Multirate Digital Signal Processing, Oversampling of Analog-to-Digital Conversion, and Undersampling of Bandpass Signals - Digital Signal Processing: Fundamentals and Applications - page 571

Passband ripples for H 2 ðzÞ¼0.02 dB
Stopband frequency range ¼ 4,500e9,000 Hz
Stopband attenuation ¼ 46 dB
Combined specifications HðzÞ:
Passband frequency range ¼ 0e2,500 Hz
Passband ripples for HðzÞ¼0.02 dB
Stopband frequency range ¼ 3,000e9,000 Hz
Stopband attenuation ¼ 46 dB

We use an FIR filter with a Hamming window. Since

f stop f pass
f sL

¼ 3;000 2;500
18;000

Df ¼ ¼ 0:0278

the length of the filter and the cutoff frequency can be determined by

N ¼ 3:3

3:3
0:0278 ¼ 118:8 Df ¼

We choose N ¼ 119, and

f pass þ f stop
2

¼ 3;000 þ 2;500
2

f c ¼ ¼ 2;750 Hz

12.1.4 Application: CD Audio Player
In this application example, we will discuss principles of the upsampling and interpolation-filter
processes used in CD audio systems to help with reconstruction filter design.
Each raw digital sample recorded on a CD audio system contains 16 bits and is sampled at the rate
of 44.1 kHz. Figure 12.11 describes a portion of one channel of the CD player in terms of a simplified
block diagram.
Let us consider the situation without upsampling and application of a digital interpolation filter. We
know that the audio signal has a bandwidth of 22.05 kHz, that is, the Nyquist frequency, and digital-to-
analog conversion (DAC) produces the sample-and-hold signals that contain the desired audio band
and images thereof. To achieve the audio band signal, we need to apply a reconstruction filter (also
called a smooth filter or anti-image filter) to remove all image frequencies beyond the Nyquist
frequency of 22.05 kHz. Due to the requirement of the sharp transition band, a higher-order analog
filter design becomes a requirement.
The design of the higher-order analog filter is complex and expensive to implement. As shown
in Figure 12.11 , in order to relieve such design constraints, we can add the upsampling process

ym () yt ()

x () wm ()

Analog
reconstruction
filter H(s)

CD
Player

Interpolation
filter H(z)

L

DAC

f s Lf s Lf s

FIGURE 12.11
Sample rate conversion in the CD audio player system.