Digital Filters - Digital Signal Processing: A Practitioner's Approach - page 52

8

5

Quadrature

In phase

4

6

3

4

2

2

1

0

0

0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0. 5

Frequency Frequency

(a) (b)

Figure 3.7 Bank of filters in matrices A and B in (3.13) and (3.14)

3.3 Infinite Sequence Generation
In many applications, we need to generate an infinite sequence of numbers for
testing or as part of the system modelling. Here are a few examples.

3.3.1 Digital Counter
In many programing applications we use counters. Such counters are obtained by
using an integrator with an input as a Kronecker delta function given by

k ¼ 1 for

only k ¼ 0, and the input-output relation

y k ¼ y k 1 þ k : ð 3 : 15 Þ

Quite often this model is used in real-time simulations for generating a ramp.

3.3.2 Noise Sequence
The primary source is a uniformly distributed noise (UDN), which can be generated
by a linear congruential generator (LCG), explained in Section 2.4.1. Figure 3.8

Figure 3.8 Non-linear infinite sequence generator

shows the relation of an LCG given as k 1 þ c Þ mod m, where the

constants a and c can be chosen to suit the purpose. This is an example of a filter
with a non-linear element in the feedback loop.

k ¼ð a