Consider a Gaussian$-$shaped signal composed of $20$ evenly spaced data points. We will assume that the $20$ data points cover $5$ or $99\%$ of the shape. The signal is very noisy and you would like to make it look better using a Software Method. An example of this type of signal is shown in the figure below. Remember, you can not propose recording extra data; you must work with the data that you already have.

For the two software methods below, respond to the questions using the specific example above. Boxcar averaging:

How many points do you average in each "box"?

What effect will that choice have on the smoothed data?

How likely is it that the smoothed result is distorted by the boxcar average?

Savitzky$-$Golay filter:

How many points do you select in each "window"?

What effect will that choice have on the smoothed data?

How likely is it that the smoothed result is distorted by the Savitzky$-$Golay filter?