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September 16th, 2017, 10:11 AM   #1
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Summing derivatives

I have some time series data (water flow through pipe A and B) in a database. The time intervals are not regular, and I do not necessarily have data for common time stamps, but I do have data over the same time span.

The database has the capability to calculate the derivative on a given time interval. For instance, if at 1 second intervals, I would return 65 values for the Flow A's derivative and 65 values for Flow B's derivative (I might need to use some longer time interval to get good results, but this is not relevant to my question). It could only do one series at a time and could not do the combined flow.

Given the results for the individual derivatives of each flow, how can I determine the 65 values for the derivative of (Flow A + Flow B)?

Thank you


Flow A
Code:
+------+------+
| time | Flow |
+------+------+
|    0 |       1 |
|    5 |       3 |
|   11 |      4 |
|   14 |      0 |
|   16 |      2 |
|   19 |      8 |
|   22 |      3 |
|   26 |      3 |
|   26 |      9 |
|   35 |      4 |
|   42 |      6 |
|   50 |      9 |
|   51 |      7 |
|   60 |      0 |
|   65 |      7 |
+------+------+
Flow B
Code:
+------+------+
| time | Flow  |
+------+------+
|     0 |       2 |
|     9 |       4 |
|   14 |     11 |
|   20 |     12 |
|   24 |       3 |
|   28 |       6 |
|   39 |       8 |
|   48 |     13 |
|   51 |       9 |
|   65 |       6 |
+------+------+
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October 11th, 2017, 07:20 PM   #2
SDK
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assuming the values for flow represent derivatives? I would interpolate both data sets using cubic splines (or any smooth B-spline scheme) and add the interpolants to evaluate on a uniform grid.

Start here:
https://en.wikipedia.org/wiki/B-spline
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October 12th, 2017, 04:34 AM   #3
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If I am reading this correctly, "interpolation" is not necessary.

You are given 65 values for the derivative of flow A and 65 values for the derivative of flow B. The derivative of "flow A plus flow B" is just the "derivative of flow A" plus the "derivative of flow A". For each time, add the two values.
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October 12th, 2017, 12:29 PM   #4
SDK
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Quote:
Originally Posted by Country Boy View Post
If I am reading this correctly, "interpolation" is not necessary.

You are given 65 values for the derivative of flow A and 65 values for the derivative of flow B. The derivative of "flow A plus flow B" is just the "derivative of flow A" plus the "derivative of flow A". For each time, add the two values.
Obviously, this is fine if your interpretation is correct. I read it differently based on the comment

Quote:
The time intervals are not regular, and I do not necessarily have data for common time stamps, but I do have data over the same time span.
In any case, he/she has an answer.
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October 12th, 2017, 04:51 PM   #5
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Oh, I see your point. The 'times' for flow A and flow B are not the same.
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