Instrument Function Filter

Applies a predefined operation (either global average, or an integral of the product of the data with a mathematical function) to the input data for each pixel.

Category	Math
Node
Parameters	FunctionType: what function to apply. This may either be GlobalAverage to calculate a global average over all channels of the input data, or a function type for which a product integral of the data will be calculated (see below) Wavelength: for product integrals this defines the center of the prodcut function FWHM: for product integrals this defines the width of the product function.
Inputs	Input: the input data
Outputs	Output: the output data, containing just a single channel with the result

Effect of the Filter

When FunctionType is GlobalAverage the filter will calculate the average of the input data over all channels.

When FunctionType is something else, a weighted average / integral will be performed with one of the following predefined functions. The predefined function will be centered around the Wavelength parameter and have a width as specified by the FWHM parameter. In the following formulas the Wavelength parameter will be referred to as $x_0$ , the Width parameter as $\mu$ .

FunctionType = Square: the function will be given by a square symmetrical to $x_0$ with width $\mu$ . If $\theta(x)$ is the Heaviside step function, then the square function may be written as $f(x) = \theta(\mu/2 + (x - x_0)) \theta(\mu/2 - (x - x_0))$ .

FunctionType = Triangle: the function will be given by a triangle that connects the points $(x_0-\mu/2, 0)$ , $(0, 1)$ , and $(x_0+\mu/2, 0)$ (and is 0 outside of the interval $[x_0 - \mu/2, x_0 + \mu/2]$ ).

FunctionType = Gauss: the function will be given by the formula $f(x) = \mathrm{exp}(- (2 (x - x_0) / \mu)^2 / 2)$ .

FunctionType = Sinc: the function will be given by the formula $f(x) = \mathrm{sinc}((x - x_0) / \mu)$ .

The result of the filter will always be a single channel per pixel containing the result of the integral (or the average).