Mathematica Tutorial

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 y_n to a linear combination of functions f_i
Fit[{{x₁,y₁},{x₂,y₂},...},{f₁, f₂,...},x]	fit the points (x_n, y_n) to a linear combination of the f_i

Fitting curves to linear combinations of functions.

This generates a table of the numerical values of the exponential function. Table is discussed in "Making Tables of Values".

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This finds a least-squares fit to data of the form c₁+c₂x+c₃x². The elements of data are assumed to correspond to values 1, 2, ... of x.

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This finds a fit of the form c₁+c₂x+c₃x³+c₄x⁵.

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This gives a table of x, y pairs.

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This finds a fit to the new data, of the form c₁+c₂sin (x)+c₃sin (2x).

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FindFit[data,form,{p₁,p₂,...},x]
	find a fit to form with parameters p_i

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[data]	numerical Fourier transform
InverseFourier[data]	inverse Fourier transform

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. "Fourier Transforms" gives more details.

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Numerical Data