Sampling - DSP Using MATLAB and Wavelets - page 168

title(my_title);
xlabel( time );
ylabel(Amplitude);

% Plot the "sampled" signals
subplot(2,1,2);
plot(n,x2,rx, n,y2,bo);
my_title = sprintf(Simulated digital signals, x=x y=o);
title(my_title);
xlabel( samples );
ylabel(Amplitude);

It is easy to gure out when to take samples. Since the sampling frequency is 500
samples/sec, the sampling period must be 1=500 = 0:002 seconds. Taking our rst
sample at time t = 0, we will take samples again at 0.002 seconds, 0.004 seconds,
0.006 seconds, and so forth.

5.4.2 Folding

We saw that any frequency greater than the sampling frequency will show up as
a lower frequency. Folding is another way of looking at the aliasing phenomenon,
where the observed frequency of a sampled signal diers from the actual frequency,
even though it is less than the sampling frequency but greater than half the sampling
frequency. Some texts use the term \folding" [11] [2] [6], while others mention this
only as \aliasing" [9] [20] [21]. It is a type of aliasing, but here we prefer the term
\folding" to distinguish it from aliasing, since the phase angle is aected. You may
also see f s =2 referred to as the folding frequency if, for example, a 600 Hz sinusoid
is sampled at f s = 1000 samples/sec, and the observed frequency is 1000600 =
400 Hz. This comes from the fact that:

cos(2600nT s + ) = cos(2(1000400)nT s + )

= cos(21000nT s 2400nT s + )

= cos(21000n=10002400nT s + )

= cos(2n2400nT s + ):

As before, we can remove an integer multiple of 2 from the cos function. Since n
is dened as an integer, we can remove the 2n term:

cos(2n2400nT s + ) = cos(2400nT s + ):