Question

A student is trying to filter their data by both averaging the prior 3 filtered measurements with the current raw measurement, all weighted equally. Write the equation for this filter, assuming y(k) is the current output and x(k) is the current raw measurement: y(k) =

Answer 1

The current output y(k) in the filter is the average of the current raw measurement x(k) and the previous three outputs, y(k-1), y(k-2), and y(k-3), weighted equally, given by y(k) = (x(k) + y(k-1) + y(k-2) + y(k-3)) / 4.

Step-by-step explanation:

To derive the equation for the filter described in the question, where y(k) is the current output and x(k) is the current raw measurement, we take the average of the prior 3 filtered measurements and the current raw measurement. If we denote the prior three outputs as y(k-1), y(k-2), and y(k-3), then the current output y(k) is computed as:

y(k) = (x(k) + y(k-1) + y(k-2) + y(k-3)) / 4

Each term is weighted equally, which means that they each contribute equally to the average that constitutes the new output.