16 362 Signal and System I Signal energy
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16. 362 Signal and System I • Signal energy and power Instantaneous power Average power in time interval t 1 to t 2 Average power over infinite period Energy in time interval t 1 to t 2 Total energy
16. 362 Signal and System I • Signal energy and power– discrete time Instantaneous power Average power in time interval N 1 to N 2 Average power over infinite period Energy in time interval N 1 to N 2 Total energy
16. 362 Signal and System I • Transform of the independent variable (1) Time-shift New point located at
16. 362 Signal and System I • Transform of the independent variable (1) Time-shift New point located at
16. 362 Signal and System I • Transform of the independent variable (2) Time-reversal New point located at
16. 362 Signal and System I • Transform of the independent variable (3) Scale New point located at
16. 362 Signal and System I Example 1 1 2 -1 -2/3 1 2 2 1 1 1 2 -2
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
16. 362 Signal and System I • Exponential and Sinusoidal signals Real exponential: C, and a are real numbers a>0, exponentially increase with t. a<0, exponentially decrease with t. Complex exponential: Euler’s relation: C, and a are real numbers
16. 362 Signal and System I • Exponential and Sinusoidal signals Energy in one period: Average power:
16. 362 Signal and System I • Exponential and Sinusoidal signals, discrete-time Real exponential: C, and a are real numbers a>0, exponentially increase with n. 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
16. 362 Signal and System I Example:
16. 362 Signal and System I • Discrete-time unit impulse and unit step function Unit impulse Unit step
16. 362 Signal and System I • Discrete-time unit impulse and unit step function
16. 362 Signal and System I • continuous-time unit impulse and unit step function Unit step Unit impulse
16. 362 Signal and System I • continuous-time unit impulse and unit step function
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.