332:345 Linear Systems & Signals Fall 2009 Sample Exam-2 Questions
4. The signal f (t)= ejo t u(t) is sent to the input of the system in problem 2 (with a = b). Show that the output will have the following form for all t,
1. For the PID controller example
332:347 Linear Systems Lab Lab 1
2. Consider the following differential equation describing a rst-order system, such as an RC circuit:
1. This lab illustrates the denition of the Dirac delta function, (t), as a
limit of ordinary functions. Consider the fo
Fall 2009 332:347 Linear Systems Lab Lab 3 1. Consider the following linear system: y(t)+4(t)+3y(t)= f (t)+2f (t) y Assuming zero-initial conditions, show that the following three input signals produce the indicated outputs expressed in the s-domain by:
Fall 2009 332:347 Linear Systems Lab Lab 4 Consider a dish antenna sitting on a rotating base that can be rotated azimuthally by a drive motor to track a ying aircraft. The dynamics of the rotating structure is described by the equations: J(t)= (t)+N(t)+N
Fall 2009 332:347 Linear Systems Lab Lab 5
1. In this part, you will study the steady-state and transient response of a
lter. Consider the following sinusoidal input signal and lter:
f (t)= sin(0 t)u(t) ,
s2 + s + 1.25
2. In this part, you will
332:345 Exam-1 Review Topics Fall 2009
Concepts of linearity and time-invariance. Examples of nonlinear and nontime-invariant systems.
Differential equation descriptions of linear systems and their solutions.
Separation of solution into homogeneous plus
332:345 Exam-2 Review Topics Fall 2009
z-transforms, denition and properties, region of convergence.
Inverse z-transforms using long division followed by partial fraction expansion.
Solving difference equations with initial conditions, e.g., load amort
332:345 Final-Exam Review Topics Fall 2009
All review Topics for Exams 1 & 2.
Cauchy-Schwarz inequality for time signals and for Fourier transforms.
Uncertainty principle for a Fourier transform pair f (t)
Fourier transform applications in commun
Sample Exam 1: Chapters 1, 2, and 3
#1) Consider the linear-time invariant system represented by
Find the system response and its zero-state and zero-input components. What are the response steady
state and transient components.
Sample Exam 1: Solutions
#1a) The homogeneous solution is obtained from
dy h (t )
+ 2 y h (t ) = 0
y h (t ) = Ce 2t
The particular solution satisfies
dy p (t )
+ 2 y p (t ) = 3
y p (t ) =
Plugging this solution into the differential equation impl
Fall 2009 332:347 Linear Systems Lab Lab 2 1. This problem demonstrates the time-invariance property of LTI systems and also studies the the numerical approximation to convolution achieved by the built-in function conv. Consider a system described by the