I HC QUC GIA H NI

TRNG I HC KHOA HC T NHIN

KHOA TON - C - TIN HC

Nguyn Hu in

PHNG PHP GII TON

NH TH NO ?

KHA LUN TT NGHIP I HC CHNH QUY

Ngnh: Phng php dy hc

Ngi hng dn: TS. Khng T

H Ni - 2011

LI GII THIU

Bn hy g cc li ni u v cm n vo y

Chng 1

C STM L GII TON

Mt s li gii thiu chng c g vo y!

1.1. Cc tm l khi tip cn bi ton

WinShell starts command line driven;Windows/Unix file format; Syntaxhighlighting; Table-Wizard; Wrap mode;

nh l 1. WinShell starts command line driven; Windows/Unix file format; Syn-tax highlighting; Table-Wizard; Wrap mode;

1.1.1. vcvxcbgxhdxfhdfhfdhd

Hnh 1.1: WinShell Logo. This image is taken from the WinShell internethomepage.

2Hnh 1.2: WinShell Logo. This image is taken from the WinShell internethomepage.

1.2. Cc tm l KHI TIP CN BI TON

Chng minh. Windows/Unix file format;WinShell starts command line driven;Syntax highlighting; Table-Wizard; xcbxcbvxbb Wrap mode;

nvbnvbmm

Chng 2

CC CNG CCN CHO GII TON

Mt s li gii thiu chng c g vo y!

Hnh 2.1: WinShell Logo. This image is taken from the WinShell internethomepage.

2.1. Cng c l g ?

WinShell is a graphical user interface for easy working with LATEX orTEX. It includes a text editor, different tool bars and user configuration op-tions. It is NOT a LATEX system. An additional LATEX package for Windowsis needed.

2.1.1. My tnh v phn mm

Some of the features are:Multi language support (English, German, French,Spanish, Italian, Polish, Swedish, Czech and Japanese); Project environment;Table-Wizard; One-instance-program; Multiple documents; Log- and Pro-jectspace; User defined programs; Configure Tool Bars (symbols, user-def.

4Hnh 2.2: WinShell Logo. This image is taken from the WinShell internethomepage.

programs, macros); Define macros; Choose font;

g f g f g f dg f dg

Windows/Unix file format; WinShell starts command line driven; Syntaxhighlighting; Table-Wizard; Wrap mode; Drag & Drop.

2.2. dfhghgf

Mt s li gii thiu chng c g vo y!

2.3. vcxbvcxb

2.1.1

Chng 3

TIP CNBNG HNH NH

Mt s li gii thiu chng c g vo y!

3.1. Trm nghe khng bng mt thy

This section is just for testing, what happens when you have a section inyour project which is double.

Hnh 3.1: WinShell Logo. This image is taken from the WinShell internethomepage.

2

Hnh 3.2: WinShell Logo. This image is taken from the WinShell internethomepage.

Chng 4

S KT HPGIA CC KIN THC

4.1. Ti sao li phi hiu bit rng

An important technique in digital image analysis is the Fourier transfor-mation (FT).

In the field of electrical engineering the parameter t (time) is often usedfor the one dimensional Fourier transformation. In this case the transforma-tion leads from the time domain to the frequency domain. This context goesback to the field of system theory, because there are

4.1.1. Discrete Fourier Transformation

A given continuous function f (x) sampled in N equidistant intervals xleads to the discrete function or series

f (x) = f (x0 + xx)= { f (x0), f (x0 + x), , f (x0 + [N 1]x)} .

The discrete value x ranges from x = 0, 1, . . . ,N 1.

4.1.2. Fast Fourier Transformation

The two dimensional image analysis uses the discrete 2D-Fourier trans-formation. Practise shows, that the calculation of a Fourier transformationgiven by above equations is an expensive operation.

7direct DFT FFT ExpenseN N2 N log2 N log2 N/N64 4.096 384 9,4%128 16.384 896 5,5%256 65.536 2.048 3,1%512 262.144 4.608 1,8%

Bng 4.1: Expense of calculation of the FFT in contrast to the direct DFT [?].

Chng 5

KT QU CUI CNG

5.1. Cn kim tra li

If you have equ al named sections in different files than both files areopend at the specific position on double-clicking. ohj

Ph lc A

Cc kin thc km theo

nothing special to say here...

A.1. y l v d1

Project environment; Table-Wizard; One-instance-program;Multiple doc-uments; Log- and Projectspace;

A.2. y l v d2

Project environment; Table-Wizard; One-instance-program;Multiple doc-uments; Log- and Projectspace;

9

Mc lc

Li gii thiu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Chng 1. C STM L GII TON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1. Cc tm l khi tip cn bi ton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1. vcvxcbgxhdxfhdfhfdhd. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2. Cc tm l KHI TIP CN BI TON. . . . . . . . . . . . . . . . . . . . . . . . . . 2

Chng 2. CC CNG CCN CHO GII TON. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1. Cng c l g ? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1.1. My tnh v phn mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2. dfhghgf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.3. vcxbvcxb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Chng 3. TIP CNBNG HNH NH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.1. Trm nghe khng bng mt thy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Chng 4. S KT HPGIA CC KIN THC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4.1. Ti sao li phi hiu bit rng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64.1.1. Discrete Fourier Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64.1.2. Fast Fourier Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Chng 5. KT QU CUI CNG. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

5.1. Cn kim tra li . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

10

Chng A. Cc kin thc km theo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9A.1. y l v d1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9A.2. y l v d2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Ti liu tham kho

12

Ch mc

feature, 3

gioithieu, 4

mode, 2

13

Li gii thiuC S TM L GII TONCc tm l khi tip cn bi tonvcvxcbgxhdxfhdfhfdhd

Cc tm l KHI TIP CN BI TON

CC CNG C CN CHO GII TONCng c l g ?My tnh v phn mm

dfhghgfvcxbvcxb

TIP CN BNG HNH NHTrm nghe khng bng mt thy

S KT HP GIA CC KIN THCTi sao li phi hiu bit rngDiscrete Fourier TransformationFast Fourier Transformation

KT QU CUI CNGCn kim tra li

Cc kin thc km theoy l v d1y l v d2