Outline_Topic 02 - Superposition is the central idea behind...

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Outline – Topic 2: Properties of Systems Fall 2006 Topic 2. Properties of Systems Only three of the properties discussed in the text (Section 1.6) are of interest at this time. Stability will be covered when needed in feedback systems. Causality. Read Section 1.6.3 Understand the basic concept. There are no problems to solve here. Time Invariance. Read 1.6.5 Study the definition. You need to understand how to use this definition to determine if a system is time-invariant. Linearity. Read 1.6.6 As above, study the definition. Study the text examples and glean the basic approach. You need to know how to apply the definition to determine if a system is linear. Most of our systems (filters, transfer functions, . ..) will be linear, but every now and then we run into a special nonlinear case, such as amplitude modulation.
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Unformatted text preview: Superposition is the central idea behind this topic and much of our work: we will decompose complicated input signals into a sum of simpler ones for which the system response is easier to find and then add the resulting simpler responses to get the resulting complicated response. Understand this concept well. Except for modulation, we will assume that our systems are LTI (linear, time-invariant) so that superposition applies, even to shifted signals (due to time-invariance). Master the concepts in videos 2.2 and 2.3. Video 2.4 shows that LTI systems do not preserve time-scaling. Consequently, time-scaling the input signal (speed up or slow down) does not necessarily mean that the LTI system output will be similarly time-scaled....
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