Page 83 - DSP Integrated Circuits

68 Chapter 3 Digital Signal Processing

S&H circuit should always be used before the A/D converter to get samples at very
precise (time) instants, since an A/D converter generally has a small, but significant,
variation in its sample instants. This variation is also significant for flash converters.
An error in the sampling period translates to an equivalent error in the sample
value. High-resolution converters therefore require high precision in the sample
instants.
Figure 3.6 shows the spectrum of an analog signal, the magnitude response of
the anti-aliasing filter, and the spectrum after the analog filter. The interesting
part of the input signal lies in the frequency band 0 - (o c. The output signal of the
anti-aliasing filter is bandlimited to the band 0 - co s. Figure 3.7 shows the spec-
trum of the corresponding sampled signal, the magnitude response for the digital
filter, and the spectrum of the output of the digital filter. Obviously, the frequency
response of the digital filter is periodic with a period of 2n. Also notice that alias-
ing occurs for frequencies above 2n-a) sT, since the sample rate; is too low. However,
this band will later be removed by the digital filter. In this case, the stopband edge
of the anti-aliasing filter must be cos < 2n/T-(Q c and the passband edge a> c. Hence,
the transition band, co s - co c, can be made much larger than in the case when the
sampling theorem has to be strictly fulfilled. In this case, the order of the anti-
aliasing filter can be significantly reduced.

Figure 3.6 Bandlimiting due to analog filtering