11.3 Sampling ‘28L For the sampled signal (1 1.48) IVe foririd llic* luriti;zrrimtal propcrty with icleal sampling, that thc q)( ot the sarnplcct signal consists of the corit iniiatiori of thr spcctruin of the nonsampled signal LVr will now i i i w s t i g a t e what infltienw nort-itlcal saniplirig has oil the trecliiency-cli)inaiiL ‘l’o siniplifiy this, wt’ will be liniitetl to rectangular aycrtims in &c(*o~daiice with (11.46) The Foririer lransforrn of (11.IS) yielcls the spectruin of the samplrd signal X(JUJ) (11.49) Comparcd with the spectrum of tlir idcal sampled signal (11.33), it is striking that the spec-trnm of thc original sigrial X ( p ) is wrightcd with tlie aperture M o r e perioclie corit inuation Figiirv I 22 sliows a possible rprctruni of the original signal % ( j d ) (a& in Figure 11.8) and the wighting of the rectaiiglr irnpulsc A? with the rectmglr, the has been taken which corresporids to an integration with duration T over the errtire sampling inter\d % Thc first zero of the si-fimction then lies exactly at the sampling frequency J = 2n/T T T Figure 11.22: Spwtriirxi of the sampled signal In order to rstjinate the eEed of sampling O K the ~ fxequency responsr, UT calruldtc thc value of the si-firnetion at tlie highest trc3queney that, X ( p ) ran contain wit hont ceiising aliasing ei~ors: ( 11.50)