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Jul 09, 2019
04:30 PM

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Jul 09, 2019
04:30 PM

Upsample or interpolate complex numbers

Does anyone know of a method to interpolate or upsample a "straight line" between 2 complex points?

For example, between points (1+1j) and (4+4j) get (arbitrary) 2 more points: (2+2j) and (3+3j).

Or as shown in picture, get vector [Matrix?] Z (not exactly, but similar) from W.

Solved! Go to Solution.

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Jul 09, 2019
08:00 PM

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Jul 09, 2019
08:00 PM

@vyerokhin wrote:

Does anyone know of a method to interpolate or upsample a "straight line" between 2 complex points?

complex "points"? You obviously mean complex numbers.

You do i the same way as with real numbers.

Maybe that way:

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Jul 09, 2019
08:00 PM

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Jul 09, 2019
08:00 PM

@vyerokhin wrote:

Does anyone know of a method to interpolate or upsample a "straight line" between 2 complex points?

complex "points"? You obviously mean complex numbers.

You do i the same way as with real numbers.

Maybe that way:

Jul 09, 2019
09:37 PM

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Jul 09, 2019
09:37 PM

Thank you very much, Werner_E!

Yes - I meant complex number. I said complex points because I was thinking in terms of plotting on a complex plain.

Jul 10, 2019
04:21 AM

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Jul 10, 2019
04:21 AM

Thanks good Mathcad sheet. I'm watching all community reply by Werner_E.

May be this is a next step of this subject.

Tokoro

Jul 10, 2019
06:07 AM

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Jul 10, 2019
06:07 AM

You like playing around with thing and had posted some interesting worksheets in the past 😉

Here is UpSamplePoly based on your idea to use "polyint":

The drawback here is that real parts and imaginary parts are treated differently and so depending on the initial data set it may yield very strange and unusable results.

Try to exchange real and imaginary parts in your sample data -> W:=Im(W)+1i*Re(W)

and see what happens 🙂

Jul 10, 2019
09:09 AM

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Jul 10, 2019
09:09 AM

Of course things look (a little bit) better if we sort W by the real parts beforehand.

Jul 10, 2019
12:04 PM

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Jul 10, 2019
12:04 PM

Here is a last version that uses polyint and still handles real and imaginary parts alike.

It may be useful in some situations, less useful in others.

Jul 10, 2019
01:01 PM

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Jul 10, 2019
01:01 PM

And here is the real last one 😉

I got rid of polyint and replaced it by cubic spline interpolation. This tends not that much to overshoot and is more stable, especially with larger data vectors.

Jul 10, 2019
09:42 PM

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Jul 10, 2019
09:42 PM

Thanks Werner. Second line in your UpSampleSplineC is a key technique of this function.

Indexes of rows(W) such as 0,1,2,3 can be used as base of both Wx and Wy for up sampling.

Using your new functions, Lissajous figures can made by up sampling.

Tokoro