SPFirst-L19

# SPFirst-L19 - Signal Processing First READING ASSIGNMENTS...

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Signal Processing First Lecture 19 Continuous-Time Signals and Systems 4/3/2006 3 READING ASSIGNMENTS ± This Lecture: ± Chapter 9, Sects 9-1 to 9-5 ± Other Reading: ± Recitation: Ch. 9, all ± Next Lecture: Chapter 9, Sects 9-6 to 9-8 4/3/2006 4 LECTURE OBJECTIVES ± Bye bye to D-T Systems for a while ± The UNIT IMPULSE signal ± Definition ± Properties ± Continuous-time signals and systems ± Example systems ± Review: L inearity and T ime- I nvariance ± Convolution integral: impulse response 4/3/2006 5 D-T Filtering of C-T Signals C-to-D D-to-C LTI System H(z) x ( t ) y ( t ) LTI ANALOG System x ( t ) y ( t ) ˆ ω =ω T s or ω= ˆ ω f s

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4/3/2006 6 ANALOG SIGNALS x(t) ± INFINITE LENGTH ± SINUSOIDS: (t = time in secs) ± PERIODIC SIGNALS ± ONE-SIDED, e.g., for t>0 ± UNIT STEP: u(t) ± FINITE LENGTH ± SQUARE PULSE ± IMPULSE SIGNAL: δ (t) ± DISCRETE-TIME: x[n] is list of numbers 4/3/2006 7 CT Signals: PERIODIC x ( t ) = 10cos(200 π t ) Sinusoidal signal Square Wave INFINITE DURATION 4/3/2006 8 CT Signals: ONE-SIDED v ( t ) = e t u ( t ) Unit step signal u ( t ) = 1 t > 0 0 t < 0 One-Sided Sinusoid “Suddenly applied” Exponential 4/3/2006 9 CT Signals: FINITE LENGTH Square Pulse signal p ( t ) = u ( t 2) u ( t 4) Sinusoid multiplied by a square pulse
4/3/2006

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SPFirst-L19 - Signal Processing First READING ASSIGNMENTS...

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