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Problems to be handed in: In this lab, you will complete the Basic, Intermediate, and Advanced Exercises for the Echo Cancellation problem considered in Section 2.10 on pages 44-46 of Buck, Daniel, and Singer(BDS). For all of the exercises, please include
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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.003: Signals and Systems-Fall 2003 COMPUTER LAB 3
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C(S), G(s)-Designed with one or more free parameters Question: How do the closed-loop poles move as we vary these parameters?-Root locus of 1+ C(SG(sH(s
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Why use feedback? Reducing effects of nonidealities Reducing Sensitivity to Uncertainties and variability Stabilizing Unstable Systems Reducing Effects of Disturbances Tracking Shaping system response Characteristics(bandwidth/speed
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Properties of ct Rational system functions a) However, if H(s)is rational, then The system is causal The roc of H(s) is to the right of the rightmost pole
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1.aM with an Arbitrary Periodic Carrier 2. Pulse Train Carrier and Time-Division Multiplexing 3. Sinusoidal Frequency modulation 4. DT Sinusoidal am 5. DT Sampling, Decimation,d Interpolation
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More efficient to transmit e&m signals at higher frequencies Transmitting multiple signals through the same medium using different carriers Transmitting through\channels, with limited passbands
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Result: Linear phase e simply a rigid shift in time, no distortion Nonlinear phase e distortion as well as shift DT
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Convergence Issues Synthesis equation: None. since integrating over a finite interval Analysis Equation: Need conditions analogous to CTFT, e. g
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Convolution Property 0(t)=h(t)*(t)←→Y(j)=H(ju)X( where h(t)←→H(ju) A consequence of the eigenfunction property
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