Fundamentals - The MPEG - page 27

Figure 2.13: With finite slope filters, aliasing is always possible, but it can be set at an arbitrarily low level by raising
the sampling rate.
There is another difficulty which is that the requirement for linear phase means the impulse response of the filter
must be symmetrical. In the time domain, such filters cannot be causal because the output has to begin before the
input occurs. A filter with a finite slope has a finite window and so a linear-phase characteristic can be obtained by
incorporating a delay of one-half the window period so that the filter can be causal. This concept will be expanded
in Chapter 3 .
[ 7 ] Porat, B., A Course in Digital Signal Processing New York: John Wiley (1996)
[ 8 ] Betts, J.A., Signal Processing Modulation and Noise , Ch 6. Sevenoaks: Hodder and Stoughton (1970)
2.7 Aperture effect
In practical sampling systems the sample impulse cannot be infinitely small in time or space. Figure 2.14 shows
that real equipment may produce impulses whose possible shapes include rectangular and Gaussian. The result is
an aperture effect where the frequency response of the sampling system is modified. The new response is the
Fourier transform of the aperture function.
Figure 2.14: The ideal zero duration/size sample required by Figure 2.10 is not met in practice. Typical sample
impulses look like this and have a filtering action called aperture effect.
In the case where the pulses are rectangular, the proportion of the sample period occupied by the pulse is defined
as the aperture ratio which is normally expressed as a percentage.
The case where the pulses have been extended in width to become equal to the sample period is known as a zero-
order hold (ZOH) system and has a 100 per cent aperture ratio as shown in Figure 2.15 ( a). This produces a
waveform which is more like a staircase than a pulse train.