This isn't a question; I'm putting this here as a reference so I can find i t in the future. This is how to build a cubic interpolator circuit that ta kes four samples and interpolates a sample between the middle two.
Given four samples, y0, y1, y2, y3, sampled with period T=1 at (arbitrary ) times t={-1,0,1,2}, and given mu, where 0
This might seem a minor quibble, but that is not a cubic spline interpolation - it is just a plain cubic curve fit and interpolation. A cubic spline is made when you have more sample points and you put together a step-wise cubic function consisting of multiple cubic parts joined together. Implementing cubic splines involves quite a bit more maths (it depends on the type of cubic spline - there are many) - making an efficient FPGA implementation could be a fun way to spend a rainy day.
Should be easy, it's 10 lines in Java:
-- Frank Buss, http://www.frank-buss.de electronics and more: http://www.youtube.com/user/frankbuss
Super! Mann zieht die Stuetzpunkte mit der Maus! That is a nice applet, but it's parametric, so it seems a little different than my application. I have a function of only one variable. -Kevin
Thanks; that is a good clarification. I just need to interpolate a point g iven four surrounding points so I guess I don't need the whole spline imple mentation. There is a wealth of information on the web about interpolation but it's difficult to find the simple extracted formula I have above. I s uppose most implementations are, like you say, not well-designed for FPGAs.
it's parametric,
one variable.
The class Spline.java is a spline of only one variable. Test.java uses it twice, for the x and y coordinate of the points.
Your example for x=-1,0,1,2 could be implemented by creating a Spline object and initializing it with the y-samples. Then call fn, with 0, 1,
2, 3 and use t for interpolating between two points.-- Frank Buss, http://www.frank-buss.de electronics and more: http://www.youtube.com/user/frankbuss
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