Multirate Digital Signal Processing, Oversampling of Analog-to-Digital Conversion, and Undersampling of Bandpass Signals - Digital Signal Processing: Fundamentals and Applications - page 597

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FIGURE 12.33

Frequency responses of the designed filter.

We implement the first-order SDMsystemusing the same continuous signal in Equation (12.22) . The
continuous signal is originally sampledat 1kHz andeach sample is encodedusing3bits. TheSDMsystem
uses an oversampling rate of 8 kHz ( L ¼ 8) and each sample is quantized using a 3-bit code. The anti-
aliasing lowpass filter is designedwith a cutoff frequency of U ¼ 2 pf max T ¼ 2 p 500 = 8 ; 000 ¼ p= 8
radians. Figure 12.33 shows the frequency responses of the designed filter while Figure 12.34
compares the time and frequency domain signals, where xðtÞ designates the continuous version, x q ðnÞ
denotes the quantized version using a regular sampling rate ( L ¼ 1), and y q ðnÞ is the enhanced version
using L ¼ 8. The detailed amplitude comparisons are given in Figure 12.35 . The measured SNRs are
14.3 dB in the regular sampling system and 33.83 dB in the oversampling SDM system. We observe
a significant SNR improvement of 19.5 dB. The detailed implementation using MATLAB is given in
Program 12.8.
Program 12.8. First-order SDM oversampling implementation.

clear all; close all;clc
ntotal ¼ 512; % Number of samples

n ¼ 0:ntotal;

L ¼ 8; % Oversampling factor

nL ¼ 0:ntotal*L;numb ¼ 3;A ¼ 2^(numb-1)-1; % Peak value

f1 A*0.2;% Frequencies and amplitudes

fmax ¼ 500;fs ¼ 1000; T ¼ 1/fs; % Sampling rate and sampling period
fsL ¼ L*fs;TL ¼ 1/fsL; % Oversampling rate and oversampling period

¼ 150;C1 ¼ 0.5*A;f2 ¼ 175;C2 ¼ A*0.3;f3 ¼ 200;C3 ¼