# hmw4 - are using. t-2 2 1 2 t 2 1 2 4 x (t) 1 x (t) 2 verte...

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Due February 10, 2010 BME 171, Spring 2010 - HOMEWORK 4 Analog Systems: Time Domain Analysis 1. A linear, stationary system is given by an ODE: dy dt + 1 τ y ( t ) = A x ( t ) , where τ and A are constants. (a) Compute and sketch the impulse response h ( t ) of this system. Label and dimension the axes. (b) Find the response y ( t ) of this system to the following input: x ( t ) = B cos( ωt ) , where B is a constant. 2. A linear, stationary system has an impulse response: h ( t ) = δ ( t ) - 1 τ e - t/τ u ( t ) . (a) Find the response of this system to input x ( t ) = u ( t ). (b) Sketch this response assuming τ = 1. (c) Without evaluating the convolution integral, ±nd the responses of this system to the inputs shown below. Specify which properties of the convolution you

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Unformatted text preview: are using. t-2 2 1 2 t 2 1 2 4 x (t) 1 x (t) 2 verte 3. The absorption and processing of glucose was studied experimentally by applying a constant rate infusion: x 1 ( t ) = 300 u ( t ) mg/min . The observed concentration proFle was: y 1 ( t ) = 54 p 1-e-. 05 t P u ( t ) mg/liter . (a) Based on these data, determine the impulse response of the system. (b) Use convolution to compute the concentration proFle y 2 ( t ) resulting from the infusion x 2 ( t ) shown below: x (t) 2 t 150 630 60 2...
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## hmw4 - are using. t-2 2 1 2 t 2 1 2 4 x (t) 1 x (t) 2 verte...

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