1. (Part one: Continuous)
Signals and Systems
(Part one: Continuous)

2. General Information Lecturer Reference Dr. Yasmine Fahmy
Signals and systems, Oppenheim A.V., Wilski A.S., Prentice Hall, 1997
Dr. Yasmine Fahmy

3. Course Contents Signals (definition, properties , important signals) 2
Systems (definition, properties)
Linear Time Invariant (LTI) Systems
Fourier Series
Fourier Transform
LTI Systems in Frequency Domain
Applications (Filters, Sampling, Modulation) 2 1 9
Dr. Yasmine Fahmy

4. variables carrying information
Signals
variables carrying information
Electrical signals
Voltages and currents in a circuit
Acoustic signals
Acoustic pressure (sound) over time
Mechanical signals
Velocity of a car over time
Video signals
Intensity level of a pixel (camera, video) over time
Dr. Yasmine Fahmy

5. Continuous / Discrete Velocity Voltage Pixels Daily stock price x(t) t
x[n] n
Velocity
Voltage
Pixels
Daily stock price
Dr. Yasmine Fahmy

6. Analog / Digital Continuous Analog Signal t Discrete Analog Signal
Continuous Quantized Analog Signal n
Dr. Yasmine Fahmy

7. Analog / Digital Sampling Quantization Coding t n n 01001111010011010 n
Sampling
Quantization
Coding
Dr. Yasmine Fahmy

8. Properties of Signals Signal Energy and Power Transformation in Time
(Shift, Reverse, Scaling)
Periodic Signals
Even and Odd Signals
Dr. Yasmine Fahmy

9. Signal Energy and Power
Energy over time interval
Average Power over time interval
Dr. Yasmine Fahmy

10. Signal Energy and Power
Total Energy
Average Power
Dr. Yasmine Fahmy

11. Transformation in Time
x(t)
Time Shift t
x(t+to)
x(t-to) t t
-to to
+to Advance -to Delay
Dr. Yasmine Fahmy

12. Transformation in Time
Time Reverse
x(t)
x(-t) t t
Dr. Yasmine Fahmy

13. Transformation in Time
x(t)
Time Scaling t
x(׀α׀ t)
x(׀α׀ t) t t
׀α ׀ < Compressed ׀α > ׀ Stretched
Dr. Yasmine Fahmy

14. Example 1 Find: The equation of x(t) The values of x(t+1) x(-t+1), , ,
Dr. Yasmine Fahmy

15. NOTE Power signals: Energy signals: Infinite Energy Finite Energy
Finite Power
Energy signals:
Finite Energy
Zero Power
Dr. Yasmine Fahmy

16. (is the minimum value of T)
Periodic Signals
x(t) = x(t+T)
Where
Period := T
Fundamental Period := To
(is the minimum value of T) t
Dr. Yasmine Fahmy

17. Example 2
Find the period of the following signals:
Dr. Yasmine Fahmy

18. Even & Odd Signals Even Odd x(t) = x(-t) x(t) = -x(-t)
Symmetric around the axis
Odd
x(t) = -x(-t)
Symmetric around the origin t t
Dr. Yasmine Fahmy

19. Even & Odd Signals For any signal x(t) x(t) = xe(t)+ xo(t) Where
xe(t)=1/2 [x(t)+x(-t)]
xo(t)=1/2 [x(t) -x(-t)]
Dr. Yasmine Fahmy

20. Example 3 Find and Sketch The Even and Odd components of x(t) X(t) 1, ,
Find and Sketch
The Even and Odd components of x(t) ,
Dr. Yasmine Fahmy

21. Example 3
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22. Lecture Overview Signal (continuous/discrete/analog/digital)
Signal Properties
Signal Energy and Power
Transformation in Time (Shift, Reverse, Scaling)
Periodic Signals
Even and Odd Signals
Dr. Yasmine Fahmy