Multirate Digital Signal Processing, Oversampling of Analog-to-Digital Conversion, and Undersampling of Bandpass Signals - Digital Signal Processing: Fundamentals and Applications - page 573

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0 10 20 30 40 50 60 70 80

Frequency (KHz)

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0 10 20 30 40 50 60 70 80

Frequency (KHz)

FIGURE 12.12

(Top) The spectrum after upsampling, and (bottom) the spectrum after applying the interpolation filter.

N ¼ 2048; % Number of samples

L 4;

fsL

¼

fs*L; % Upsampling rate
%Upsampling filter (see Chapter 7 for FIR filter design)
Bup

¼

¼ firwd(97,1,2*19025*pi/fsL,0,4);

n ¼ 0:1:N-1; % Generate the time indices

x ¼ 5*sin(2*pi*16000*n*T); % Generate the test signal

% Upsampling by a factor of L
w ¼ zeros(1,L*N);
for n ¼ 0:1:N-1
w(L*n þ 1) ¼ x(n þ 1);
end
NL ¼ length(w); % Number of the upsampled data
W ¼ 2*abs(fft(w,NL))/NL;W(1) ¼ W(1)/2; % Compute the one-sided
% amplitude spectrum

f ¼ [0:1:NL/2-1]*fs*L/NL; % Map the frequency index to its frequency in Hz

f ¼ f/1000; % Convert to kHz

% Interpolation
y ¼ filter(Bup,1,w); % Perform the interpolation filter
Y ¼ 2*abs(fft(y,NL))/NL;Y(1) ¼ Y(1)/2; % Compute the one-sided
% amplitude spectrum