Digital Signal Processing Reference
In-Depth Information
The dashed line shows how the sampled signal will appear if
we connect the sample dots and smooth out the signal. Notice
that since the actual (solid line) signal is changing so rapidly
between sampling instants, this movement is not apparent in the
sampled version of the signal. The sampled version appears to be
a lower-frequency signal than the actual signal. This effect is
known as aliasing.
We need a way to quantify how fast we must sample to
accurately represent a given signal. We also need to better
understand exactly what is happening when aliasing occurs. It
may seem strange, but there are some instances when aliasing
can be useful.
Let's go back to the analogy of the strobe light, and try another
thought experiment. Imagine a spinning wheel, with a single dot
near the edge. Let's set the strobe light to flash every
1
/
8
of
a second, or eight times per second. Below is shown what we see
over six flashes, depending on how fast the wheel is rotating.
Time increments from left to right in all figures.
The reality is that once we sample a signal (this is what we are
doing by flashing the strobe light), we cannot be sure what has
happened in-between flashes. Our natural instinct is to assume
that the signal (or dot in our example) took the shortest path from
where it appears in one flash to its position in the subsequent
flash. But, as we can see in the examples above, this can be
misleading. The dot could be moving around the circle in the
opposite direction (taking the longer path) to get to the point
where we see it on the next flash. Or imagine that the circle is
rotating in the assumed direction, but it rotates one full revolu-
tion plus “a little bit extra” every flash (the 9 Hz diagram). What
Wheel rotating counterclockwise once per second, or 1 Hertz (Hz)
Figure 3.3.
The dot moves
1
/
8
of a revolution with each strobe
ash.
Figure 3.4. Now the dot moves
twice as fast, ¼ of a revolution
with each strobe
ash.
Wheel rotating counterclockwise twice per second, or 2 Hz
