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Assign2_FourierSeries

# Assign2_FourierSeries - coefficients b k of w t and the...

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EE3210 Assignment 2: Fourier Series Due: (before lecture) Oct 7, 2009 (Marks will be deducted for late submission.) 1. Find the derivative of the following signal: ) 1 ( ) ( ) 1 ( 2 = t u e t x t , where u ( t ) is the unit step function. (Hint: Use the Chain Rule.) 2. Determine the Fourier series representation of the following signal: . 3. Determine the Fourier series representation of the periodic signal x ( t ), with period 2 π and x ( t ) = t for – π < t < π . 4. Let x ( t ) be a continuous-time periodic signal with Fourier series coefficients, { a k }. Given that ) 1 ( ) ( t x t w = , find a relationship between the Fourier series
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Unformatted text preview: coefficients { b k } of w ( t ) and the coefficients { a k }. 5. For the discrete-time signal ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = 3 4 sin ] [ ππ n n x , determine the Fourier series coefficients. (Hint: Use Euler formula to express x [ n ] in terms of complex exponential functions.) 6. Consider the following discrete-time signal x [ n ], which is periodic with period 6: ..., x [0] = 1, x [1] = 1, x [2] = 1, x [3] = 1, x [4] = 0, x [5] = 0 … Find its Fourier series coefficients....
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