Multirate Digital Signal Processing, Oversampling of Analog-to-Digital Conversion, and Undersampling of Bandpass Signals - Digital Signal Processing: Fundamentals and Applications - page 590

5 2

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5 2

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5 2

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Sample number Frequency (Hz)

FIGURE 12.26

Signal comparisons in both the time and frequency domains.

fmax ¼ 500;fs ¼ 1000;T ¼ 1/fs; % Maximum frequency, sampling rate, sampling period
fsL 1/fsL;% Oversampling rate and oversampling period

% Sampling at fs

¼ L*fs;TL ¼

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); % Quantized signal at the minimum sampling rate

NN ¼ length(n);

f ¼ [0:ntotal-1]*fs/NN;

M M/L; % Delay in terms of samples due to anti-aliasing filtering

B ¼ firwd(2*M þ 1,1,2*pi*fmax/fsL,0,4); % Anti-aliasing filter design (5% transition
% bandwidth)
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);
xxq ¼ round(xx); % Quantized signal
% Down sampling
y ¼ filter(B,1,xxq);% Anti-aliasing filtering
yd ¼ y(1:L:length(y));% Downsample
figure (2)
subplot(3,2,1);plot(n,x, ' k ' );grid;axis([0 500 -5 5]);ylabel( ' x(t) ' )
Ak ¼ 2*abs(fft(x))/NN; Ak(1) ¼ Ak(1)/2;

¼ 32*L;nd ¼