Fourier series: Periodic signals and lti Systems ()=∑H(k k= ak一→H(ko)ak “g Soak-→|H(jkco)lkl H(7k)=1H(k0e∠B(ko) or powers of signals get modified through filter/system ncludes both amplitude phase akeJhwon
Fouriers derivation of the ct fourier transform x(t)-an aperiodic signal view it as the limit of a periodic signal as t→∞ For a periodic signal the harmonic components are spaced Oo=2π/ T apart. AsT→∞,Obo→>0, and harmonic components are space
Motivation for the Laplace transform CT Fourier transform enables us to do a lot of things, e. g Analyze frequency response of lTi systems Sampling Modulation Why do we need yet another transform? One view of Laplace Transform is as an extension of the Fourier
3.1 X(eo)=2xnJe-jon where x[n] is a real sequence. Therefore X(e)=Rl∑xnlo/。 ∑xR(-mu)=∑ x[n]cos(on),and xmm)=m∑刈nm∑刈mc-m)=-2 xn] sin(oon) Since cos(on)and sin(on)are, respectively, even and odd functions of o, Xre(eJo) is an even function of o
PROBLEM SET 7 Issued: October 28. 2003 Due: November 5. 2003 REMINDER: Computer Lab 2 is also due on November 7 Reading Assignments Lectures #14-15 PS#7: Chapter 7(through Section 7. 4)and Chapter 8(through Section 8.4) of o&W Lectures #16-18 PS#8: Section 7.5 and Chapters 8 and 9(through Section 9.6)of O&W Exercise for home study(not to be turned in, although we will provide solutions)
PROBLEM SET 11 SOLUTIONS Problem 1(O&W 1029(d)) In this problem we are asked to sketch the magnitude of the Fourier transform associated with the pole-zero diagram, Figure P10.29(d). In order to do so, we need to make some
Department of Electrical Engineering and Computer Science 6.003: Signals and Systems-Fall 2003 Final Exam Tuesday, December 16, 2003 Directions: The exam consists of 7 problems on pages 2 to 33 and additional work space on pages 34 to 37. Please make sure you have all the pages. Tables of Fourier series properties, CT and DT Fourier transform
Department of Electrical Engineering and Computer Science 6.003: Signals and Systems-Fall 2003 Thursday, November 13. 2003 Directions: The exam consists of 5 problems on pages 2 to 19 and additional work space on pages 20 and 21. Please make sure you have all the pages. Tables of Fourier series properties as well as CT Fourier transform and DT Fourier transform properties and pairs are supplied to you as a separate set of pages. Enter all your work and
