Portrait of Jean Baptiste Joseph Fourier Image removed due to copyright considerations Signals& Systems, 2nd ed. Upper Saddle River, N.J. Prentice Hall, 1997, p 179

Another(important! ) example: Periodic Impulse train n(t)=∑(t Sampling function important for sampling .2T

Convolution Property 0(t)=h(t)*(t)←→Y(j)=H(ju)X( where h(t)←→H(ju) A consequence of the eigenfunction property

Result: Linear phase e simply a rigid shift in time, no distortion Nonlinear phase e distortion as well as shift DT

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

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

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

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

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.003: Signals and Systems-Fall 2003 COMPUTER LAB 3

Reading Assignments: Lectures #1-2& PS#1: Chapter 1 of Oppenheim and Willsky(O& W), including (see p. 71) Lectures #3-4 PS#2: Chapter 2 of Oppenheim and Willsky(O&w)