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quiz03_review

# quiz03_review - Quiz III Review Signals and Systems 6.003...

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Quiz III Review Signals and Systems 6.003 Massachusetts Institute of Technology April 26th, 2010 (Massachusetts Institute of Technology) Quiz III Review April 26th, 2010 1 / 1

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Quiz 3 Details Date: Wednesday April 28th, 2010 Time: 7.30pm–9.30pm Content: (boundaries inclusive) Lectures 1–20 Recitations 1–20 Homeworks 1–11 (Massachusetts Institute of Technology) Quiz III Review April 26th, 2010 2 / 1
Review Outline CT Fourier Series CT Fourier Transforms DT Frequency Response DT Fourier Series DT Fourier Transforms Fourier Relations The Impulse Train and Periodic Extension Filters (Massachusetts Institute of Technology) Quiz III Review April 26th, 2010 3 / 1

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CT Fourier Series Periodic signals can be represented by a sum of harmonics The integral over one period of a harmonic is equal to zero, except for k=0. e jk ω 0 t dt = T δ [ k ] T The ”analysis” equation gives us the Fourier coeﬃcients 1 j 2 π a k = x ( t ) e T kt dt T T The ”synthesis” equation reconstructs the periodic signal kt T x ( t ) = x ( t + T ) = a k e j 2 π k = −∞ (Massachusetts Institute of Technology) Quiz III Review April 26th, 2010 4 / 1
CT Fourier Transform The aperiodic extension: The Fourier series can be generalized to an aperiodic signal by viewing the signal as a periodic

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