Introduction - Introduction to Digital Signal Processing and Filter Design - page 23

Analog Preconditioning

Analog
Low Pass Filter

Sample
and
Hold

Digital
Signal
Processor

Analog
Low Pass
Filter

Analo g

ADC DAC

Input
x(t)

Output
y(t)

Figure 1.17 Example of a digital signal processing system.

1.5 ANALOG AND DIGITAL SIGNAL PROCESSING

The basic elements in digital filters are the multipliers, adders, and delay ele-
ments, and they carry out multiplication, addition, and shifting operations on
numbers according to an algorithm determined by the transfer function of the
filters or their equivalent models. (These models will be discussed in Chapter 3
and also in Chapter 7.) They provide more flexibility and versatility compared
to analog filters. The coefficients of the transfer function and the sample values
of the input signal can be stored in the memory of the digital filter hardware or
on the computer (PC, workstation, or the mainframe computer), and by changing
the coefficients, we can change the transfer function of the filter, while chang-
ing the sample values of the input, we can find the response of the filter due
to any number of input signals. This flexibility is not easily available in ana-
log filters.
The digital filters are easily programmed to do time-shared filtering under time-
division multiplexing scheme, whereas the analog signals cannot be interleaved
between timeslots. Digital filters can be designed to serve as time-varying filters
also by changing the sampling frequency and by changing the coefficients as a
function of time, namely, by changing the algorithm accordingly.
The digital filters have the advantage of high precision and reliability. Very
high precision can be obtained by increasing the number of bits to represent
the coefficients of the filter transfer function and the values of the input signal.
Again we can increase the dynamic range of the signals and transfer function
coefficients by choosing floating-point representation of binary numbers. The
values of the inductors, capacitors, and the parameters of the operational amplifier
parameters and CMOS transistors, and so on used in the analog filters cannot
achieve such high precision. Even if the analog elements can be obtained with
high accuracy, they are subject to great drift in their value due to manufacturing
tolerance, temperature, humidity, and other parameters—depending on the type
of device technology used—over long periods of service, and hence their filter
response degrades slowly and eventually fails to meet the specifications. In the
case of digital filters, such effects are nonexistent because the wordlength of
the transfer coefficients as well as the product of addition and multiplication
within the filter do not change with respect to time or any of the environmental
conditions that plague the analog circuits. Consequently, the reliability of digital
filters is much higher than that of analog filters, and this means that they are more
economical in application. Of course, catastrophic failures due to unforeseen
factors are equally possible in both cases. If we are using computers to analyze,