This preview shows pages 1–11. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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....
View
Full
Document
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.
 Spring '11
 DennisM.Freeman

Click to edit the document details