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quiz2v2_s04

quiz2v2_s04 - PROBLEM SPR-04-Q.2.1 A periodic signal x(t is...

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PROBLEM SPR-04-Q.2.1: A periodic signal x ( t ) is represented as a Fourier series of the form x ( t ) = k =-∞ ( - j 3 k - 3 δ [ k ] ) e j 400 π kt (a) Determine the fundamental period of the signal x ( t ) , i.e., the minimum period. T 0 = 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 ) = 5 cos ( 800 π t ) + x ( t ) The new signal, y ( t ) can be expressed in the following Fourier Series with new coefficients { b k } : y ( t ) = k =-∞ b k e j 400 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 0 b 1 b 2 b 3

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PROBLEM SPR-04-Q.2.2: For each short question, pick a correct frequency 3 (from the list on the right only) and enter the number in the answer box 4 : Question (a) Determine the Nyquist rate for sampling the signal x ( t ) defined by: x ( t ) = e { e j 4000 π t + e j 3000 π t } .
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