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MIT6_003S10_lec03

MIT6_003S10_lec03 - 6.003 Signals and Systems Feedback...

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6.003: Signals and Systems Feedback, Poles, and Fundamental Modes February 9, 2010

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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. + X Y Delay By contrast, the difference machine does not have feedback. 1 Delay + X Y

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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 0 X Y x [ n ] = δ [ n ] y [ n ] n n 1 0 1 2 3 4 1 0 1 2 3 4 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 0 X Y x [ n ] = δ [ n ] y [ n ] n n 1 0 1 2 3 4 1 0 1 2 3 4 Each cycle creates another sample in the output.

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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 0 X Y x [ n ] = δ [ n ] y [ n ] n n 1 0 1 2 3 4 1 0 1 2 3 4 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. X + Y Delay p 0 x [ n ] = δ [ n ] y [ n ] n n 1 0 1 2 3 4 1 0 1 2 3 4 Each cycle creates another sample in the output.

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Last Time: Feedback, Cyclic Signal Paths, and Modes The effect of feedback can be visualized by tracing each cycle through the cyclic signal paths. X + Y Delay p 0 x [ n ] = δ [ n ] y [ n ] n n 1 0 1 2 3 4 1 0 1 2 3 4 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. X + Y Delay p 0 x [ n ] = δ [ n ] y [ n ] n n 1 0 1 2 3 4 1 0 1 2 3 4 Each cycle creates another sample in the output. The response will persist even though the input is transient.

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Geometric Growth: Poles These unit-sample responses can be characterized by a single number the pole which is the base of the geometric sequence. Delay + p 0 X Y n y [ n ] = p 0 , if n > = 0 ; 0 , otherwise. y [ n ] y [ n ] y [ n ] n n n 1 0 1 2 3 4 1 0 1 2 3 4 1 0 1 2 3 4 p 0 = 0 . 5 p 0 = 1 p 0 = 1 . 2
Check Yourself How many of the following unit-sample responses can be represented by a single pole?

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MIT6_003S10_lec03 - 6.003 Signals and Systems Feedback...

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