Multirate Digital Signal Processing, Oversampling of Analog-to-Digital Conversion, and Undersampling of Bandpass Signals - Digital Signal Processing: Fundamentals and Applications - page 589

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FIGURE 12.25

Frequency responses of the designed filter.

the designed filter while Figure 12.26 compares the signals in the time and frequency domains,
respectively, where xðtÞ denotes the continuous version, x q ðnÞ is the quantized version using a regular
sampling rate of 1 kHz, and y q ðnÞ is the enhanced version using the oversampling system with L ¼ 4.
The detailed amplitude comparisons are given in Figure 12.27 . The measured signal-to-noise ratios
(SNRs) are 14.3 dB using the regular sampling system and 21.0 dB using the oversampling system.
Since L ¼ 4, the achieved signal is expected to have 4-bit quality (0 : 5 log 2 4 ¼ 1 bit improvement).
From simulation, we achieve an SNR improvement of approximately 6dB. The improvement will stop
when L increases due to the fact that when the sampling increases the quantization error may have
correlation with the sinusoidal signal. The degradation performance can be cured using the dithering
technique (Tan and Wang, 2011), which is beyond our scope.
Program 12.7. Oversampling implementation.

clear all; close all,clc
ntotal ¼ 512;
n ¼ 0:ntotal; % Number of samples
L ¼ 4; % Oversampling factor
nL ¼ 0:ntotal*L; % Number of samples for oversampling
numb ¼ 3; % Number of bits
A ¼ 2^(numb-1)-1; % Peak value
f1 ¼ 150;C1 ¼ 0.5*A;f2 ¼ 175;C2 ¼ A*0.3;f3 ¼ 200;C3 ¼ A*0.2; % Frequencies and amplitudes