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 10123 4 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 10123 4 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 10123 4 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 10123 4 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 10123 4 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 10123 4 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 10123 4 4 4 p 0 . 5 p 0 =1 p 0 . 2
Check Yourself How many of the following unit-sample responses can be represented by a single pole? n n n n n

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Check Yourself How many of the following unit-sample responses can be represented by a single pole? 3 n n n n n
Geometric Growth The value of p 0 determines the rate of growth.

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## This note was uploaded on 12/14/2011 for the course EE 6.003 taught by Professor Freeman during the Fall '11 term at MIT.

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MIT6_003S10_lec03 - 6.003: Signals and Systems Feedback,...

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