- #1
roam
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- Homework Statement
- I am trying to find the best method to determine the average constant spacing between the consecutive dips in the following oscilloscope traces.
- Relevant Equations
- $$\frac{\sigma_{N}}{\sqrt{N}}$$
I have collected a large number of oscilloscope traces (these relate to the modes of a laser cavity). Four sets are shown here:
There are two ways for finding the average spacing ##\Delta t## between the adjacent dips:
1. Measure all the individual ##\Delta t##s from each measurement separately and then average everything together.
2. Combine all the measurements into one single curve by averaging them. Then we only have 11 ##\Delta t##s to calculate and average into a single value. This seems to be a quicker method, but a problem with this is that the traces slightly vary in time so the position of the dips do not perfectly coincide (they have to be offset manually).
I believe the estimated error in the average will be given by ##\frac{\sigma_{N}}{\sqrt{N}}##. So, which method is more reliable, and how would the errors vary depending on the method?
Any explanation would be greatly appreciated.
There are two ways for finding the average spacing ##\Delta t## between the adjacent dips:
1. Measure all the individual ##\Delta t##s from each measurement separately and then average everything together.
2. Combine all the measurements into one single curve by averaging them. Then we only have 11 ##\Delta t##s to calculate and average into a single value. This seems to be a quicker method, but a problem with this is that the traces slightly vary in time so the position of the dips do not perfectly coincide (they have to be offset manually).
I believe the estimated error in the average will be given by ##\frac{\sigma_{N}}{\sqrt{N}}##. So, which method is more reliable, and how would the errors vary depending on the method?
Any explanation would be greatly appreciated.