20092ee102_1_S09-102-HW-6

20092ee102_1_S09-102-HW-6 - Spring 2009: Put First Letter...

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Unformatted text preview: Spring 2009: Put First Letter of LAST Name in the corner %% ( Otherwise Your HW Will Be LOST! ) PRINT: (LAST , Middle, First): EE102: SYSTEMS & SIGNALS HW: # 6 A LATE HW IS A NON-HW! Posted: May 7 Hand In To Me 1 : May 14 Attach This Sheet To Your HW (Otherwise It Will Be Lost!) Note: MatLab can be useful here 1. Calculate the following integrals, for all integers m, n : Z 2 sin mt sin nt dt = ? , m = n = ? , m 6 = n Z 2 cos mt cos nt dt = ? , m = n = ? , m 6 = n Z 2 sin mt cos nt dt = ? , m = n = ? , m 6 = n What can you conclude from your calculations ? 2. Consider the following signals: f ( t ) = 1 2 , f 1 ( t ) = r 3 2 t, f 2 ( t ) = r 45 8 t 2 1 3 , t [ 1 , 1] 1 during the break of the Thursday Lecture 1 For this problem we define (the dot or scalar product) h f ( t ) , g ( t ) i := Z 1 1 f ( t ) g ( t ) dt (i) Verify whether the signals { f i ( t ) , i = 0 , 1 , 2 } are (mutually) orthogo-...
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20092ee102_1_S09-102-HW-6 - Spring 2009: Put First Letter...

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