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Chapter 2 Notes

# Chapter 2 Notes - Chapter 2 Static and Dynamic...

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1 Chapter 2 Static and Dynamic Characteristics of Signals Signals ± Signals classified as 1. Analog – continuous in time and takes on any magnitude in range of operations 2. Discrete Time – measuring a continuous variable at finite time intervals 3. Digital – discretized magnitude at discrete times ± Quantization assigns a single number to represent a range of magnitudes of a continuous signal ± This is done by a Analog to Digital A/D converter

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2 Signal Wave Form ± Static – does not vary with time and can be considered over long periods, like the life of a battery. ± Dynamic Signal – time dependent y(t) Definitions ± Deterministic Signal –as igna l that varies in time in a predictable manner, such as a sine wave, a step function, or a ramp function. ± Steady Periodic lwhose variation of the magnitude of the signal repeats at regular intervals in time. Definitions cont’d ± Complex Periodic Waveform contains multiple frequencies and is represented as a superposition of multiple simple periodic waveforms. ± Aperiodic Waveforms – deterministic signals that do not repeat at regular intervals (step function). ± Nondeterministic Signal lw ith no discernible pattern of repetition.
3 For periodic signal: c = amplitude f = 1/T cycles/sec (hz) T = period ω = 2 Π frad/sec Signal Analysis ± Assume y=current If power is equal to P=I 2 R, then energy is dissipated in resistor from t 1 to t 2 Y t t ytd t t t dt = ∫∫ (( ) ) / ( ) 2 1 2 1 Signal Analysis ± ± To find a fixed current I e that produces some energy dissipation in time t 1 to t 2 , E t t Pdt T T It Rd t == 2 1 2 1 2 [() ] E t t Pdt t t IR d t IR t t t t t ee =− = 2 1 2 1 22 21 2 1 2 ()[ ( ) ] It t t t It d t I eR M S (/ ( ) ) [() ] 1 2 1 2

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4 ± A time dependent analog signal can be approximated by a discrete set of N numbers over the time period from t 1 to t 2 y(t) {y(r δ t)} r=1,2,N where δ t = sampling time Mean Value ± For discrete time signals, approximate the mean value RMS yN y i i N = = (/ ) 1 1 y rms i i N = = 1 1 2 Signal Averaging Period ± The choice of time period for signal analysis depends on the type of signal ± For simple periodic, use time period equal to the period of the function. That gives a good representation of long term average value and RMS value.
5 Signal Averaging Period ± Averaging a simple periodic signal over a time period that is not exactly the period of the function can produce misleading results. ± However, as the averaging time period becomes long relative to the signal period, the resulting values will accurately represent the signal.

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Chapter 2 Notes - Chapter 2 Static and Dynamic...

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