sample02 - ENEE 241 EXAM 2 SAMPLE PROBLEMS Calculators will...

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ENEE 241 EXAM 2: SAMPLE PROBLEMS Calculators will not be allowed. The following formulas will be given on the exam sheet: Time Domain Frequency Domain x [ n ] = 1 N N - 1 X k =0 X [ k ] e j (2 π/N ) kn ←→ X [ k ] = N - 1 X n =0 x [ n ] e - j (2 π/N ) kn x = 1 N VX ←→ X = Wx α x + β y ←→ α X + β Y x * ←→ RX * Rx ←→ RX P m x ←→ F - m X F m x ←→ P m X X ←→ N Rx x ƒ y ←→ 1 N ( X ~ Y )[ k ] = 1 N X T P k RY ( x ~ y )[ n ] = x T P n Ry ←→ X ƒ Y PROBLEM 1 The continuous-time real-valued signal s ( t ) is a sum of two real-valued sinusoids of frequency no higher than 25 Hz, plus a DC offset (i.e., a constant). It is sampled at times t = nT s , where n = 0 ,..., 19 and T s = 0 . 02 seconds. The amplitude and phase spectra of the sampled signal are shown in the figure below. |S[ k ]| 0 4 8 12 16 19 8 S[ k ] π 14 10 8 10 0.7π -0.7π 0.4π -0.4π Use the information given above to write an equation for s ( t ), valid for all t R .
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PROBLEM 2 The time-domain signal s = £ a b c d 0 0 0 0 T has DFT given by S = £ 4 4 - j (2 - 2) 2 4 + j (2 + 2) 8 4 - j (2 + 2) 2 4 + j (2 - 2) T (i) Compute the numerical value of a - b + c - d . (ii)
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sample02 - ENEE 241 EXAM 2 SAMPLE PROBLEMS Calculators will...

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