and on LTl-systcwi with irnpulue response h(f)= C , - t & ( t ) (11.20) as shown in Figure 11.5 Comparing (LI.I!I) and (11.17) we rcwgnise that tlir period i s 2' = Figure 11.5: C'onvolutioit of a periodic iirpiit signal with a n aprriodic ixrrpulsie rebporise The frequency response of a, systern is obt,airied from the sy&m fiirictiori for s =jw: (11.2 1) The Fourier transform of the inpiit signid is a linc spectrum: 2nz4r;6(w- 27rk) (11.22) k Thc output sigiial likewise has a lirie spectrim, as for tht product Y ( p )= N ( J u ) X ( J W )wt' , ohtiii,in I ( 11I23) The final invcrse trar~sfolntgives the Fouric~series of tlie oiitpnt signal Its Fouriei c.oefficimts are thc product of the Foiirier cocfficicnts of the input sigriill and tlw ern freqitency rcyonsc at the frecpiencies of the individual spectal lincs Cuiivolution of any pw3odir signal with per iotl T that cwi he rcprcscntccl by its Foiiricr coe-fficients Ak (11.17), with ail aperiodic sigiid h(f) yields