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
Question: Are there sets of basic\ signals so that a) We can represent rich classes of signals as linear combinations of these building block signals b) The response of ltI Systems to these basic signals are both simp and insightful Fact: For LtI Systems(CT or dt) there are two natural choices for these building blocks Focus for now:
2.7 A linear system S has the relationship +∞ yn]=]gn-2k] k=-∞0 between its input xn] and outputy[n] g[n]=un]-un-4] (a)x[n]=[n-1]y[n=u[n-2]-u[n-6] (b)x[n=6[n-2]yn=u[n-4]-u[n-8 (c)S is time-varying