sample quiz2-answer - Sample Quiz(Close book 1-page formula...

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Sample Quiz (Close book, 1-page formula sheets allowed) Put and hand in answers on quiz . You may use back pages Name: ID# . Each bullet is 5 points unless stated otherwise. Problem 1 (Signal Space Representations) The Hadamard matrix given for example by - = 1 1 1 1 2 H . Give the Hadamard matrix for 4 H . What is the property relating the Hadamard codes (rows of the Hadamard matrix? How is this property used for the forward link in cellular CDMA communications? Consider 2FSK with ) ) ( 2 cos( 2 ) ( t f m f T E t s c m + = π for T t 0 and m =0, 1. Show that the two signals are orthogonal if T f 2 / 1 = .
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Find an orthonormal basis for the signals. Then plot the signals in the signal space of the orthonormal basis. (10%) Suppose the signal suffers a Doppler shift of frequency of T f 10 / 1 = . In other words, the signals are now ) ) 10 1 ( 2 cos( 2 ) ( 0 t T f T E t s c + = π and ) ) 10 6 ( 2 cos( 2 ) ( 1 t T f T E t s c + = π . By projecting the signals onto the orthonormal basis, plot the new signal points which are skewed by Doppler shift.
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