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Java for Digital Signal Processing

In a Nut Shell

(Draft: February 1, 2007)

Jarmo T. Alander

University of Vaasa, Finland

Department of Electrical Engineering and Automation

Java for

Digital Signal Processing

(AUTO1030 course)Spring 2007

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This document can be found in the Web at

ftp://ftp.uwasa.fi/cs/AUTO/AUTO1030/JavaDSPprinter.pdf

as this printer friendly hand-out version, or at

ftp://ftp.uwasa.fi/cs/AUTO/AUTO1030/JavaDSP.pdf

as a slide show. All comments are warmly welcome.

ftp://ftp.uwasa.fi/cs/AUTO/AUTO1030/DSP.java

contains the Java source code used in this document.

c2006, 2007 Jarmo T. Alander. These are the revised (February 1, 2007) web notes of a lecture of Java usage for DSP.

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Java & DSP CONTENTS

Contents

1 Introduction 4

1.1 Project group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 Why Programming and DSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Why Java . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Why not DSP assembler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.5 Why not Matlab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.6 Why mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.7 Why image processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.8 Why in English . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.9 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.10 Examples of signal processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Numerics 6

2.1 Arithmetic operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Division and multiplication by 2n can be done efficiently . . . . . . . . . . . . . . . . . . 6

3 Methods 7

3.1 Methods and classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.2 Example 1: constant vector or signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.3 Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.4 Constant vector by Java . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.5 Example 2: Moving average . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.6 Method as a black box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.7 Example 3: combining methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.8 Example 4: derivative1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.9 Example 5: method add . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.10 Example 6: FIR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.11 Example N (long): NIRS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.12 Sqrt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.13 S/N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4 Classes 19

4.1 DSP class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.2 Example class DSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.3 Graphical representation: container . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5 Image Processing 23

6 Hyperimage processing 24

6.1 What is hyperimage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

7 Conclusions and Future 25

7.1 Future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

7.2 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

7.3 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

A Solutions to problems 27

A.1 Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

A.2 Useful links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

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Java & DSP CONTENTS

Trademarks

Java is a registered trademark of Sun Microsystems, Inc.

This document was typeset by the author using Leslie Lamports LATEX (http://www.latex-project.org/ )

extension of Donald Knuths TEX typesetting system and Beamer (http://latex-beamer.sourceforge.net/ )

extension of LATEX for slides.

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Java & DSP 1 INTRODUCTION

1 Introduction

Abstract

This is a draft for a tutorial for Java programming for solving basic signal processing problems. The

goal of this tutorial is to help students to learn how to use computer programming as a tool to design

and implement signal processing methods. This tutorial contains basics of Java syntax and semantics,

examples of DSP problems solved by Java, and references to further reading.

Keywords: digital signal processing, image processing, Java, object-oriented programming,

1.1 Project group

Persons more or less influenced this tutorial include

Prof. Jarmo Alander: first draft

DI Janne Koljonen: Java examples (Virtual Keeper)

Econ. Olli Snellman: Java multimedia programming

DI Petri Vlisuo: Java examples

Dr. Timo Mantere: Java examples and testing

BSc Olli Kanniainen: Java examples.

The idea and need to write this tutorial emerged from the difficulties encountered by the students to

solve exercises using programming approach essential in modern engineering design and creativity.

Programming is like eating an elephantdo it piece by piece.

1.2 Why Programming and DSP

Signals is digital format are suitable only for digital electronics and computer processing, the latter of

which is more flexible and also the main processing type. This means that most signal processing is done

by computer programs in computers and embedded systems like mobile phones, CD-players, and digital

cameras. Before microprocessors, signal processing was done by analog electronics.

1.3 Why Java

The high level programming language Java is gaining more and more popularity as a tool for programming

large software systems for smaller and smaller devices. It is a general purpose programming language also

suitable for signal processing. In this tutorial we will only take some parts of the language, and leave the

rest for the main programming studies.

