Digital Signal ProcessingDigital Signal Processing( week 3 )( week 3 )

Digital Image Processing Digital Image Processing LAB.LAB.

Review of Complex NumbersReview of Complex Numbers

Representation of Complex Numbers Catersian plane

real part : x=Re(z) image part : y=Im(z) j =

Im(z)

Re(z)x

y(x,y)

jyxz

1

Digital Image Processing Digital Image Processing LAB.LAB.

Review of Complex NumbersReview of Complex Numbers

Representation of Complex Numbers Complex plane

magnitude : r , (denote, |z|) argument : θ , (denote, arg z)

Im(z)

Re(z)x

y

θ

jrez

r rz

Digital Image Processing Digital Image Processing LAB.LAB.

Review of Complex NumbersReview of Complex Numbers

Representation of Complex Numbers Catersian plane ⇔ Complex plane

Catersian plane Complex plane

cosrx

sinry

22 yxr

)arctan(x

y

sincos jrrre j

Digital Image Processing Digital Image Processing LAB.LAB.

Complex Exponential SignalsComplex Exponential Signals

representation

a complex-valued function of t A : the magnitude, |z(t)| = A

(w0t+Φ) : the angle of z(t) Φ : phase shift w0 : frequency (rad/sec)

)( 0)( jAetz

)sin()cos( 00 tjAtA

Digital Image Processing Digital Image Processing LAB.LAB.

PropertiesProperties

the Rotating Phasor Interpretation

the magnitude : multiply the angle : add

111

jerz 222

jerz

2121213

jj eerrzzz

일 때 ,

Digital Image Processing Digital Image Processing LAB.LAB.

PropertiesProperties

the Rotating Phasor Interpretation

jAeX )(00)( tjtjjtj AeeAeXetz

tjXetz 0)( 일 때 ,

tt 0)( ,where

Digital Image Processing Digital Image Processing LAB.LAB.

PropertiesProperties

Euler Formulas

sincos jrrre j 2

cos

jj ee

j

ee jj

2sin

⇔

Digital Image Processing Digital Image Processing LAB.LAB.

PropertiesProperties

Addition of Complex Numbers

111 jyxz

222 jyxz )()( 2121213 yyjxxzzz

일 때 ,

Digital Image Processing Digital Image Processing LAB.LAB.

PropertiesProperties

Addition of Complex Numbers

(a) Represent x1(t) and x2(t) by the phasors :

)180

7020cos(7.1)(1 ttx )

180

20020cos(9.1)(2 ttx

???)()()( 213 txtxtx

180

70

11 7.11jj eeAX

180

200

22 9.12jj eeAX

Digital Image Processing Digital Image Processing LAB.LAB.

PropertiesProperties

Addition of Complex Numbers(b) Convert both phasors to rectangular form:

(c) Add the real parts and the imaginary parts:

(d) Convert back to polar form:

(e) The final formula

597.15814.01 jX 6498.0785.12 jX

9476.0204.1213 jXXX

180

79.141

3 532.1j

eX

)180

79.14120cos(532.13 tx

Digital Image Processing Digital Image Processing LAB.LAB.

PropertiesProperties

Addition of Complex Numbers

Digital Image Processing Digital Image Processing LAB.LAB.

MatlabMatlab

ftp://image.dgu.ac.kr id : dsp pass : dsp

“DSP \ spfirst.zip” 다운로드

압축 풀고 ,

File → Set Path Add path “/spfirst”

교재 CD 없는 학생

Digital Image Processing Digital Image Processing LAB.LAB.

MatlabMatlab

Insert CD (in your textbook) & Run Matlab

File → Set Path Add path “CD/Matlab/spfirst”

교재 CD 있는 학생

Digital Image Processing Digital Image Processing LAB.LAB.

MatlabMatlab

함수 UCPLOT( )

Plot a circle with specified center and radius

ZVECT( ) Plot vectors in complex z-plane from zFrom to zTo

ZPRINT( ) Printout complex # in rect and polar form

ZCAT( ) Plot vectors in z-plane end-to-end

Digital Image Processing Digital Image Processing LAB.LAB.

MatlabMatlab

예 제 각 함수를 이용하여 연습하시오

zvect( ) zprint( ) zcat( )

1+j

j

3-4j

ejπ

ej2π/3

Digital Image Processing Digital Image Processing LAB.LAB.

MatlabMatlab

Digital Image Processing Digital Image Processing LAB.LAB.

MatlabMatlab

Digital Image Processing Digital Image Processing LAB.LAB.

MatlabMatlab

Digital Image Processing Digital Image Processing LAB.LAB.

과 제과 제

Digital Image Processing Digital Image Processing LAB.LAB.

과 제과 제

Digital Image Processing Digital Image Processing LAB.LAB.

과 제과 제

작성한 M 파일과 HWP(DOC) 파일 압축

파일명 : 04_ 학번 _ 성명 .zip

수업시간 끝나기 전까지

E-mail : young220 @ paran.com

Digital Image Processing Digital Image Processing LAB.LAB.

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