Upsampling — Imaging Artifacts

This example shows how to upsample a signal and how upsampling can result in images. Upsampling a signal contracts the spectrum. For example, upsampling a signal by 2 results in a contraction of the spectrum by a factor of 2. Because the spectrum of a discrete-time signal is 2π-periodic, contraction can cause replicas of the spectrum normally outside of the baseband to appear inside the interval [-π,π].

Create a discrete-time signal whose baseband spectral support is [-π,π]. Plot the magnitude spectrum.

f = [0 0.250 0.500 0.7500 1];
a = [1.0000 0.5000 0 0 0];

nf = 512;
b = fir2(nf-1,f,a);
Hx = fftshift(freqz(b,1,nf,'whole'));

omega = -pi:2*pi/nf:pi-2*pi/nf;
xlabel('\times\pi rad/sample')

Upsample the signal by 2. Plot the spectrum of the upsampled signal. The contraction of the spectrum has drawn subsequent periods of the spectrum into the interval [-π,π].

y = upsample(b,2);
Hy = fftshift(freqz(y,1,nf,'whole'));

hold on
hold off
text(0.65*[-1 1],0.45*[1 1],["\leftarrow Imaging" "Imaging \rightarrow"], ...

See Also

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