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
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
SAMPLING We live in a continuous-time world most of the signals we encounter are CT signals, e.g. x(). How do we convert them into Dt signals x[n? Sampling, taking snap shots of x(t) every Seconds
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
Inverse laplace transforms Laplace Transform Properties The System Function of an Lti System Geometric Evaluation of laplace Transforms and Frequency responses
Geometric Evaluation of z-Transforms and dT Frequency Responses First- and Second-Order Systems System Function Algebra and block diagrams Unilateral z-Transforms
