stest1-2005 - t u(2-t(a Determine whether x t is a power...

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Name BME 171, Spring 2005 - TEST #1 1. Consider an LTI system with delay, whose output to an input x ( t ) = 6 u ( t ) is y ( t ) = 3(1 - e - 5( t - 2) ) u ( t - 2) . (a) What is the impulse response of this system? Compute and make a sketch. (b) Without using convolution, compute the response of this system to the input x 1 ( t ) = - 12 u ( t - 8). Sketch both the input and the response. Do not forget to label the axes and to indicate all pertinent features. 2. The filter is given by the block diagram shown below (left): n z -1 z -1 z -1 + + x[n] y[n] y[n] (a) Find and sketch impulse response h [ n ] of this filter. Determine the type and the order of this filter. (b) Consider an input x [ n ] = 2 u [ n + 2] u [2 - n ]. The response y [ n ] of the filter to this input is shown above (right) but the axes are incomplete. Show how you can determine the position of the vertical axis, the support of the output, and the scale of the vertical axis. Then complete the plot of y [ n ].
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3. An LTI system has an impulse response: h ( t ) = 3 e - t u ( t ) . The input to this system is
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Unformatted text preview: ( t ) u (2-t ). (a) Determine whether x ( t ) is a power signals, an energy signal, or neither. (b) Determine whether the system is BIBO stable. What can you conclude regard-ing the response of this system to x ( t )? (c) The response to input x ( t ) can be computed by evaluating the convolution integral: y ( t ) = Z ∞-∞ x ( λ ) h ( t-λ ) dλ. (1) Draw a sketch indicating the position of the two functions inside the convo-lution integral at time t = 0 . 5. Carefully label all pertinent features on the graph. 4. Consider a sinusoidal signal x ( t ):-8-6-4-2 2 4 6 8-4 4 t x(t) (a) Write this signal in the form of a rotating phasor, ¯ x ( t ) = X e jωt , where X is a complex number. (b) Assuming that x ( t ) was sampled with frequency f s = 2 Hz, determine a sinu-soidal signal x a ( t ) that will be represented by the same samples as x ( t ) due to aliasing. 2...
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