Page 44 - Analog and Digital Filter Design

2
CHAPTER

TIME AND FREQUENCY RESPONSE

This chapter describes filter frequency and time domain responses for a number
of filter response types (e.g., Butterworth) and filter orders. This information on
the frequency and time domain responses will be of use for all filter designs,
whether passive, active, or digital.

Normalized frequency response graphs are used, with the passband edge usually
being at a frequency of 1 rad/s (for the reasons discussed in Chapter 1). The fre-
quency domain is described in terms of attenuation relative to this normalized
frequency. Hence, the attenuation at, say, 10 times the cutoff frequency will be
the value given on the graph where the curve crosses the frequency axis at 10
rad/s. On the frequency response graphs there is one curve for each filter order.
thus 10 curves allow the relative performance of different filter orders to be com-
pared. Higher filter orders give greater stopband attenuation but require more
components.

Tables of normalized component values are given in this chapter for analog
passive lowpass filters. Formulae used to derive many of these component values
are given in the Appendix. The use of these tables to produce lowpass, highpass,
bandpass, and bandstop filters will be given in Chapters 4, 5, 6, and 7 respec-
tively. Tables for the design of analog active filters and digital IIR filters will be
given in Chapter 3.

Filter Requirements

Filters are intended to pass some signal frequencies but stop others. Before a
design can commence, the designer needs to consider the signals that need to be
processed in this way. Does the filter have to pass DC? Are the signals impul-
sive? Which frequencies must pass and which must be stopped? How much atten-
uation (i.e., reduction in signal amplitude) is required? Once this information is