1. 16.362 Signal and System I Signal energy and power Instantaneous power Energy in time interval t1 to t2 Average power in time interval t1 to t2 Total energy Average power over infinite period

2. 16.362 Signal and System I Signal energy and power– discrete time Instantaneous power Energy in time interval N1 to N2 Average power in time interval N1 to N2 Total energy Average power over infinite period

3. 16.362 Signal and System I Transform of the independent variable (1) Time-shift New point located at

4. 16.362 Signal and System I Transform of the independent variable New point located at (1) Time-shift

5. 16.362 Signal and System I Transform of the independent variable New point located at (2) Time-reversal

6. 16.362 Signal and System I Transform of the independent variable New point located at (3) Scale

7. 16.362 Signal and System I Example 1 1 2 1 1 2 1 1 2 1 1 2 -2 -2/3 2/3

8. 16.362 Signal and System I Periodical signal Even and odd signals even odd Any signal has its even and odd signal part Even part Odd part

9. 16.362 Signal and System I Exponential and Sinusoidal signals a>0, exponentially increase with t. Real exponential:C, and a are real numbers a<0, exponentially decrease with t. Complex exponential:C, and a are real numbers Euler’s relation:

10. 16.362 Signal and System I Exponential and Sinusoidal signals Energy in one period: Average power:

11. 16.362 Signal and System I Exponential and Sinusoidal signals, discrete-time a>0, exponentially increase with n. Real exponential:C, and a are real numbers a<0, exponentially decrease with n. Complex exponential:C, and a are real numbers Periodicity properties of discrete-time complex exponential:  0 has a period of 2  N has a period of 2  /  0

12. 16.362 Signal and System I Example:

13. 16.362 Signal and System I Discrete-time unit impulse and unit step function Unit impulse Unit step

14. 16.362 Signal and System I Discrete-time unit impulse and unit step function

15. 16.362 Signal and System I continuous-time unit impulse and unit step function Unit impulse Unit step

16. 16.362 Signal and System I continuous-time unit impulse and unit step function

17. 16.362 Signal and System I Continuous-time and discrete-time systems Continuous-time Discrete-time System diagram and properties will be discussed in later chapters.