Sampling a i d Periodic Signals The highest frequency component is damped by nearly 4 dB; for all lower fie- quencies the damping is lower.. In many applications this effect can be toler
Trang 1282 1 1 Sampling a i d Periodic Signals
The highest frequency component is damped by nearly 4 dB; for all lower fie- quencies 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 sarn- ple 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
1 econst ruct ion
It is riot only necessary do consider side-effects from thc irrrpleincntatioii when sani- pling, 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 do not use these signals, arid use instead sitmple-and-hold cir- cuits 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
The rectangle irnpulse
impulse train and the corresponding reclangle function does not lie symmetrical to the sample points, instead
I
Figure 1 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