11 Sampling a i d Periodic Signals 282 The highest frequency component is damped by nearly dB; for all lower fiequencies the damping is lower An integration time z, t h a t is shorter Lhan Cl~e sampling interval likewise reduces the damping effect In many applications this effect can be tolerated and where appropriate can be balanced out by a suitable post-connected aperture correction filler, FOI example, most ‘1’V cameras hm7e a n aperture correctiori filter that compensates for the filtering effect of the row sampling of the image In fact components at frequencies above half the sarnple frequency are strongly daniped by interpolation but they are riot suppressed enough Lhat t hr resultant aliasing is tolerable If hiirh frequency components c r cur they still should be suppressed by a special anti-aliasing pre-filter , that blocks fregicmciw ahove half the sample frequency econst ruction It is riot only necessary consider side-effects from thc irrrpleincntatioii when sanipling, but also during reconstruction of the continuous signals from their sample values AlthoiigIi the description of reconstruction using an impulse train (11.36 t o 11.38) is theoretically very elegant, impulse traiiis and approximations using short high voltage peaks arc not practical for use in electrical circuits Real digital-analog converters therefore not use these signals, arid use instead sitmple-and-hold circuits and staircase functions whose step height is the weight of lhe coir espoiiding delt,n inipulw and SO corresponds t o the actual sample vahie We still keep the advarit ages of the delta impulse train, however The staiici-lbe functioiis can bc thought of as a delta impulse train intclpolatcd with a rectangle of width T (11.51) Figure 11.23 shows an impulse train and the corresponding reclangle function The rectangle irnpulse does not lie symmetrical to the sample points, instead I Figure 1 23: Signal interpolated with a sample-and-hold circuit shifted from the symmetrical position by T / Z , so because of the shift theorem, s