1. SIGNALS and SYSTEMS

2. What is a signal?

3. SIGNALS and SYSTEMS What is a signal? What is a system?

4. SIGNALS and SYSTEMS What is a signal? What is a system?

5. SIGNALS and SYSTEMS What is a signal? What is a system? Signal: time varying function produced by physical device (voltage, current, etc.)

6. SIGNALS and SYSTEMS What is a signal? What is a system? Signal: time varying function produced by physical device (voltage, current, etc.) System: device or process (algorithm) having signals as input and output Input x(t) output y(t)

7. SIGNALS and SYSTEMS

8. ax(t) ay(t) a 1 x 1 (t) + a 2 x 2 (t) a 1 y 1 (t) + a 2 y 2 (t) Superposition

9. SIGNALS and SYSTEMS Periodic signals -- f(t+T) = f(t) Period = T (seconds) Frequency = 1/ Period (“cycles” / sec. = Hertz (Hz)

10. SIGNALS and SYSTEMS Periodic signals -- f(t+T) = f(t) Period = T (seconds) Frequency = 1/ Period (“cycles” / sec. = Hertz (Hz) Radian frequency: (radians/sec.)

11. SIGNALS and SYSTEMS Reference: Signals, Systems and Tranforms Leland B. Jackson Addison Wesley

12. SIGNALS and SYSTEMS

13. 100MHz square wave What bandwidth required for transmission?

14. SIGNALS and SYSTEMS Periodic Signal --- Composed of sinusoids MATLAB Demo

15. SIGNALS and SYSTEMS Periodic Signal --- Composed of sinusoids

16. Fourier Series is the “fundamental frequency”

17. Fourier Series Integration limits: when, then so we get:

18. Fourier Series Euler:

19. Fourier Series We can show ; recall that

20. Phasors: Phasors