284 11 SarnDling arid Periodic Signals Interpolation njlicii the film is played back is v ~a5y to iiiiplrmtmt w hell each image is projected for the corresponding lcngth iine, altliougli in fa(%,llicly ale riot there for thc eritire interval T = 1/248, as hc%wen two images the film has to l w moved There is no pr:wtical interpolatiori filter available foi this optical signal, as in Figuie 11.9, so the re-occurrences of the spectrum at 24 are iiot removcd and w e p m c e i v d by the eyes as Aiclcr Tlic fiicker up t o around 60 Hz, but tlie first re-occuiieiice at 24Hz To avoid this problem, a trick can be used: iristeittl of interrupting on of an image once for tlie filiri transport it is interrupted twice (see 5) The inkvupting i s done with a niechanical hlirrtl which i s easily implcmcnt It doubl~st h arriple rate (to 48 HE), and pairs of coriseqitential sample valiics are equal because they c ~ r r i efrom the same original ‘ L movement of film The effectiveiicss of the clouble projcction proccdurc can be cxp1;~inctlt2icorc.tically IVe reprrserit the doublr projcction of a11 image as the ilupulsc>responsc of x i inte~~)olati(~ri filter (see Figure 11.25) and find the spectrum: (11.53) (11.55)