoid is shifted from its origin.

If the sinusoid is shifted by tθ seconds, then the phase is

Sinusoids

(period)

)()( Ttyty

Period: The time after which the signal repeats itself:

Frequency: Inverse of period

(phase)

tθ

T





Discrete-Time Signals

A discrete-time signal, commonly referred to as a sequence, is only

defined at discrete time instances, where t is defined to take integer

values only.

Discrete-time signals may also be written as a sequence of numbers

inside braces:

n indicates discrete time, in integer intervals, the bold-face denotes time t=0.

Discrete time signals are often generated from continuous time signals

by sampling which can roughly be interpreted as quantizing the

independent variable (time)

},9.2,7.3,2.0,1.1,,2.0,{]}[{

2.2nx

,2,1,0,1,2,)()()(

ntxnTxnxsnTts

Ts=Sampling interval / period

fs = 1/Ts = sampling frequency





Sampling

Think of sampling as a switch, that stays closed for an infinitesimally

small amount of time. It takes samples from the continuous time

signal

Ts

RP





Sampling

Since we naturally interpret the signals in the continuous time domain,

we also need to convert the discrete time signals back to continuous

time D/A conversion

A fundamental question: how close should the samples be to each

other so that a continuous time signal can be uniquely reconstructed

from a discrete time signal How to choose Ts, the sampling period?





Ponder!

What Ts is small

enough?

And what happens

if Ts is not chosen

small enough?

RP





Systems

Not your typical systems: airline system, security system, irrigation

system, etc. are of no interest to us

For our purposes, a DSP system is one that can mathematically

manipulate (e.g., change, record, transmit, play, transform) digital

signals

Furthermore, we are not interested in processing analog signals either,

even tough most signals in nature are analog signals

DSP SystemAnalog

signal

Processed

analog signalADC DAC

Digital

signal

Digital

signal

RP





Components of a

DSP System

DSP System

(Digital Filter)

Analog

signal

Processed

analog signalQuantizer D/A

Digital

signal

Analog

LPF

Digital

signal

Quantized

signalAnalog

signal

Sampled

signal

HOLD

Sampler

Binary

Converter

Discrete

signal

A/D Converter

Band-limiting

Filter

D/A Converter

RP





Components of a

DSP System





Another Example

Analog Signal Output of sample & hold

Output of A/D Converter (quantized binary) Output of Digital Processor (binary)

Output of D/A Converter (analog) Output of LPF - Analog Signal

M





Analog – to – Digital –

to – Analog …?

Why not just process the signals in continuous time domain? Isn’t it just a waste of time,

money and resources to convert to digital and back to analog…?

Why DSP? We digitally process the signals in discrete domain, because it is

More flexible , more accurate, higher performance, easier to mass produce

Easier to design

• System characteristics can easily be changed by programming

• Any level of accuracy can be obtained by use of appropriate number of bits.

More deterministic and reproducible – less sensitive to component values, etc.

Many things that cannot be done using analog processors can be done digitally

• Allows multiplexing, time sharing, multichannel processing, adaptive filtering

• Easy to cascade, no loading /drift effects, signals can be stored indefinitely w/o loss

• Allows processing of very low frequency signals (or any arbitrary transfer function), which requires

unpractical component values in analog world

On the other hand, it can be

Slower, sampling issues (current max 100GS/sec, more typical 1 GS/s)

More expensive, increased system complexity, consumes more power.

Yet, the advantages far outweigh the disadvantages Today, most continuous time signals

are in fact processed in discrete time using digital signal processors





Processing

So what is processing…? What kind of processing do we do?

This depends on the application

Communication – Modulation and demodulation

Signal security – Encryption and decryption

Multiplexing and demultiplexing – Sending many signals through common channel

Data Compression – Reduce space/computation required to store/process data

Signal denoising – Filtering for noise reduction

Speaker / system identification

Audio processing – Signal enhancement, equalization

Image processing – Image denoising, enhancement, watermarking, reconstruction

Data analysis and feature extraction – Recognize structure in data

Frequency / spectral analysis – Alternate approach to time domain analysis

Signal generation – TOUCH-TONE® dialing.

