In the last session we generated a sequence of numbers using the program
coswave.m. Let's call the sample number i and the i'th
sample x[i]:


1

32000

2

30601

3

26529

4

20138

5

11987

6

2788

7

6654

8

15514

9

23019

10

28513

11

31514

12

31762

13

29234

14

24151

15

16958

16

8283

17

1116

18

10418

19

18809

20

25556

21

30070


Some simple operations on lists of numbers:
1) Sum or integral, x[i]. If x[i] has positive and negative values, it is better to take the absolute (i.e. unsigned) value of x[i], written x[i]. The most common way of calculating this is to first calculate the square of x[i], x[i]^{2}, and then take the square root, x[i]^{2}. This is a measure of the overall energy of a signal.
2) Obviously, x[i]^{2} gets bigger and bigger as x[i] gets longer. More usually, we are interested in the average amplitude of a signal, as calculated over n samples: (x[i]^{2}/n). This is called the root mean square or RMS amplitude, since it is the square root of the mean of the square of n samples.
An Octave program for calculating RMS amplitude is given here.
3) Local averaging ... (follow the link).