Introduction to Filters and Filter Design Software - Practical Analog and Digital Filter Design - page 6

has two passbands. The lower passband extends from zero to f pass1 , while the upper
passband extends from f pass2 to infinity (for analog filters). Within the stopband,
the single stopband gain parameter a stop is used. However, individual gain
parameters for the lower and upper passbands, a pass1 and a pass2 (in dB) respectively,
could be used if necessary.
Figure 1.4 Bandstop filter specification.
An excellent example of a bandstop application would be a 60-Hz notch filter
used in sensitive measurement equipment. Most electronic measurement
equipment today runs from an AC power source using a 60-Hz input frequency.
However, it is not uncommon for some of the 60-Hz signal to make its way into
the sensitive measurement areas of the equipment. In order to eliminate this
troublesome frequency, a bandstop filter (sometimes called a notch filter in these
applications) could be used with f stop1 set to 58 Hz and f stop2 set to 62 Hz. The
passband edge frequencies could be adjusted based on the other technical
requirements of the filter.
1.2 FILTER APPROXIMATION
The response of an ideal lowpass filter is shown in Figure 1.5, where all
frequencies from 0 to f o are passed with a gain of 1, and all frequencies above f o
are completely attenuated (gain = 0). This type of filter response is physically
unattainable. Practical filter responses that can be attained are also shown. As a
filter's response becomes closer and closer to the ideal, the cost of the filter (time
delay, number of elements, dollars, power consumption, etc.) will increase. These
practical responses are referred to as approximations to the ideal. There are a
variety of ways to approximate an ideal response based on different criteria. For
example, some designs may emphasize the need for minimum distortion of the
signals in the passband and would be willing to trade off stopband attenuation for