Each can be expressed as a mathematical operation performed on the signal. DSP, is then the system that performs this operation.





Filtering

By far the most commonly used DSP operation

Filtering refers to deliberately changing the frequency content of the signal,

typically, by removing certain frequencies from the signals

For denoising applications, the (frequency) filter removes those frequencies in the

signal that correspond to noise

In communications applications, filtering is used to focus to that part of the

spectrum that is of interest, that is, the part that carries the information.

Typically we have the following types of filters

Lowpass (LPF) – removes high frequencies, and retains (passes) low frequencies

Highpass (HPF) – removes low frequencies, and retains high frequencies

Bandpass (BPF) – retains an interval of frequencies within a band, removes others

Bandstop(BSF) – removes an interval of frequencies within a band, retains others

Notch filter – removes a specific frequency





Filtering

An Example

t=0:0.0001:0.1;x1=sin(2*pi*50*t);T=linspace(0, 100, 1001);subplot(4,1,1)plot(T, x1)axis([0 100 -1 1])ylabel('50 Hz')subplot(4,1,2)x2=sin(2*pi*110*t);plot(T, x2)axis([0 100 -1 1])ylabel('110 Hz')subplot(4,1,3)x3=sin(2*pi*210*t);plot(T, x3)axis([0 100 -1 1])ylabel('210 Hz')y=x1+x2+x3;subplot(4,1,4)plot(T, y)axis([0 100 -2 2])ylabel('Combined')xlabel('Time, ms')

0 10 20 30 40 50 60 70 80 90 100-1

0

1

50 H

z

0 10 20 30 40 50 60 70 80 90 100-1

0

1

110 H

z

0 10 20 30 40 50 60 70 80 90 100-1

0

1

210 H

z

0 10 20 30 40 50 60 70 80 90 100-2

0

2

Com

bin

ed

Time, ms

Sampling freq.: 10000 samples/s

RP





Frequency Spectrum

Y=abs(fft(y));F=linspace(0, 5000, 500);plot(F, Y(1:500))gridY=Y/abs(max(Y));plot(F, Y(1:500))gridxlabel('Frequency, Hz')ylabel(‘Normalized Magnitude')title('Frequency Spectrum')

50 100 150 200 2500

0.2

0.4

0.6

0.8

1

Frequency, Hz

No

rma

lzie

d M

ag

nit

ud

e

Frequency Spectrum

0 1000 2000 3000 4000 50000

0.2

0.4

0.6

0.8

1

Frequency, Hz

No

rma

lzie

d M

ag

nit

ud

e

Frequency Spectrum

RP





Filtering

80 Hz 150 Hz

110 Hz 80 Hz 150 Hz

50 Hz 110 Hz 210 Hz

M





Touch-Tone Dialing

Dual-tone multifrequency (DTMF) signals

1000 Hz

1200 Hz

600 - 700 Hz

1600 - 1700 Hz M





About DSP…

Is this another one of those classes that tests our endurance on abstract

math torture…?

Indeed! Here is an example…





About DSP

…and here is another one…well, actually it is simpler then it appears.





So What Good Is This?

The real world applications of DSP is innumerous

Signal analysis, noise reduction /removal : biological signals - such as ECG, EEG,

blood pressure - NDE signals, such as ultrasound, eddy current, magnetic flux,

oceanographic data, seismic data, financial data - such as stock prices as a time

series data - , audio signal processing, echo cancellation

Communications – analog communications, such as amplitude modulation,

frequency modulation, quadrature amplitude modulation, phase shift keying, phase

locked loops, digital and wireless transmission – CDMA (code division multiple

access) / TDMA (time division multiple access), time division multiplexing,

frequency division multiplexing, internet protocol

Data encryption, watermarking, fingerprint analysis, speech recognition, biometrics

Image processing and reconstruction, MRI, PET, CT scans

Signal generation, electronic music synthesis

And many many many more….