Java programmers do it more modularly,

1.4 Why not DSP assembler

Signal processing is done much with special DSP processors having special tailored commands to do nu-

merical calculations. Java was preferred here because it can be used also in very many other applications,contrary to DSP programming, which is not used much outside the DSP community.

1.5 Why not Matlab

This programming introduction to DSP could also have been done using Matlab. However, Java is a general

purpose language useful also in more general setting of automation software and beyond. Hence program-

ming skills in Java are more useful for anybody not intending to concentrate only on DSP.

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Java & DSP 1 INTRODUCTION

1.6 Why mathematics

Digital signal processing is based on mathematical methods and notations, most of which are easy 1 to

implement using any programming language. These mathematical concepts include real and complex

arithmetics, basic functions, iteration, vectors, and matrices. We will look these by a few simple examples

taken from DSP.

1.7 Why image processing

Vision is perhaps the most important sense:

it makes human-computer interaction natural.

it has endless number of applications, and

it is in a rapid development phase due to computing and digital electronics.

More and more tasks are aided by graphical user-interfaces with extremely high quality image features. In

these kinds of applications Java is a good choise for a programming language.

Information as images are often excellent for human interpretation and consultations. The human eye,

even if being in very many ways an excellent device, has some weak points that can be quite easily assisted

by a modern computer system. The weaknesses include:

Limited contrast resolution, which can be often adjusted by rather simple scaling algorithms.

Lack of absolute image memory makes it difficult to monitor slow processes like tumour growth or

tensile testing []. A computer can memorise precisely image information as long as needed. There

are also rather simple algorithms to compare images, display the differences, and to calculate the

amount of differences. [?]

Hence we will use quite many image processing examples in what follows.

1.8 Why in English

These notes are written in English so that both Finnish and foreign students can use these notes.

1.9 Motivation

Before going into details of Java and DSP, a word of motivation: Remember, that programming skills are

highly esteemed in labour market. About half (50%) of industrial productivity is due to ITC development,

and that is based on programming new applications.2

1.10 Examples of signal processing

The following list gives an example of signal processing applications done by our group.

Under construction ...

1This is really true.2The rest is due to all the other engineering branches altogether, hence what ever you develop, half of it should be ICT, on the

average.

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Java & DSP 2 NUMERICS

2 Numerics

The basic numerical types in Java are shown in table 1. As can be seen the integer type is long enough for

any basic signal processing, where ADC signals are processed. Typically ADC signals contain only 8 to 16,

sometimes even 24, significant bits. In what follows we are mainly using integers (int 32bits) to represent

signal values and integer arrays (int[]) to represent signal sequences like time series.

Table 1: Numerical types in Java.

type size range

byte 1 byte (8 bits) -128 ... 127

short 2 bytes (16 bits) -32 768 ... 32 767

int 4 bytes (32 bits) -2 147 483 648 ... 2 147 483 647

long 8 bytes (64 bits) -263 ... 2631

float 4 bytes (32 bits) 3.41038 about 7 decimal positionsdouble 8 bytes (64 bits) 1.710308 about 15 decimal positions

2.1 Arithmetic operations

Evaluating a formula in floating point arithmetics is sensitive to the execution order of the operations. Here

some advice:

Always sum in increasing order. Otherwise precision may be lost in floating point scaling.

Avoid subtraction of nearly equal values. Again the floating point scaling is the potential reason of

loss of precision.

Division of zero is always a headache for a programmer of numerical software. Test before division

that the denominator is not too small ( 0).

Using integers instead of floating point values we can avoid some problems, while unfortunately geting

some integer dependent problems like imprecise function values. A decent compromise is fixed pointnumbers that use integers to represent decimal numbers of given decimal places. In practise we can e.g.

compute by values 100 times larger than the real ones (from ADC etc) and output values with decimal point

between the second and third less significant digit positions.

2.2 Division and multiplication by 2n can be done efficiently

In case we have division (or multiplication) of a binary coded integer by 2n the fastest way to do it is just to

shift the integer n steps right:

i/8 is equivalent to i3.

