Eshaghi - amplitude and frequency 2

# Eshaghi - amplitude and frequency 2 - Introduction to...

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Introduction to Waveforms & Frequency Spectra Amir Eshaghi Sept. 8, 2010 Waveforms static y(t) = A 0 t y(t) A 0 periodic y(t) = A 0 + Csin( ω t+ φ ) t y(t) A 0 step y(t) = A 0 U(t) t y(t) A 0 ramp y(t) = Kt 0 < t < t f t y(t) t f pulse y(t) = Kt 0 < t < t f t y(t) t 1 t=0 0 A 0 y(t + T) = y(t) period, T frequency = f = 1/T = ω/ 2 π Amplitude, A 2

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3 Waveforms: Mean Value continuous t y(t) A 0 2 1 2 1 t t t t y( t )dt y dt = example t 2 t 1 The time period over which you take the average matters. What should one use? A 0 = dc offset 4 continuous t y(t) 2 1 2 21 t t rms yd t y tt = example t 2 t 1 If the signal has no dc component, the rms value is a measure of the magnitude of the fluctuations. Waveforms: RMS Value
0 5 10 15 20 25 30 35 40 45 50 -3 -2 -1 0 1 2 3 Time Amplitude Sin((2*Pi*50*t) 3*Sin(2*pi*50*t) 5 amplitude, A frequency = f = 1/T (Hz) ω = 2 π f (radians/sec) period, T f = 1/T = 1/20*10 -3 = 50 Hz Time vs. Frequency Representation 0 50 100 150 200 250 300 350 400 0 1 2 3 4 5 6 Frequency (Hz) (milliseconds) 6 f = 1/T = 1/(10*10 -3 ) = 100 Hz Frequency 0 50 100 150 200 250 300 350 400 0 1 2 3 4 5 6 Frequency (Hz) 0 50 100 150 200 250 300 350 400 0 0.5 1 1.5 2 2.5 3 3.5 4

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## This note was uploaded on 11/28/2010 for the course ENES enes100 taught by Professor Staff during the Spring '10 term at Maryland.

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Eshaghi - amplitude and frequency 2 - Introduction to...

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