EECE 340 Homework, Fall 2007

American University of Beirut Department of Electrical and Computer Engineering EECE 440 Signals and Systems Homework 2: Due Thursday March 8, 2007 at 12:00 noon Problem 1 Determine and plot the convolution integral f1(t)*f2(t) for: a) b) Problem 2 Determine the transfer function C(s)/V(s) of the System below Problem 3 Consider the unit feedback system shown below: a) Determine the error signal E(s). b) Determine the range of K for the system to be stable. - + V(s) Problem 4 The transfer function of a linear control system is given by: 2 ( ) 1 ( ) 3 2 C s R s s s = + + a) Determine the state equation for this system. b) Determine the corresponding output equation. Problem 5 The input signal of the LTI system shown below (initially at rest) is x(t) = u(t)-u(t-3) The impulse responses of the subsystems are: ( ) 2 1( ) ( ) t t h t e e u t − − = + 3 2( ) t ( ) h t e = − u t a) Compute the impulse response h(t) of the overall system. b) Find an equivalent system (same impulse response) configured as a parallel interconnection of two LTI subsystems. c) Sketch the input signal x(t). Compute the output signal y(t). Matlab Problem 1 Write an M file that computes the transfer function C(s)/R(s) of the system above given that: 1 2 5 3 3 2 1 + + + + = s s s s G ; G2 = 4; 4 1 1 H = s + ; and 2 2 1 2 2 + + + = s s s H . Problem 2 Use Matlab to determine whether the system with the transfer function shown below is stable. Get a state space representation of the system. 2 6 5 3 2 3 4 ( ) 2 7 3 1 s s H s s s s s s + + = − + − + +