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ps2 - MIT OpenCourseWare http/ocw.mit.edu 2.161 Signal...

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MIT OpenCourseWare http://ocw.mit.edu 2.161 Signal Processing: Continuous and Discrete Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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9 ± ( r a d / s ) F ( j 9 ) 1 0 0 - 1 0 0 5 0 0 - 5 0 0 5 9 ± ( r a d / s ) H ( j 9 ) 2 0 0 - 2 0 0 4 0 0 - 4 0 0 2 W ( r a d / s ) H ( j W ) W 1 - W c c MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Problem Set 2 Assigned: Sept. 18, 2008 Due: Sept. 25, 2008 Problem 1: A waveform f ( t ) with a real even spectrum F ( j Ω) is filtered by an ideal band-pass filter with a purely real frequency response H ( j Ω) Determine the filter response y ( t ). Is this a causal filter? Problem 2: Find the impulse response of an ideal high-pass filter, with cut-off frequency Ω c : 1
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( a ) N = 1 5 ( b ) N = 3 1 ( c ) N = 6 3 Hints: Feel free to do this any way you wish, but you may find it useful to consider H ( j Ω) as a superposition of functions with known FT relationships. In particular, the solution of Prob. 5 in PS 1 might be
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