# lab4 - Lab 4: LTI Systems in Matlab and Simulink. In this...

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Lab 4: LTI Systems in Matlab and Simulink. In this lab we will compare the response of two different (but related) LTI systems. Consider the first-order circuit shown to the right. You might recognize it as a filter circuit. The input signal is injected at the port on the left. By measuring the output that results across the resistor R , or across the capacitor C we obtain two distinct but related systems. System H(s): Lowpass Filter: For the output across the capacitor, the transfer function (assuming zero initial conditions) is: H ( s ) = 1 RC 1 s + 1 RC ! " # \$ % Assuming the time constant satisfies RC = 1, we can write: H(s) = Lowpass Filter H ( s ) = 1 s + 1 G(s) = Highpass Filter The response to an input step function u ( t ) is the charging of the capacitor up to 1 volt. On the other hand, an impulse response should correspond to a charged capacitor discharging from one down to zero. System G(s): Highpass Filter For the output across the resistor, the transfer function is: G ( s ) = 1 ! H ( s ) = 1 – 1 s + 1 = s s + 1 The advantage of including both these systems, is that it enables us to check our results graphically, by verifying that the responses of the two systems add up to the input signal. We will inject each of the piecewise linear systems from the first part of this lab into both filters. Start of Exercises Exercise 1: Open Matlab and create a new Simulink model by selecting the menu sequence File>>New>>Model. If you do not see the Library Browser, use the View Menu at the top of the model window to show it. Select the Signal Builder icon and drag it to the left side of the model window. Adjust the time range to run from –4 to +4 and the Y display to run from –1 to 4. Change the snaps to 0.5 units. Now create the signal shown to the right by adding three points to define its triangular pulse. Hold down the shift key to do this.

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## This note was uploaded on 09/22/2009 for the course ECES 302 taught by Professor Carr during the Spring '08 term at Drexel.

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lab4 - Lab 4: LTI Systems in Matlab and Simulink. In this...

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