MIT6_003S10_lec09

MIT6_003S10_lec09 - 6.003: Signals and Systems Frequency...

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6.003: Signals and Systems Frequency Response March 4, 2010
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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 its unit-sample/impulse response is es- pecially insightful for some systems.
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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.
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Hubble Space Telescope optical + atmospheric blurring optical blurring 2 10 1 2 θ 2 1 2 θ [arc-sec]
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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
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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
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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
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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
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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
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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
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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
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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
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Check Yourself original
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MIT6_003S10_lec09 - 6.003: Signals and Systems Frequency...

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