The -operator shifts the bits of the first operand to the right by the amount given as the second operand

(here 3; 23 = 8). The reverse -operator can be used when multiplication by 2n is needed:16*i is equivalent to i4.

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Java & DSP 3 METHODS

3 Methods

In what follows we will briefly introduce the most important concepts and constructions of Java -language

in the framework of introductory signal processing application. We will not be extremely purist with respect

to Java definitions. When in doubt, please make experiments with our Java interpreter or consult the Java

tutorials by the Sun Microsystems (http://java.sun.com/docs/books/tutorial/ ) or still better do

both.

Allways remember the KISS principle: Keep It Simple Stupid.

3.1 Methods and classes

Subroutines, functions, and procedures are all called methods in Java. Here we will collect a set of methods

to a subroutine package, called class in Java language terminology.

Before looking classes more carefully, we start by writing a few methods and by that way learn basic

constructions of Java.

3.2 Example 1: constant vector or signal

Our first method will create a vector of n integer items all set to a given constant c:

public static int[] constant(int n, int c) ///** create an n item constant vector = c*/ // comment

{ // create a constant vector

int[] R = new int[n]; // reserve space

for(int i=0; i


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int c parameter c of type integer.

int[] R = new int[n]; allocation of space (creation of an object) for the result. When returning a

non-scalar value we have to reserve memory space (new) for it. Operator = is an assignment of the

created vector to variable R (or actually a link to the memory).

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3.4 Constant vector by Java

In Java we can also write directly constant initialisation vectors:

int[] ZeroVector = {0, 0, 0};

Which one is better depends on the situation: tiny vectors are usually easier to write explicitly than program

while it is best to program longer vectors. Writing constant(10000,999999) will save a lot, lot, ... of

boring and errorprone typing.

Exercise 3.1 Implement the delta function: i,j = 1, when i = j, andi,j = 0, when i = j, outputting aninteger array of given length (parameter n).

Observe, that due to maintenance reasons it is usually good to avoid scattering constants other than 0

and 1 around the program code. Use symbolic constants instead.

3.5 Example 2: Moving average

Our second example will be a method that evaluates a moving average of a given time series x[] using

moving window of width 2n+1:

public static int[] moving(int[] x, int n) // COMMENTS:

/** average of x using window size 2x+1 */ // comment

{ // moving average of window 2n+1

if (n


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S += x[I-]+x[J++]; Operators - and ++ are shorthand notations for expressions I = I - 1 and J = J + 1.

This notation is inhereted from C-language, and used where utmost efficiency is needed. Namely they

are often found as machine level commands (increment or decrement by 1). Similarly S+=x is a short

hand notation for S=S+x also this is usually translated into an efficient special machine code command

(the contents of the accumulator register is increased by x).

Summing is done starting from the center of the window and proceeding towards the ends of the

window.

R[i] = S/W; In a finished program every division should be checked to be valid. W should not be zero,

which is true because W=2*n+1= 0, for nIN.

3.6 Method as a black box

In order to clarify Java concepts we use some simple graphics like rectangular boxes and other similar

constructions. The methods constant and moving are shown in figure 1. Parameters are represented by

arrows pointing to the left side of the method box, while the type returned by the method is shown by an

arrow pointing outwards from the right side of the method box. The types of the parameters and the output

are shown above or under the arrows.

The term black box means that the observer i.e. the one who is using a method does not know the details

of its implementation inside the black box. It is enough to know the interface, the parameter and outputtypes, and what the method should do.

The details of the method could not interest less the observerthe details are left just for the programmer

of the method.

constant -int[]-int-int

int[] constant(int,int)

moving -int[]-int[]-int

int[] moving(int[],int)

Figure 1: Box representation of the definition of the methods constant and moving.

3.7 Example 3: combining methods

In this example we will combine our two methods into a simple signal filtering example. Our task is to

apply the moving average filter to a constant time series to see what really happens.

