# PE1 - y k = sin x k-1(b(5 points y t = sin t-1 x t(c(5...

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EEE 203 – Signals and Systems Practice Exam #1 21 February 2008 1. Consider continuous-time signals x ( t ) and y ( t ) deﬁned by x ( t ) = u ( t ) - u ( t - 2) and y ( t ) = 1 / 4 for 0 t < 3 / 4 3 / 2 for 3 / 4 t < 2 5 / 4 for 2 t < 11 / 4 (a) (5 points) Express y ( t ) in terms of x ( t ). (b) (10 points) Using only the basic LTI components, diagram a system whose unit step response is y ( t ). 2. Convolve the following discrete-time signals. DO NOT sketch the result, but give an explicit algebraic exprtession for the value of [ x * h ]( k ). In both parts, α is a ﬁxed positive constant. (a) (15 points) x ( k ) = α k - N u ( k - N ) h ( k ) = - α k + N u ( k ) , N > 0 (b) (10 points) x ( k ) = 1 α δ ( k - N 1 ) h ( k ) = αu ( k - N 1 ) - αu ( k - N 2 ) , 0 < N 1 < N 2 3. For each of the following systems, tell whether it is memoryless, causal, linear, and time-invariant. (a) (5 points)
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Unformatted text preview: y ( k ) = sin( x ( k-1)) (b) (5 points) y ( t ) = sin( t-1) x ( t ) (c) (5 points) y ( k ) = sin(2 πk ) x ( k + 1) + sin(2 πk + π/ 2) x ( k ) 4. (10 points) Evaluate the integral Z 1 + + ∞ X m =-∞ cos(16 πt ) δ ( t-m/ 4) dt 5. (15 points) Sketch the signal x ( t ) = u (-t 2 + 5 t-4)-2 u (3-t ) + 2 u (2-t ) 6. A continuous-time LTI system has impulse response h ( t ) = sin( πt ). (a) (5 points) Is this a causal system? (b) (5 points) Is this a FIR or IIR system? (c) (10 points) Show that the output corresponding to the input signal x 1 ( t ) = x ( t-1) is y 1 ( t ) =-y ( t )....
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