1 / 25

Signal Characteristics Common Signal in Engineering Singularity Function

Signal Characteristics Common Signal in Engineering Singularity Function. Section 2.2-2.3. Signal Characteristics. Review Even function Odd function Periodic Signal. Represent x e (t) in terms of x(t). X e (t) X(t)= X e (t)+X o (t) X e (t)=X(t)-X o (t) Xo(t)=-Xo(-t)

damien
Download Presentation

Signal Characteristics Common Signal in Engineering Singularity Function

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Signal CharacteristicsCommon Signal in EngineeringSingularity Function Section 2.2-2.3

  2. Signal Characteristics • Review • Even function • Odd function • Periodic Signal

  3. Represent xe(t) in terms of x(t) • Xe(t) • X(t)=Xe(t)+Xo(t) • Xe(t)=X(t)-Xo(t) • Xo(t)=-Xo(-t) • X(-t)=Xe(-t)+Xo(-t) • Xe(t)=X(t)-Xo(-t)=X(t)+X(-t)-Xe(-t) • Therefore Xe(t)=[X(t)+X(-t)]/2 • Similarly Xo(t)=[X(t)-X(-t)]/2

  4. Even Function Example(1) • Xe(t)=X(t)+Xo(t) • X(t) is the sum of an even part and an odd part. (X(t)=Xe(t)+Xo(t)) • Let X(t) be a unit step function

  5. Even Function Example(2) X(t) X(-t) (X(t)+X(-t))/2 gives you an even function!

  6. Odd Function Example(1) X(t) X(-t) (X(t)-X(-t))/2 gives you an odd function!

  7. Odd Function Example • Mathemtica function: • Use Exp[-t/2] to represent exponential • Use UnitStep[t] to zero out t<0 • Generate an odd and an even function

  8. Answer

  9. Periodic Signal • X(t) is period if X(t)=X(t+T), T>0 • T is the period • To is the minimum value of T that satisfies the definition • A signal that is not period is aperiodic. To

  10. Is This Signal Periodic?

  11. A Systematic Procedure The sum of continuous-time periodic signal is period if and only if the ratios of the periods of the individual signals are ratios of integers Example: x(t)=x1(t)+x2(t)+x3(t)

  12. Is This Signal Periodic? x(t)=x1(t)+x2(t)+x3(t)+x4(t) π is irrational, aperiodic

  13. Common Signals in Engineering X(t)=Ceatoccurs frequently in circuits! C and a can be complex! C and a are real C is complex and a is imaginary C and a are complex

  14. Euler’s Formula

  15. Mathematica Example

  16. Complex Exponential in Polar Form

  17. Case 1: C and a are real (Bacterial growth)

  18. Case 2: C=complex, a is imaginary

  19. Application Example

  20. Case 3: C=Complex and a=complex

  21. Singular Functions • Unit Step Function • Rectangular Function • Impulse Response

  22. Unit Step Function

  23. Properties of Unit Step Function u(2t-1) u(at-1)=u(t-1/a) u(t-1/2)

  24. u(t)=1-u(-t)

  25. Multiple Plots Using Mathematica

More Related