20082ee102_1_hw6

20082ee102_1_hw6 - SPRING 2008: Put First Letter * of LAST...

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SPRING 2008: Put First Letter * of LAST Name in the corner →→%% (* Otherwise Your HW will be LOST) PRINT: (LAST, Middle, First):——————————————————– HW: # 6 A LATE HW IS NEVER A HW! Posted: May 8st Hand In: May 15th Attach This Sheet To Your HW 1. The Laplace Transformation of φ n ( t ), t [0 , ) are: Φ n ( s ) = 2 s + 1 ( s - 1 s + 1 ) n ,n = 0 , 1 . (i) Find φ n ( t ), n=0,1. (ii)Calculate the scalar products < φ n ( t ) m ( t ) > := Z 0 φ n ( t ) φ m ( t ) dt,m,n = 0 , 1 . i.e. calculate < φ 0 ( t ) 0 ( t ) >,< φ 0 ( t ) 1 ( t ) >,< φ 1 ( t ) 1 ( t ) > Can you conclude that the signals φ n ( t ) are orthonormal? (iii) Given f ( t ) := te - t ,t 0 . Calculate the following scalar products: < f ( t ) n ( t ) >,n = 0 , 1 . Sketch f(t) and f 2 ( t ) deﬁned by: f 2 ( t ) := Σ 1 n =0 < f ( t ) n ( t ) > φ n ( t ) 1

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Do they look kind of alike? (iv)Calculate the number
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20082ee102_1_hw6 - SPRING 2008: Put First Letter * of LAST...

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