2025-L16su10 - ECE2025 Summer 2010 Lecture 16...

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1 7/6/2010 1 ECE2025 Summer 2010 Lecture 16 Continuous-Time Signals and Systems 09 July 10 7/6/2010 3 ANNOUNCEMENTS ± July 12-13 ± Turn in Homework 7 ± July 14-15: ± Turn in Lab #7 ± Do Lab #8 ± July 16: ± Quiz 3 7/6/2010 4 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 7/6/2010 5 Continuous-Time Analysis ± Put aside 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
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2 7/6/2010 6 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 = ˆ f s 7/6/2010 7 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 7/6/2010 8 CT Signals: PERIODIC x ( t ) = 10cos(200 π t ) Sinusoidal signal Square Wave INFINITE DURATION 7/6/2010 9 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
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3 7/6/2010 10 CT Signals: FINITE LENGTH Square Pulse signal p ( t ) = u ( t 2) u ( t 4) Sinusoid multiplied by a square pulse 7/6/2010 11 What is an Impulse? ± A signal that is concentrated at one point. lim Δ→ 0 δ Δ ( t ) = ( t ) Δ ( t ) dt = 1 −∞ 7/6/2010 12 ± Assume the properties apply to the limit: ± One “ INTUITIVE” definition is: Defining the Impulse Unit area ( τ ) d −∞ = 1 Concentrated at t=0 ( t ) = 0, t 0 lim 0 Δ ( t ) = ( t ) 7/6/2010 13 Sampling Property f ( t ) ( t ) = f (0) ( t ) f ( t ) Δ ( t ) f Δ ( t )
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4 7/6/2010 14 General Sampling Property f ( t ) δ ( t t 0 ) = f ( t 0 ) ( t t 0 ) 7/6/2010 15 Properties of the Impulse Concentrated at one time Sampling Property Unit area Extract one value of f(t) Derivative of unit step f ( t ) ( t t 0 ) = f ( t 0 ) ( t t 0 ) ( t t 0 ) dt
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This note was uploaded on 10/21/2010 for the course ECE 2025 taught by Professor Juang during the Summer '08 term at Georgia Institute of Technology.

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2025-L16su10 - ECE2025 Summer 2010 Lecture 16...

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