Fundamentals - The MPEG - page 28

Figure 2.15: (a) In a zero-order-hold (ZOH) system, the samples are stretched to the sample period and the
waveform looks like a staircase. (b) Frequency response with 100 per cent aperture nulls at multiples of sampling
rate. Area of interest is up to half sampling rate.
To see how the use of ZOH compares with ideal Shannon reconstruction, it must be recalled that pulses of
negligible width have a uniform spectrum and so the frequency respose of the sampler and reconstructor is flat
within the passband. In contrast, pulses of 100 per cent aperture ratio have a sin x / x spectrum which falls to a null at
the sampling rate, and as a result is about 4 dB down at the Nyquist frequency as shown in Figure 2.15 ( b).
Figure 2.16 (a) shows how ZOH is normally represented in texts with the pulses extending to the right of the
sample. This representation is incorrect because it does not have linear phase as can be seen in (b). Figure 2.16 ( c)
shows the correct representation where the pulses are extended symmetrically about the sample to achieve linear
phase (d). This is conceptually easy if the pulse generator is considered to cause a half-sample-period delay
relative to the original waveform. If the pulse width is stable, the reduction of high frequencies is constant and
predictable, and an appropriate filter response shown in (e) can render the overall response flat once more. Note
that the equalization filter in (e) is conceptually a low-pass reconstruction filter in series with an inverse sin x / x
response.