Digital Signal Processing (3)

ECE 09.351

Spring 2010

Class Homepage: engineering.rowan.edu/~polikar/ECE351

Instructor: Dr. Robi Polikar

Office& Phone: 136 Rowan, 256-5372 (voice-mail available)

Office Hours: Mondays 1500 – 1630, or by appointment, or according to open

door policy: you may come at any time if and when the office door is open

E-mail: [email protected]

Class Meeting: Monday 1215 – 1330 (239), Wednesday 0845-1000 (237) Friday 1050 – 1330 204/206 Lab

Required Text: Digital Signal Processing 3/e, Mitra, McGraw Hill, 2006

Reference Texts: Digital Signal Processing. Hayes, Schaum’s Outline Series, 1999.

Digital Signal Processing using MATLAB, Ingle and Proakis, Thomson, 2007.

Signal Processing First, McClellan, Schafer and Yoder, Prentice Hall, 2004

Digital Signal Processing Using Matlab, Ingle and Proakis, PWS, 2002.





DSP At a Glance

• Introduction, Components of a DSP System, DSP Applications, Concepts of

Frequency and Filtering

•Signals and Systems

• Commonly used signals in DSP – unit step and impulse, sinusoids, complex

exponentials, classification of signals, periodicity, energy vs. power signals

• Discrete time systems – classification of discrete systems (linearity, causality, time invariance,

memory, stability), characterization of LTI systems – impulse response, convolution,difference

equations, finite and infinite impulse response (FIR/IIR) systems

•Representation of Signals in Frequency Domain

• Concept of spectrum / frequency

• Frequency representation of continuous time signals - Fourier series and Fourier transform (review)

• Sampling theorem – aliasing, Nyquist criterion, interpretation of spectrum in discrete time domain

• Frequency representation of discrete time signals

• Discrete time Fourier transform (DTFT) ,

• Discrete Fourier transform (DFT) and Fast Fourier transform (FFT),

• Properties of and relationships between various Fourier transforms,

• Concepts of circular shift and convolution, decimation and interpolation of discrete signals.

•The z-transform

•Definition and properties

• Relation to DTFT/DFT

• Concepts of zeros and poles of a system, region of convergence (ROC) of z-transform

• Inverse z-transform (to be covered in CC Module - Complex Systems)





DSP At a Glance

• Linear Time Invariant (LTI) Systems in Transform Domain

• Concept of filtering – revisited, lowpass, bandpass and highpass filters

• The frequency response and transfer function of a system

• Types of transfer functions

• FIR filters, ideal filters, linear phase filters, zero locations of linear phase FIR filters,

• IIR filters, pole and zero locations of IIR filters, all pass filters, comb filters

• Stability issues for IIR filters

•Filter Design and Implementation

• Digital filter specifications, selection of filter type, estimation of filter order

• FIR filter design using windows

• IIR filter design using bilinear transformation

• Analog filter design – Butterworth, Chebyshev, Elliptic, Bessel filters

• Spectral transformations for designing a filter with new characteristics based on a previously

designed filter

•Filter Structures

• FIR filter structures – direct and cascade form

• IIR filter structures, Lattice form

•Finite Wordlength Effects

• Analog to digital and digital to analog conversion

• Number representations – fixed point and floating point numbers

• Quantization of fixed and floating point numbers, coefficient quantization

• Quantization noise analysis, Overflow effects

Practical Issues and Advanced Topics (time permitting)




DSPSignals

Sinusoids &

Exponentials

Impulse, step,

rectangular

Phasors

Frequency

Characterization

Time domain

representation

Representation in

frequency domain

Spectrum

Power / Energy Periodicity Cont. / Discrete

Convolution

Regular / Circular

Sampling

Nyquist Thm.

CFT

Transforms

ZPoles & Zeros

ROC

DFTDTFT FFT

(LTI) Systems

Discrete LTI

Systems

Classification

Impulse Resp.

