lec03 - 6.003: Signals and Systems Feedback, Poles, and...

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Unformatted text preview: 6.003: Signals and Systems Feedback, Poles, and Fundamental Modes September 17, 2009 Last Time: Multiple Representations of DT Systems Verbal descriptions: preserve the rationale. To reduce the number of bits needed to store a sequence of large numbers that are nearly equal, record the first number, and then record successive differences. Difference equations: mathematically compact. y [ n ] = x [ n ] x [ n 1] Block diagrams: illustrate signal flow paths. 1 Delay + x [ n ] y [ n ] Operator representations: analyze systems as polynomials. Y = (1 R ) X Last Time: Feedback, Cyclic Signal Paths, and Modes Systems with signals that depend on previous values of the same signal are said to have feedback . Example: The accumulator system has feedback. Delay + X Y By contrast, the difference machine does not have feedback. 1 Delay + X Y Last Time: Feedback, Cyclic Signal Paths, and Modes The effect of feedback can be visualized by tracing each cycle through the cyclic signal paths. Delay + p X Y 1 0 1 2 3 4 n x [ n ] = [ n ] 1 0 1 2 3 4 n y [ n ] Each cycle creates another sample in the output. Last Time: Feedback, Cyclic Signal Paths, and Modes The effect of feedback can be visualized by tracing each cycle through the cyclic signal paths. Delay + p X Y 1 0 1 2 3 4 n x [ n ] = [ n ] 1 0 1 2 3 4 n y [ n ] Each cycle creates another sample in the output. Last Time: Feedback, Cyclic Signal Paths, and Modes The effect of feedback can be visualized by tracing each cycle through the cyclic signal paths. Delay + p X Y 1 0 1 2 3 4 n x [ n ] = [ n ] 1 0 1 2 3 4 n y [ n ] Each cycle creates another sample in the output. Last Time: Feedback, Cyclic Signal Paths, and Modes The effect of feedback can be visualized by tracing each cycle through the cyclic signal paths. Delay + p X Y 1 0 1 2 3 4 n x [ n ] = [ n ] 1 0 1 2 3 4 n y [ n ] Each cycle creates another sample in the output. Last Time: Feedback, Cyclic Signal Paths, and Modes The effect of feedback can be visualized by tracing each cycle through the cyclic signal paths. Delay + p X Y 1 0 1 2 3 4 n x [ n ] = [ n ] 1 0 1 2 3 4 n y [ n ] Each cycle creates another sample in the output. Last Time: Feedback, Cyclic Signal Paths, and Modes The effect of feedback can be visualized by tracing each cycle through the cyclic signal paths. Delay + p X Y 1 0 1 2 3 4 n x [ n ] = [ n ] 1 0 1 2 3 4 n y [ n ] Each cycle creates another sample in the output. The response will persist even though the input is transient. Geometric Growth: Poles These system responses can be characterized by a single number the pole which is the base of the geometric sequence....
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This note was uploaded on 08/24/2011 for the course EECS 6.003 taught by Professor Dennism.freeman during the Spring '11 term at MIT.

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lec03 - 6.003: Signals and Systems Feedback, Poles, and...

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