Manipulating Numerical Data
When you have numerical data, it is often convenient to find a simple formula that approximates it. For example, you can try to "fit" a line or curve through the points in your data.
| Fit[{y1,y2,...},{f1, f2,...},x] | fit the values  to a linear combination of functions  |
| Fit[{{x1,y1},{x2,y2},...},{f1, f2,...},x] | fit the points  to a linear combination of the  |
Fitting curves to linear combinations of functions.
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This finds a least-squares fit to
of the form
. The elements of
are assumed to correspond to values
,
, ... of
.
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This finds a fit of the form
.
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This gives a table of
,
pairs.
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This finds a fit to the new data, of the form
.
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| FindFit[data,form,{p1,p2,...},x] | find a fit to form with parameters  |
Fitting data to general forms.
This finds the best parameters for a linear fit.
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This does a nonlinear fit.
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One common way of picking out "signals" in numerical data is to find the Fourier transform, or frequency spectrum, of the data.
Fourier transforms.
Here is a simple square pulse.
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This takes the Fourier transform of the pulse.
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Note that the Fourier function in Mathematica is defined with the sign convention typically used in the physical sciences—opposite to the one often used in electrical engineering. "Discrete Fourier Transforms" gives more details.
