Operations on Continuous Time Signals

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Shifting, Scaling, Reflection and Symmetric operations on a Continuous Time Signal. Presented in East West University.

1. Operations on continuous time signals 1

2. Presented By 1. Md. Jayedul Islam 2015-2-65-017 2. Al-Amin Islam Hridoy 2016-1-60-023 3. Nawan Islam 2016-1-60-027 2

3. Overview Introduction Operations Conclusion 3

4. Introduction What is signal? Signals are detectable physical quantities or variables by means of which messages or information can be transmitted. Example include human voice, television pictures, teletype data, atmospheric temperature etc. 4

5. Types of Operations Shifting operation Reflection operation Scaling operation Symmetric Even Symmetric Odd Symmetric Even And Odd Part 5

6. Let’s Consider a signal: The Graphical Expression of the signal:   6

7. Shifting Operation It represents time-shifted version of x ( t ). That is x ( t – t ) If t > 0, the signal is delayed by t seconds If t < 0, the signal represents an advanced replica of x ( t ) 7

8. Applying shifting Operation   8

9. Applying shifting Operation Similarly:   9

10. Scaling Operation Scaled version of x(t) is x(ƞ t). If | ƞ| >1 the signal is compressed if | ƞ| <1 the signal is expanded. 10

11. Applying Scaling Operation Compressed version:   11

12. Applying Scaling Operation Expand version:   12

13. Reflection Operation Reflection version is x(- t), which is the reversion of x(t ). It flips the signal horizontally horizontal axis acts as the mirror transformed image is exactly the mirror image of the parent signal Also - x(t ), which is the upside down reversion of x(t). It flips the signal vertically vertical axis acts as the mirror 13

14. Applying Reflection Operation   14 Reflection with X Axis Reflection with Y Axis Reflection with both X & Y Axis

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16. Even or Odd symmetric I f x(t) = x(-t), then the signal is Even symmetric If x(t) = -x(-t), then the signal is Odd symmetric Here x(-t) is the reflected version with X Axis Here –x(-t) is the reflected version with both X & Y Axis 16

17. Even Symmetric: 17 Here, the signal is not even symmetric. Comparing x(t) and x(-t)

18. Odd Symmetric: 18 Here, the signal is not odd symmetric. Comparing x(t) and -x(-t)

19. Even Part and Odd Part The Even part of a signal is defined by, The Odd part of a signal is defined by,   19

20. Conclusion In our project, we have showed how to implement signal transformation mathematically and graphically applying the operations like shifting , scaling , reflection , symmetric , even and odd part in order to convey the signal information. 20

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