4.12.1 Linear Systems

Question 1

Explain the superposition principle.

Answer 1

The net result caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually

f(s1 + s2) = f(s1) + f(s2)

Question 2

What is the advantage of studying a linear system?

Answer 2

The responses of a linear system are the same independent of the input magnitudes (it allows for extrapolation).

Question 3

What is a problem with studying linear systems?

Answer 3

In practice, they “don’t exist”.

However, most sensorimotor systems have a substantial ‘linear range’ where the main assumptions hold. For example: the position of the eye is for most inputs linearly related to the firing rate. But the position of the eye “saturates”, so if one continued to increase neural output, the output would be ‘non linear’.

Question 4

What does it mean to say that an eye is a low-pass filter?

Answer 4

The eye smoothens rapid changes in sharp contraction forces in the eye muscles.

Question 5

Which phases of eye movements are denoted by (a) and (b)?

Answer 5

(a) fixation
(b) saccade

Question 6

Is the following statement true or false?

A low-pass filter can be produced by a linear system.

Answer 6

True.

Question 7

If R₀ is baseline spike rate and R_m is a measured rate of firing, and E is the eye position, what is the unit of measurement of constant k in this equation?

Answer 7

Spikes per second per degree

Question 8

What does R_m(t) denote in this equation?

Answer 8

The firing rate of the abducens nerve

Question 9

What does the parameter r represent in this equation?

Answer 9

The dampening constant of the eye plant.

Question 10

If we want to recreate a saccade and we know that the plant is a low-pass filter, what are the two input functions we need to produce?

Answer 10