Question

For each of the following tables of values coming from a sensor, would it be best to use the values, the first derivative, or the second derivative to threshold noise? Explain. Apply the method you chose and identify the threshold rule (i.e. If x > y or x < y then noise)

SensorFirst Second values Deriv. Deriv Sensor First Second values Deriv. Deriv 15 18 100 105 113 124 138 158 169 186 206 229 255 24 28 29 32 35 38

Answer 1

Solution:

i)

Sensor Values	First	Second
15
18	>3
21	>3	>0
24	>3	>0
28	>4	>1
33	>5	>1
29	>-4	>-9
32	>3	>7
35	>3	>0
38	>3	>0
41	>3	>0

ii)

Sensor Values	First	Second
100
105	>5
113	>8	>3
124	>11	>3
138	>14	>3
158	>20	>6
169	>11	>-9
186	>17	>6
206	>20	>3
229	>23	>3
255	>26	>3

For both i. and ii., the values are increasing and therefore do not lend themselves to a threshold rule. For i. both the first and second derivative indicates constant change that can be expressed as a threshold rule. For ii., the second derivative indicates a constant change that can be expressed as a threshold rule.

i.       

First Derivative, if x <> 3 then noise

Second Derivative, if x <> 0 then noise

ii.

Second Derivative, if x <> 3 then noise

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