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
