lec11 - 6.003: Signals and Systems Frequency Response...

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Unformatted text preview: 6.003: Signals and Systems Frequency Response October 20, 2009 Mid-term Examination #2 Wednesday, October 28, 7:30-9:30pm, Walker Memorial. No recitations on the day of the exam. Coverage: cumulative with more emphasis on recent material lectures 112 homeworks 17 Homework 7 will include practice problems for mid-term 2. However, it will not collected or graded. Solutions will be posted. Closed book: 2 page of notes ( 8 1 2 11 inches; front and back). Designed as 1-hour exam; two hours to complete. Review sessions during open office hours. Conflict? Contact freeman@mit.edu by Friday, October 23, 5pm. 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 ] = k = x [ k ] h [ n k ] CT: y ( t ) = ( x h )( t ) = x ( ) h ( t ) d 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. Hubble Space Telescope Hubble images before and after upgrading the optics. before after http://hubblesite.org 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 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 Check Yourself original clip 1: HF HF LF LF none original clip 1: HF HF LF LF none original clip 2: HF HF LF LF none original clip 2: HF HF LF LF none clip 1 clip 2 1. HF HF 2. LF LF 3. HF LF 4. LF HF 5. none of the above Check Yourself original clip 1: HF HF LF LF none original clip 1: HF HF LF LF none original clip 2: HF HF LF LF none original clip 2: HF HF LF LF none clip 1 clip 2 1. HF HF 2. LF LF 3. HF LF 4. LF HF 5. none of the above Check Yourself original clip 1: HF HF LF LF none original clip 1: HF HF LF LF none original clip 2: HF HF LF LF none original clip 2: HF HF LF LF none clip 1 clip 2 1. HF HF 2. LF LF 3. HF LF 4. LF HF 5. none of the above Check Yourself original clip 1: HF HF LF LF none original clip 1: HF HF LF LF none original clip 2: HF HF LF LF none original clip 2: HF HF LF LF none clip 1 clip 2 1. HF HF 2. LF LF 3. HF LF 4. LF HF 5. none of the above Check Yourself...
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lec11 - 6.003: Signals and Systems Frequency Response...

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