MIT6_003S10_lec09_handout

# MIT6_003S10_lec09_handout - 6.003: Signals and Systems...

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6.003: Signals and Systems 6.003: Signals and Systems Frequency Response March 4, 2010 Lecture 9 March 4, 2010 Review Last time, we saw how a linear, time-invariant (LTI) system can be characterized by its unit-sample/impulse response. DT: y [ n ]=( x h )[ n ]= x [ k ] h [ n k ] k = −∞ ± CT: y ( t )=( x h )( t )= x ( τ ) h ( t τ ) −∞ Characterizing a system by its unit-sample/impulse response is es- pecially insightful for some systems. Microscope Blurring can be represented by convolving the image with the optical “point-spread-function” (3D impulse response). target image = Blurring is inversely related to the diameter of the lens. Frequency Response Today we will investigate a diﬀerent way to characterize a system: the frequency response . Many systems are naturally described by their responses to sinusoids. Example: audio systems Hubble Space Telescope 2 10 1 2 θ optical + atmospheric blurring 2 1 2 θ optical blurring [arc-sec] Check Yourself How were frequencies modiﬁed in following music clips? HF: high frequencies : increased LF: low frequencies : decreased clip 1 clip 2 1. HF HF 2. LF LF 3. HF LF 4. LF HF 5. none of the above 1

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± 6.003: Signals and Systems Lecture 9 March 4, 2010 Demonstration Frequency Response Preview If the input to a linear, time-invariant system is an eternal sinusoid, then the output is also an eternal sinusoid: same frequency possibly diﬀerent amplitude, and possibly diﬀerent phase angle. x ( t ) = cos( ωt ) t y ( t )= M cos( + φ ) t LTI system The frequency response is a plot of the magnitude M and angle φ as a function of frequency ω . Measure the frequency response of a mass, spring, dashpot system. x ( t ) y ( t ) Frequency Response Calculate the frequency response.
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## This note was uploaded on 11/07/2011 for the course ELECTRICA 6.003 taught by Professor Staff during the Summer '10 term at MIT.

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MIT6_003S10_lec09_handout - 6.003: Signals and Systems...

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