Let the constant time series be ten (10) times one (1) and the window size of the moving average filter

W= 22+1 = 5.

Our codeline is shown in the graphical representation of figure 2.

int[] S1 = moving(constant(1, 10), 2);

int[]constant --n=10

-c=1 r r r r r r r r r r moving -

-

-n=2 r r

r r r r r r

r r

S1

Figure 2: Box representation of command int[] S1 = moving(constant(10,1),2).

Exercise 3.2 Take a moving average of the output of a delta function method of the exercise 3.1.

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3.8 Example 4: derivative1

Our next method called derivative1 will estimate the derivative of a time series by taking the difference

between the consecutive items of the time series.

public static int[] derivative1(int[] x) //

/** the 1st derivative of series x */ //

{ // derivative by difference xi - xi+1

int N = x.length; // length ofxint[] R = new int[N]; // reserve space for result

for(int i=1; i


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int[] S4 = derivative1(add(S1,S2));

S1

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Figure 4: Application of method derivative1 to the added output of our previous examples.

/** FIR filter of x using coeff a */ // FIR filter; coeffa

{ //

int N = x.length; // length ofx

int M = a.length; // length ofa

int[] R = new int[N]; // reserve space for result

int W=0; //

for(int i=0; i


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Figure 6 below shows a typical NIR spectrum of human skin taken for clinical research purposes. You can

find more information on this medical application of signal processing from the web address below:

More information from:

ftp://ftp.uwasa.fi/cs/report05-4/TTIprinter.pdf or

ftp://ftp.uwasa.fi/cs/report05-4/TTI.pdf

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1000 1200 1400 1600 1800 2000

Figure 6: A NIR spectrum of human skin (spectrum A)

There should be some small details in the spectrum, peaks and valleys, that are of interest to the clinician

for diagnostic purposes. In order to find them we try to filter away the background by derivating the

spectrum by our derivative1 method. The result is shown in figure 7.

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Figure 7: The first derivative of NIR spectrum A using derivative1 method.

Our derivative1 method is not good in suppressing noise. According to theory a better method should

be e.g. der101. The result of applying der101 to our example spectrum is shown in figure 8.

Exercise 3.7 Method der101 estimates the derivative of a series x by formula x[i] = x[i+1]-x[i-1].

Implement methodder101 returning the derivative series.

The peaks and valleys in NIRS vary much in size. The basic properties of peaks and valleys are their

location and height. The peak location gives the wavelength, which is further inversely proportional to

the energy difference between the vibrational states of the molecule, which further give information on

the physics and chemistry of the object measured. In our example case the peaks correspond to certain

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1000 1200 1400 1600 1800 2000

Figure 8: The first derivative of NIR spectrum A using der101 method.

molecules or parts of molecules and their interactions that strongly absorb certain NIR wavelengths. The

peak height is proportional to the concentration of the given molecule.

Geometrically in the first derivative spectrum the peak or valley location i.e. the highest or lowest point

correspond to points where the derivative signal crosses zero.

The third important property of peak or valley is its width. There are several ways to define width, how-

ever. Here we will approximate the width by the distance between the peak and valley of the corresponding

second derivative signal at the peak or valley.

In order to evaluate the basic properties of peaks and valleys we need methods to evaluate derivatives

and peak locations. The easies way of implementing the second derivative is to apply the first derivative

twice, like:

int[] D1 = der101(S);

int[] D2 = der101(D1);The fourth important peak/valley property is its area, which can be estimated once the local background

is estimated.

The details of spectra vary much. Hence, the values of derivatives also vary much. This complicates

the graphical display of derivatives. The dynamics of derivation can be suppressed by a logarithm or root

function for graphical display. Figure ?? shows the results of applying square root function (method Sqrt)

to the output of our der101 derivation method. Similarly figure 9 shows the derivative of another skin

spectrum done by applying der101 and square root dampening.

