《MIT6_003S10_lec03》.pdfVIP

6.003: Signals and Systems Feedback, Poles, and Fundamental Modes February 9, 2010 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. x [n] + y [n] −1 Delay 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. X + Y −1 Delay 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 p0 Delay 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 tr