Selected Topics in Applied Signal Processing - Digital Signal Processing: An Introduction with MATLAB and Applications - page 169

1.2

| X s ( f )|

1

0.8

0.6

0.4

0.2

0 f , kHz

−10 0 10 20 30 40 50

Fig. 3.30 Anti-aliasing cutoff and attenuation in CD. Shaded areas should be removed by an
analog filter, while the area in between can be removed later by a digital filter

way to achieve this filtering is use an ideal analog 'brick wall' filter, but such
filters are impossible to implement in practice. Fortuitously, increasing the
sampling rate relaxes the conditions on the LPF, enabling a lower order filter to
be used.
As an illustration of the advantages of oversampling, consider the audio
compact disc (CD). The audible spectrum extends up to 20 kHz. Hence, one needs
a sampling frequency of at least 40 kHz. CD's use f s = 44.1 kHz and 16-bits
quantization. The stop band for this system extends from 20 to 22.05 kHz, and
within this band the filter must produce an 80 dB drop (so as to prevent aliasing).
This requires a 50th-order analog Butterworth filter (with a cutoff frequency of
20 kHz). Such a large order Butterworth filter is highly impractical. In addition to
space problems, large filter orders are very difficult to realize because they are
more vulnerable to errors due to the tolerances of the filter components.
The solution to the above problem is to increase the sampling rate to
4f s = 176.4 kHz. Now to prevent aliasing, there needs to be an 80 dB roll-off
between 88.2 and 20 kHz. This requires only a 5th-order Butterworth filter with a
cutoff frequency of 20 kHz, which is a significant reduction in analog components.
After the analog anti-aliasing filtering is applied a digital filtering is applied to
achieve a very sharp cutoff. Subsequent to that filtering, downsampling to
f s = 44.1 kHz occurs. This downsampling is necessary for reduction of storage
requirements without any loss of information. Figure 3.30 explains the above
process.

3.6.3 Delta Modulation

In multibit A/D conversion the signal samples are quantized and encoded. The
samples are usually coded into M bit code words, where M is typically 16. As an
alternative

to conventional multi-bit conversion, one can quantize just the