3.12 Sqrt

Method Sqrt compressing signal dynamics for graphical display is as follows:

public static int[] Sqrt(int[] x, double a) //

/** square root of abs x scaled by a */ //sign(x) a sqrt(|x|){ //

int N = x.length; // length ofx

int[] R = new int[N]; // reserve space for result

for(int i=0; i


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Java & DSP 4 CLASSES

4 Classes

A Java class is an aggregation of attributes (variables) and methods (functions). In addition we can create

new copies of class variables. In Java, and in general in other object-oriented langueges, these copies in

computers memory are called objects.

4.1 DSP classThe simplest class contains only methods and can be seen as a method or subroutine package, where some

of the methods may call other methods in the same class.

4.2 Example class DSP

The following class called DSP was used in our first method examples.

public class DSP //

{ //

public static int[] constant(int n, int c) //

/** ... */ // create a constant vector

{ //

int[] R = new int[n]; // reserve space

for(int i=0; i


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Java & DSP 4 CLASSES

4.3 Graphical representation: container

Because the most important function of a class is to be a container holding all methods and attributes

together, we will use an oval shaped container as the symbol of a class and object of a class:

DSP

add()-

-

-

DSP

fun()-

-

-

?6

a1 a2

Figure 17: Method add of class DSP using no attributes of DSP. Another method fun updating attribute a1

and reading another attribute a2 of class DSP.

Still working on this subject ... hold on, please.

22


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Java & DSP 5 IMAGE PROCESSING

5 Image Processing

In this section we will see how basic image processing methods can be implemented in Java. An image is

typically represented by a two-dimensional integer array:

int[][] Image = new int[1024][1024];

reserves space for a 10241024 pixel one color (grey tone) image.

For processing an image array we need two loops like this:public static int[][] Ifun(int[][] Image) //

/** ... */ // an image processing function

{ //

int N = Image.length; // height of Image

int M = Image[0].length; // width of Image

int[][] R = new int[N][M]; // space for result

for(int i=0; i


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Java & DSP 6 HYPERIMAGE PROCESSING

6 Hyperimage processing

6.1 What is hyperimage

The by far most common image types are grey tone and color images. It is also possible to increase the

number of colors in a color image far beyond the three necessary for visible color images as well as going

beyond visible light to ultraviolet and infrared even beyond. Figure 19 shows schematically the relation

between pixel, image, and hyperimage.

HyperimageProcessing

6

?

Image Processing

6

?

Chemometrics(Spectroscopy)

image[][](photo)

6

?

pixel[](spectrum)

hyperimage[][][]

-

6

qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq

qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq66

melanoma??

ulcers

a

Figure 19: Pixel, image, and hyperimage

Still working on this subject ... hold on, please.

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Java & DSP 7 CONCLUSIONS AND FUTURE

7 Conclusions and Future

7.1 Future

The anticipated future activities could include signal processing Java package, exercises, some of which

interactive, graphical tools for demonstrating the above, and graphical tools for teaching programming in

Java.

7.2 Acknowledgements

Mr. P. Vlisuo is acknowledged for introducing Beamer slide processing.

7.3 Further reading

Arto Wikla, "Ohjelmoinnin perusteet Java-kielell [Principles of Programming using Java Language]", Ota-

DATA, Espoo, 1999.

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Java & DSP 7 CONCLUSIONS AND FUTURE

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Figure 20: Comparison of spectra of figure 14

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Java & DSP A SOLUTIONS TO PROBLEMS

A Solutions to problems

Not any yet, sorryplease supply some.

A.1 Abbreviations

ADC Analog Digital Converter

CAD Computer Aided Design

DI Diplomi-Insinri (MSc eng.)

DSP Digital Signal Processing

FIR Finite Impulse Response (filter)

HCI Human-Computer Interface

NIR Near-InfraRed

NIRS NIR Spectroscopy

A.2 Useful links

Our homepage:

http://www.uwasa.fi/TAU

AUTO1030 homepage:

http://www.uwasa.fi/TAU/AUTO1030

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