studyGuide - Exam 1 Topics - - - - Representations o System

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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/feed-forward 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. non-oscillatory modes; pole characteristics that lead to all possible combinations o Modes related to double/triple poles o Complex number representations g Real and imaginary parts g Polar form g 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 non-zero samples) o Determining the impulse response o Determining the poles/modes - Translating complex poles o From real-imaginary 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, anti-causality, two-sidedness and what they mean in the transform domain (ROC) and the time domain - Z transform definition and topics like
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studyGuide - Exam 1 Topics - - - - Representations o System

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