Digital Signal Processing Reference
In-Depth Information
Chapter 3
Low-Pass Filters
This chapter presents the important features of 66 predesigned low-pass filters.
These features are presented in a data sheet format, which we believe allows easy
filter cross-referencing and assessment. In addition to the frequency and impulse
response functions, a table of pertinent performance attributes is provided for each
filter. These capture the characteristics of the predesigned digital filter in its
entirety. Apart from the visual representation of the filters and their tabulated
performance data, the filter coefficients are listed in electronic format and
appended to this topic.
3.1 GENERAL CHARACTERISTICS
There are aspects of the characteristics of the Gaussian-windowed FIR filter
family that are of general interest. These characteristics show trends that allow the
user to predict the attributes of other members of the filter family if required.
3.1.1
F
-3dB
Frequency and Filter Length
In many filtering applications the -3dB frequency
F
-3dB
has become a
recognizable parameter for defining the cut-off frequency of low-pass filters. In
digital filtering though, it is easier to define the cut-off frequency
F
c
, as the
frequency at which the magnitude attains an absolute value of 0.5, since this is
guaranteed by design. The consequence of using the
F
-3dB
measure is that it varies
with filter length since the sharpness of the transition width is a function of the
filter order. Additionally, as the filter order increases, the transition width
decreases, and
F
-3dB
approaches
F
c
asymptotically. Because of this, there is a fairly
predictable relationship between these two measures. As such, for historical
reasons we have tabulated the
F
-3dB
frequency in this topic. Figure 3.1 shows the
effect of filter order on the -3 dB frequency for various cut-off frequencies
F
c
, as
well as the relationship between these two parameters. The response for
L
+1 = 99
and 155 have been removed as they are almost coincident with length 255.
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