Figure 12-31 illustrates a CD playback system, also described earlier in this chapter. A laser optically scans the tracks on a CD to produce a digital signal. The digital signal is then demodulated, and parity bits are used to detect bit errors due to manufacturing defects, dust, and so on and to correct them. The demodulated signal is again oversampled by a factor of 4 and hence the sampling rate is increased to 176.4 kHz for each channel. Each digital sample then passes through a 14-bit DAC, which produces the sample-and-hold voltage signals that pass the anti-image lowpass filter. The output from each analog filter is fed to its corresponding loudspeaker. Oversampling relaxes the design requirements of the analog anti-image lowpass filter, which is used to smooth out the voltage steps.
Figure 12-31. Simplified decoder of a CD recording system.
The earliest system used a third-order Bessel filter with a 3 dB passband at 30 kHz. Notice that the first-order sigma-delta modulation (first-order SDM) is added to the 14-bit DAC unit to further improve the 14-bit DAC to 16-bit DAC.
Let us examine the single-channel DSP portion shown in Figure 12-32.
Figure 12-32. Illustration of oversampling and SDM ADC used in the decoder of a CD recording system.
The spectral plots for the oversampled and interpolated signal x(n), the 14- bit SDM output y(n), and the final analog output audio signal are given in Figure 12-33.
Figure 12-33. Spectral illustrations for oversampling and SDM ADC used in the decoder of a CD recording system.
As we can see in plot (a) in the figure, the quantization noise is uniformly distributed, and only in-band quantization noise (0 to 22.05 kHz) is expected. Again, 14 bits for each sample are kept after oversampling. Without using the first-order SDM, we expect the effective ADC resolution due to oversampling to be
n = 14 + 0.5 × log2 (176.4/44.1) = 15 bits,
which is fewer than 16 bits. To improve quality further, the first-order SDM is used. The in-band quantization noise is then shaped. The first-SDM pushes quantization noise to the high-frequency range, as illustrated in plot (b) in Figure 12-33. The effective ADC resolution now becomes
n = 14 + 1.5 × log2 (176.4/44.1) – 0.86 ≈ 16 bits.
Hence, 16-bit ADC audio quality is preserved. On the other hand, from plot (c) in Figure 12-33, the audio occupies a frequency range up to 22.05 kHz, while the DSP Nyquist limit is 88.2, so the low-order analog anti-image filter can satisfy the design requirement.
Part 4 examines the undersampling of bandpass signals.
Note that wavelet transform and subband coding are also in the area of multirate signal processing. We do not pursue these subjects in this book. The reader can find useful fundamental information in Akansu and Haddad (1992), Stearns (2003), Van der Vegte (2002), and Vetterli and Kovacevic (1995).
Related articles:
- Design: ADCs for DSP, part 1
- Product: Low noise 16-bit delta sigma A/D converter upgrades system accuracy
- Paper: Benefits of Sigma Delta ADCs
Printed with permission form Academic Press, a division of Elsevier. Copyright 2007. "Digital Signal Processing, Fundamentals and Applications" by Li Tan. For more information about this title and other similar books, please visit www.elsevierdirect.com.
