Digital Signal Processing Reference
In-Depth Information
Another means of classifying filters is by the implementation method used.
Some filters will be built to filter analog signals using individual components
mounted on circuit boards, while other filters might simply be part of a larger
digital system which has other functions as well. Several implementation methods
will be described in the third section of this chapter as well as the differences
between analog and digital signals. However, it should be noted that digital filter
design and implementation will be considered in detail starting in Chapter 5, while
the first four chapters concentrate on filter approximation theory and analog filter
implementation.
In the final section of this chapter we discuss WFilter, an analog and digital
filter design package for Windows
®
, which is included on the software disk.
WFilter determines the transfer function coefficients necessary for analog filters or
for digital FIR or IIR filters. After the filter has been designed, the user can view
the pole-zero plot, as well as the magnitude and phase responses. The filter design
parameters or the frequency response parameters can also be edited for ease of
use. In addition, for analog filters, the Spice circuit file can be generated to aid in
the analysis of active filters. After digital filters have been designed, they may be
used to filter wave files and the results can be played for comparison (a sound card
must be present). Further discussion of WFilter and the C code supplied with this
text can be found in Appendix B.
1.1 FILTER SELECTIVITY
As indicated earlier, a filter's primary purpose is to differentiate between different
bands of frequencies, and therefore frequency selectivity is the most common
method of classifying filters. Names such as lowpass, highpass, bandpass, and
bandstop are used to categorize filters, but it takes more than a name to completely
describe a filter. In most cases a precise set of specifications is required in order to
allow the proper design of a filter. There are two primary sets of specifications
necessary to completely define a filter's response, and each of these can be
provided in different ways.
The frequency specifications used to describe the passband(s) and stopband(s)
could be provided in hertz (Hz) or in radians/second (rad/sec). We will use the
frequency variable
f
measured in hertz as filter input and output specifications
because it is a slightly more common way of discussing frequency. However, the
frequency variable ω measured in radians/second will also be used as WFilter's
internal variable of choice as well as for unnormalized frequency responses since
most of those calculations will use radians/second.
The other major filter specifications are the gain characteristics of the
passband(s) and stopband(s) of the filter response. A filter's gain is simply the
ratio of the output signal level to the input signal level. If the filter's gain is greater
than 1, then the output signal is larger than the input signal, while if the gain is
less than 1, the output is smaller than the input. In most filter applications, the gain
