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Digital Signal Processing ( week 3 )

Digital Signal Processing ( week 3 ). Review of Complex Numbers. Representation of Complex Numbers Catersian plane real part : x=Re(z) image part : y=Im(z) j =. Im(z). x. Re(z). y. (x,y). Review of Complex Numbers. Representation of Complex Numbers Complex plane

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Digital Signal Processing ( week 3 )

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  1. Digital Signal Processing( week 3 )

  2. Review of Complex Numbers • Representation of Complex Numbers • Catersian plane • real part : x=Re(z) • image part : y=Im(z) • j = Im(z) x Re(z) y (x,y)

  3. Review of Complex Numbers • Representation of Complex Numbers • Complex plane • magnitude : r , (denote, |z|) • argument : θ , (denote, arg z) Im(z) θ x Re(z) r y

  4. Review of Complex Numbers • Representation of Complex Numbers • Catersian plane ⇔ Complex plane

  5. Complex 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)

  6. Properties • the Rotating Phasor Interpretation • the magnitude : multiply • the angle : add 일 때,

  7. Properties • the Rotating Phasor Interpretation 일 때,

  8. Properties • Euler Formulas ⇔

  9. Properties • Addition of Complex Numbers 일 때,

  10. Properties • Addition of Complex Numbers (a) Represent x1(t) and x2(t) by the phasors :

  11. Properties • 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

  12. Properties • Addition of Complex Numbers

  13. Matlab 교재 CD 없는 학생 • ftp://image.dgu.ac.kr • id : dsp • pass : dsp • “DSP \ spfirst.zip”다운로드 • 압축 풀고, • File → Set Path • Add path “/spfirst”

  14. Matlab 교재 CD 있는 학생 • Insert CD (in your textbook) & Run Matlab • File → Set Path • Add path “CD/Matlab/spfirst”

  15. Matlab • 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

  16. Matlab • 예 제 • 각 함수를 이용하여 연습하시오 • zvect( ) • zprint( ) • zcat( ) 1+j j 3-4j ejπ ej2π/3

  17. Matlab

  18. Matlab

  19. Matlab

  20. 과 제

  21. 과 제

  22. 과 제 • 작성한 M 파일과 HWP(DOC) 파일 압축 • 파일명 : 04_학번_성명.zip • 수업시간 끝나기 전까지 • E-mail : young220 @ paran.com

  23. 수고 하셨습니다

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