Exam 1
Topics

Representations
o
System functional/Transfer function (product of factors vs. partial fraction forms)
o
Difference equations
o
DT signal as a (possibly infinite) sum of R
n
terms
o
DT signal as a weighted sum of modes (p
n
)
o
DT signals as a plot or list of values
o
Block diagram (cascades, feedback/feedforward sums)
o
Pole diagram (root locus)

Poles and modes of a system, including such topics as
o
Characteristics of real vs. imaginary poles in the time domain
o
Constraints on imaginary poles
o
Convergent, divergent, and perpetual modes; oscillatory vs. nonoscillatory modes; pole
characteristics that lead to all possible combinations
o
Modes related to double/triple poles
o
Complex number representations
gid1
Real and imaginary parts
gid1
Polar form
gid1
Pairs of complex numbers as sines or cosines

Sample function and impulse response, including
o
Definitions
o
Relation between the impulse response and the system functional
o
Relation to modes and poles

Outputs given arbitrary inputs and how the form of the output relates to modes and poles

Partial fractions and when to use them
Useful Skills (This is not an exhaustive list.
It simply gives highlights a few skills
to give you a flavor of what you should know how to do.)

Translating between any combination of the representations or representational forms listed above.

Given a system functional, difference equation, or block diagram
o
Determining the output for any simple input (e.g., a step function or signal with only a few
nonzero samples)
o
Determining the impulse response
o
Determining the poles/modes

Translating complex poles
o
From realimaginary form to polar form and vice versa
o
Pairs of poles into sines and cosines and vice versa
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Exam 2
Topics

Differential Equations, the impulse response as a particular solution, the relationship between poles
and the form of the homogeneous solution

Laplace transform definition and topics like
o
Properties of Laplace transforms (esp. integration, differentiation, and convolution)
o
Common transforms and how they vary based on the ROC (esp. delta functions, one pole
transforms, transforms with two distinct poles, repeated pole transforms)
o
Region of convergence – what is it and how does it affect inverse transforms
o
Stability, causality, anticausality, twosidedness and what they mean in the transform
domain (ROC) and the time domain

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 Spring '11
 DennisM.Freeman
 Digital Signal Processing, Fourier Series, Impulse response

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