Multirate Digital Signal Processing, Oversampling of Analog-to-Digital Conversion, and Undersampling of Bandpass Signals - Digital Signal Processing: Fundamentals and Applications - page 598

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Sample number Frequency (Hz)

FIGURE 12.34

Signal comparisons in both the time and frequency domains.

% Sampling at fs ¼ 1000 Hz

x ¼ C1*sin(2*pi*f1*n*T) þ C2*sin(2*pi*f2*T*n þ pi/6) þ C3*sin(2*pi*f3*T*n þ pi/4);

xq ¼ round(x); % Quantization

NN length(n);

M ¼ 32*L;nd ¼ M/L; % Delay in terms of samples for anti-aliasing filtering
B ¼ firwd(2*M þ 1,1,2*pi*fmax/fsL,0,4); % Design of an anti-aliasing filter
figure(1)
freqz(B,1,1000,fsL);
% Oversampling
xx ¼ C1*sin(2*pi*f1*nL*TL) þ C2*sin(2*pi*f2*nL*TL þ pi/6) þ C3*sin(2*pi*f3*nL*TL þ pi/4);
% The first-order SDM processing
yq ¼ zeros(1,ntotal*L þ 1 þ 1); % Initializing the buffer
y ¼ yq;
for i ¼ 1:ntotal*L
y(i þ 1) ¼ (xx(i þ 1)-yq(i)) þ y(i);
yq(i þ 1) ¼ round(y(i þ 1));
end
xxq ¼ yq(1:ntotal*L þ 1); % Signal quantization
% Downsampling
y ¼ filter(B,1,xxq);
yd ¼ y(1:L:length(y));
f ¼ [0:ntotal-1]*fs/NN;

¼