Introduction - Introduction to Digital Signal Processing and Filter Design - page 20

very large scale integration (VLSI) technology. The analog signals were con-
verted to sampled data signals by these filters and the signal processing was
treated as analog signal processing. But later, the signals were transitioned as
discrete-time signals, and the theory of discrete-time systems is currently used to
analyze and design these filters. Examples of an LC filter, an active- RC filter,
and a switched-capacitor filter that realize a third-order lowpass filter function
are shown in Figures 1.12-1.14.
The evolution of digital signal processing has a different history. At the begin-
ning, the development of discrete-time system theory was motivated by a search
for numerical techniques to perform integration and interpolation and to solve
differential equations. When computers became available, the solution of phys-
ical systems modeled by differential equations was implemented by the digital

R 2

+

L 2

R s

v 2 R L

c 2 _

c 1

v 1

−

Figure 1.12 A lowpass analog LC filter.

+

v 2

+
−

v 1

−

Figure 1.13 An active- RC lowpass analog filter.