Digital Signal Processing Reference
In-Depth Information
90%
τ
R
10%
Figure 3.4
Definition of rise time
τ
R
in relation to the step response.
3.1.3
Rise Time
τ
R
The rise time
R
of a low-pass filter is defined as the time between the 10% and
90% values of the step response of the filter. This is shown in Figure 3.4, and is
somewhat nonstandard from a design perspective, but is consistent with the type
of measurements carried out in an R&D laboratory.
There is an inverse relationship between the rise time
τ
R
and the cut-off
frequency
F
c
. The general rise time characteristic of the filters presented in this
chapter is shown in Figure 3.5. The open circles in the figure are for all filters
except those of lengths
L
+1 = 33. The least squares fit of these results suggests a
relationship of the form
τ
12
10
8
6
4
2
0
0
2.5
5
7.5
10
12.5
15
Reciprocal Cut-off Frequency, 1/
F
c
Figure 3.5
Relationship between rise time and cut-off frequency.
