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Unformatted text preview: PROBLEM s04Q.2.1: A periodic signal x ( t ) is represented as a Fourier series of the form x ( t ) = ∞ X k =∞ ( j k + 5 δ [ k ] ) e j . 5 π kt (a) Determine the fundamental period of the signal x ( t ) , i.e., the minimum period. T = sec. (Give a numerical answer.) (b) Determine the DC value of x ( t ) . Give your answer as a number. DC = (c) Define a new signal by adding a sinusoid to x ( t ) y ( t ) = 2 cos ( 1 . 5 π t π) + x ( t ) The new signal, y ( t ) can be expressed in the following Fourier Series with new coefficients { b k } : y ( t ) = ∞ X k =∞ b k e j . 5 π kt Fill in the following table, giving numerical values for each { b k } in polar form:. Hint: Find a simple relationship between { b k } and { a k } . b k Mag Phase b 3 b 2 b 1 b b 1 b 2 b 3 PROBLEM s04Q.2.2: For each short question, pick a correct frequency 7 (from the list on the right only) and enter the number in the answer box 8 : Question (a) If the C/D converter output is x [ n ] = A cos ( .....
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 Spring '08
 JUANG
 Fourier Series, Signal Processing, Periodic function, 2e j2 cos

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