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Unformatted text preview: 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 uiz 3 Details Date: Wednesday April 28th, 2010 Time: 7.30pm9.30pm Content: (boundaries inclusive) Lectures 120 Recitations 120 Homeworks 111 (Massachusetts Institute of Technology) Quiz III Review April 26th, 2010 2 / 1 eview 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 T 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 t dt = T [ k ] T The analysis equation gives us the Fourier coecients 1 j 2 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 k = (Massachusetts Institute of Technology) Quiz III Review April 26th, 2010 4 / 1 T Fourier Transform The aperiodic extension:...
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This note was uploaded on 12/14/2011 for the course EE 6.003 taught by Professor Freeman during the Spring '11 term at MIT.
 Spring '11
 Freeman

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