SIGNALS & SYSTEMS

1. SIGNALS & SYSTEMS Bikash Kumar Behera

2. What do you mean by signal? • Describes physical phenomena • Information contained in signal is some form of variation

3. How to Represent Signals? • Mathematically represented as a function of one or more independent variables. • Examples • Voltages and currents in a circuit • Acoustic pressure (sound) over time • Velocity of a car over time • Intensity level of a pixel (camera, video) over time

4. Classification of Signals • Continuous and discrete-time signals • Even and odd signals • Periodic signals, non-periodic signals • Causal and anti-causal signals • Right-handed and left-handed signals

5. Continuous and discrete-time signals • Continuous signal • - It is defined for all time t : x(t) • Discrete-time signal • - It is defined only at discrete instants of time : x[n]

6. Even and odd signals • Even signals : x(-t)=x(t) • Odd signals : x(-t)=-x(t) • Even and odd signal decomposition • xe(t)= 1/2·(x(t)+x(-t)) • xo(t)= 1/2·(x(t)-x(-t))

7. Periodic signals, non-periodic signals • Periodic signals • - A function that satisfies the condition • x(t)=x(t + T) for all t • - Fundamental frequency : f=1/T • - Angular frequency : = 2/T • Non-periodic signals

8. Causal and anti-causal Signals • Causal signals : zero for all negative time • Anti-causal signals : zero for all positive time causal signal Antic-ausalsignal

9. Right-handed and left-handed Signals • Right-handed and left handed-signal : zero between a given variable and positive or negative infinity

10. Basic Operations on Signals • Operations performed on dependent variable • Operations performed on the independent variable

11. Operations performed on dependent variable • Amplitude scaling • Addition • Multiplication • Differentiation • Integration

12. Operations performed on the independent variable • Time scaling • a > 1 : compressed • 0 < a < 1 : expanded

13. Operations performed on the independent variable • Time reversal

14. Operations performed on the independent variable • Time shifting

15. Elementary Signals • Step function

16. Elementary Signals • Impulse function

17. Elementary Signals • Ramp function