Processing of Signals - Digital Signal Processing: A Practitioner's Approach - page 16

1.6 Signal Seen by the Computing Engine
With so much compulsive morphing, the final digitised signal 10 takes the form

$ ! R ð t Þ %

1

f y k g¼ y ð t Þð t T s k Þ þ k : ð 1 : 35 Þ

k ¼1

y k ¼ ^ y k þ k : modelling of Discrete Signal

In (1.35) we have not included any noise that gets added due to the channel through
which the signal is transmitted. Besides that, in reality the impulse function

ð t Þ is

approximated by a narrow rectangular pulse of finite duration.

1.6.1 Mitigating the Problems
Quantisation noise is purely controlled by the number of bits of the converter. The
windowing effect is minimised by the right choice of window functions or choosing
data of sufficient duration. There are scores of window functions [5] to suit different
applications.

1.6.1.1 Anti-Aliasing Filter

It is necessary to have a band-limited signal before converting the signal to discrete
form, and invariably an analogue lowpass filter precedes an A/D converter, making
the signal band-limited. The choice of the filter depends on the upper bound of the
sampling frequency and on the nature of the signal.

1.6.2 Anatomy of a Converter
There are three distinct parts to an A/D converter, as shown in Figure 1.11:

Switch
Analogue memory
Conversion unit

Output y k

Input y ( t )

Converter

Switch

Analogue memory

Figure 1.11 Model of an A/D converter

10

The signal y k is a floating-point representation of the signal b y k c .