MPFXExpConvExpPeak

MPFXExpConvExpPeak (cw, yw, xw)

The MPFXExpConvExpPeak function implements a single peak with no Y offset in the format of an all-at-once fitting function. The peak shape is that of an exponential convolved with another exponential.

MPFXExpConvExpPeak is similar to the MPFXEMGPeak, but it has a sharp onset. It fills the wave yw with peak values as if a simple wave assignment was executed.

Parameters

cw	Coefficient wave. The Gaussian peak shape is defined by the coefficients as follows:
	cw[0]: Peak location. cw[1]: Peak height. cw[2]: Inverse of the decay constant of one exponential. cw[3]: Inverse of the decay constant of the other exponential.
	cw must be a double precision wave.
yw	Y wave into which values are stored.
	yw may be either double precision or single precision.
xw	X wave containing the X values at which the peak function is to be evaluated.
	xw may be either double precision or single precision.

Details

The following equations and discussion use these definitions:

c0 = cw[0], c1 = cw[1], c2 = cw[2], c3 = cw[3]

The peak location given by c0 is not the actual peak location; it is simply a parameter that offsets the peak in the X direction. The actual location is given by

$$\displaystyle l o c=\frac{\ln \left(\frac{c 2}{c 3}\right)}{c 2-c 3}+c 0$$

The actual peak height is given by

$$\displaystyle h=\frac{c 1 \cdot c 2\left\{\left(\frac{c 2}{c 3}\right)^{-\frac{c 2}{c 2-c 3}}-\left(\frac{c 2}{c 3}\right)^{-\frac{c 3}{c 2-c 3}}\right\}}{c 3-c 2}$$

The peak area is given by c1/c3.

We are not aware of an analytic expression for the full width at half maximum (FWHM).

This function is primarily intended to support the Multipeak Fitting package.

To use MPFXExpConvExpPeak as a fitting function, wrap it in an all-at-once user-defined fitting function:

Function FitVoigtPeak(Wave cw, Wave yw, Wave xw) : FitFunc
	Variable dummy = MPFXExpConvExpPeak(cw, yw, xw)
End

The assignment to "dummy" is required because you must explicitly do something with the return value of a built-in function.

If the waves do not satisfy the number type requirements, the function returns NaN. A successful invocation returns zero.

See Also

All-At-Once Fitting Functions