Processing of Signals - Digital Signal Processing: A Practitioner's Approach - page 18

Figure 1.12 It is playing with numbers

There are well-defined, logical, mathematical or heuristic rules to play with them.
To demonstrate this concept of playing (Figure 1.12), we shall conclude this chapter
with a simple example of playing with numbers.
Let y 2 ; ...g be a sequence of numbers so acquired. Its mean at

discrete time k is defined as

f y k g¼f y 1 ;

k X

k

1

k ¼ y i : ð 1 : 37 Þ

i ¼ 1

The above way of computing the mean is known as a moving-average process. We
recast the (1.37) as k k ¼ P i ¼ 1 y i and for k þ 1 we write it as

ð k þ 1 Þ k þ 1 ¼ X

k þ 1

y i

i ¼ 1

¼ X

k

y i þ y k þ 1 ð 1 : 38 Þ

i ¼ 1

¼ k k þ y k þ 1 : ð 1 : 39 Þ