Multirate Digital Signal Processing, Oversampling of Analog-to-Digital Conversion, and Undersampling of Bandpass Signals - Digital Signal Processing: Fundamentals and Applications - page 587

Decimator

m-bit ADC
oversampling

Anti-aliasing LPF

M

f s

f

s '

2 f

max

Oversampling rate Minimum sampling rate

P ()

In-band noise

2

q

f

s

f s
2

f s
2

f max

f max

FIGURE 12.24
Oversampling ADC system.

distributed signal in a full range with a sufficiently long duration. It is not generally true in practice.
See research papers authored by Lipshitz et al. (1992) and Maher (1992). However, using the
assumption will guide us to some useful results for oversampling systems.
The quantization noise power is the area obtained from integrating the power spectral density
function in the range of f s = 2to f s = 2. Now let us examine the oversampling ADC, where the
sampling rate is much larger than that of the regular ADC; that is f s >> 2 f max . The scheme is shown in
Figure 12.24 .
As we can see, oversampling can reduce the level of noise power spectral density. After the
decimation process with the decimation filter, only a portion of quantization noise power in the range
from f max and f max is kept in the DSP system. We call this an in-band frequency range .
In Figure 12.24 , the shaded area, which is the quantization noise power, is given by

Z N

P f df ¼

2
12 2 2 m

2 f max
f s

2 f max
f s

$ A

2

Quantization noise power ¼ s

q ¼

(12.18)

N

Assuming that the regular ADC shown in Figure 12.23 and the oversampling ADC shown in
Figure 12.24 are equivalent, we set their quantization noise powers to be the same to obtain

2
12 $ 2 2 n ¼

2
12 2 2 m

A 2 f max

f s

$ A (12.19)

Equation (12.19) leads to two useful equations for applications:

f s
2 f max

and

n ¼ m þ 0 : 5 log 2 (12.20)

f s ¼ 2 f max 2 2 ðnmÞ (12.21)