S11_202Hhwk4

# S11_202Hhwk4 - ECE 202H Spring 2011 Page 1 of 4 ECE 202H...

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Unformatted text preview: ECE 202H Spring 2011 Page 1 of 4 ECE 202H: Homework #4 Due: 24 February 2011 at 1:30 PM (5 Points) Questions that are marked with a circled asterisk ⊛ are to be submitted at the beginning of class on the specified due date. All other problems are provided for practice and are representative of problems that may be included on exams. Solutions to all problems will be posted after the due date. Foundational Mathematics 1. ⊛ This question will illustrate an important concept known as orthogonality . Suppose that and are integers. Demonstrate the following relation: 2¡ ¢−1 £=0 ¤2¥ = ¦ § , = 0, ≠ 2. Two continuous-time functions ( ) and ( ) are said to be orthogonal on the interval ( , ) if ¨ ( ) ∗ ( ) = 0 © ª where * indicates complex conjugate. Let and be integers. Also let be the period of the product, ( ) ∗ ( ) . Show that the following statements are true: a. ( ) = cos( ) and ( ) = sin( ) are orthogonal over the interval « − ¬ 2 , ¬ 2 ­ for any choice of and . b. ( ) = cos( ) and ( ) = cos( ) are orthogonal over the interval « − ¬ 2 , ¬ 2 ­ as long as ≠ . c. ( ) = sin( ) and ( ) = sin( ) are orthogonal over the interval « − ¬ 2 , ¬ 2 ­ as long as ≠ ....
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S11_202Hhwk4 - ECE 202H Spring 2011 Page 1 of 4 ECE 202H...

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