Multirate Digital Signal Processing, Oversampling of Analog-to-Digital Conversion, and Undersampling of Bandpass Signals - Digital Signal Processing: Fundamentals and Applications - page 569

for n ¼ 0:1:N-1
w1(L*n þ 1) ¼ x(n þ 1);
end
NL ¼ length(w1); % Length of upsampled data
W1 ¼ 2*abs(fft(w1,NL))/NL;W1(1) ¼ W1(1)/2; % Compute the one-sided
% amplitude spectrum
f ¼ [0:1:NL/2-1]*fs*L/NL; % Map frequency index to its frequency in Hz
subplot(3,1,1);plot(f,W1(1:1:NL/2));grid
xlabel(

Frequency (Hz) );

' '

w2 ¼ filter(Bdown,1,w1); % Perform the combined anti-aliasing filter

W2 ¼ 2*abs(fft(w2,NL))/NL;W2(1) W2(1)/2; % Compute the one-sided

% amplitude spectrum

¼

y2 w2(1:M:NL);

NM ¼ length(y2); % Length of the downsampled data
Y2 ¼ 2*abs(fft(y2,NM))/NM;Y2(1) ¼ Y2(1)/2;% Compute the one-sided
%amplitude spectrum
% Map frequency index to its frequency in Hz before downsampling
fbar ¼ [0:1:NL/2-1]*24000/NL;
% Map frequency index to its frequency in Hz
fsM ¼ [0:1:NM/2-1]*(fs*L/M)/NM;
subplot(3,1,2);plot(f,W2(1:1:NL/2));grid; xlabel( ' Frequency (Hz) ' );
subplot(3,1,3);plot(fsM,Y2(1:1:NM/2));grid; xlabel( ' Frequency (Hz) ' );

¼

2

1.5

1

0.5

0

0 2000 4000 6000 8000 10000 12000

Frequency (Hz)

2

1.5

1

0.5

0

0 500 1000 1500

Frequency (Hz)

FIGURE 12.9B

(Top) Spectrum after anti-aliasing filtering, and (bottom) spectrum after downsampling.