Digital Signal Processing Reference
In-Depth Information
Example:
To show that the previous example was not just a coincidence, we will repeat the
above experiment with a rectangle and a triangle, Figure 3.32.
Figure 3.32: A rectangle and a triangle.
This time, we see that the resulting one-dimensional signals are dierent, as we
might expect (Figure 3.33). With the rectangle, we see the 1D signal gradually get
smaller, then get larger again until it reaches the same height. Next, it gets a bit
smaller, then back to its original height. This pattern repeats. From the center, the
corners are going to be the furthest points away, and we see this as the top height.
As we trace the boundary of the rectangle, the distance to the center gets a little
smaller, then larger until we reach the next corner. As we trace the next side, the
distance gets smaller and then back to the original distance at the corner. Since the
second side is not as long as the rst, the gradual dip in height is not as prominent.
With the triangle, the corners are not equidistant from the center (due to the use
of a simple averaging function to nd the center), thus we see three peaks in the
dotted one-dimensional object representation, but two of them are not as far away
from the center as the third one. We started from the upper-right corner, though
the starting position does not matter since the correlation calculations consider the
shift of the signal.
max correlation coeff: 0.6272
When we calculate the correlation coecients, we nd the maximum as only
0.6272. We can conclude that that objects do share some similarity, but they are
far from a match.
3.9
Summary
Finite Impulse Response (FIR) lters are presented in this chapter, including their
structure and behavior.
Three important properties that FIR lters possess are