Linearity

Time Inv.

Causality Memory

Stability

Time Domain Rep.

Diff. Equation

Ideal vs. Practical

Freq. Domain Rep.

Filtering

LPF HPF BPF BSF APF Notch

FIR / IIR

Filter Design

FIR IIR

Windows

Linear Phase

Specs

Bilinear. Tran.

Butterworth

Chebychev

Elliptic

Stability

Filter Structure

FIR IIR

Direct

Cascade

Lattice

Transfer Func.

Frequency Res.

Quantization

Finite

Worldlength

A/D D/A

Number Rep.

Fixed/Floating

Quantization

Noise

Overflow

Effects

Advanced Topics

Random Signal Analysis

Multirate Signal Proc.

Time Frequency Analysis

Adaptive Signal Process.


What did we Learn today?

What is DSP: Signals and systems for processing signals

Components of a DSP system

Sampling: Ponder! – How often shall we take samples? What happens

if we do not take samples fast enough?

Filtering: The main function of DSP systems – remove unwanted

components of the signal by manipulating its frequency content

Applications of DSP: Virtually unlimited…It is all around you!





Will I actually Learn Something

of Useful in This Class?

Of course! You will learn digital signal processing through filtering!

Semester exercise:

Download the noisy signal from the class webpage. Play around with it through

out the semester as we learn new filtering techniques

Design an appropriate filter to clean the high frequency noise in the signal.

At the end of the semester, we will play everyone’s signal and determine which one

sounds best (names will only be known to the instructor during the competition).

All designs will be graded and best ones will be awarded bonus points.

Rules:

You must work on your own

You must develop your own filter. You will be asked to explain your design, and

provide full disclosure including your code.

We may increase the complexity of the project by changing the noisy signal later in

the semester.





For Friday & Next Monday

Friday – Review & prerequisite quiz

The review will include continuous time signals and systems, complex numbers,

phasor notation, etc. however we will not have time review the entire background

material – Make sure that you go over the topics listed on the class webpage.

• Also see Math and Matlab Review files on class web page.

Monday – Jan 25 (Dr. Polikar at NSF - Guest Lecture)

Look at the sample concept maps provided later in this presentation.

Prepare a concept map of your current DSP knowledge. Yes, your DSP knowledge

at this time is very limited. This will be used to compare a concept map to be

prepared at the end of the semester to show you your progress this semester.

Concept maps should only include concepts you know! Do NOT use topic names

from tentative contents lists, unless you are very familiar with that topic!

Take home prereq quiz due class time – Quiz will be graded!

Read Chapter 1 & 2 of your book, and play around with the software that comes

with it. Please Take reading assignments seriously. Quizzes may be given on these.

Don’t forget to ponder about sampling.





Concept Maps

Concept maps are tools for organizing and representing knowledge1

Concept maps include “concepts” which are connected by lines to form “propositions”. The

lines are labeled to specify the relationship between the concepts.

They are typically represented in a hierarchical fashion, with more general concepts at the

top / center, and more specific, less general ones at the the bottom or extremities.

The hierarchy depends on some context in which the knowledge is applied, such as with

respect to a specific question.

Cross links may connect concepts that are at different geographical locations of the map.

Such links represent the multidisciplinary nature of the topic and the creative thinking

ability of the person preparing the map.

Creating concept maps is not very easy, and requires some amount of familiarity with the

technique as well as the context. No concept map is ever final, as it can be continually

improved. One should be careful however, against frivolously creating concepts and/or

links between them (which result in invalid propositions).

Concept maps provide a very powerful mechanism for presenting the relationships between

concepts as well as the preparer level of understanding of these concepts.

1. J.D. Novak, http://cmap.coginst.ufw.edu/info





Sample Concept Maps

(Not Complete)

What is a plant?

Conce

pts Cross link

Links

Link

labels





Sample

Concept Maps




lecture1

Documents

random signal

signal repeats

sampled signal

cleaned signal

goal of signal processing

digital signals

signal carries information

digital signal cd audio