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Algorithms |
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| Baseline Correction |
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| Baseline Correction - Simple Offset Correction |
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A constant Y value is subtracted from each point of the spectrum.
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Baseline Correction - 2-Point Baseline |
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Plots a connecting line through the two selected points, as shown in the graphic below, and subtracts it from the trace. The baseline is calculated using the standard linear equation:
y = Mx + B where
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 and 
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Baseline Correction, Multi-Point Baseline |
This method performs baseline leveling by connecting lines through the selected points and subtracting them from the trace, as shown in the graphic below.
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| Baseline Correction, Interactive Polynomial Baseline |
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Fits a cubic polynomial function to the baseline. The coefficients are calculated by deresolving the current baseline to four (4) points evenly spaced along the spectrum plus the point currently being adjusted. They are then calculated using the same algorithm as in Function Fit Baseline. |
| Baseline Correction, Function Fit Baseline |
This method fits a polynomial of 1st through 6th order (Y=A+Bx^2+CX^3...etc), exponential (Y=Ae^(BX)), logarithm (Y=A+B(ln(X))), or power function (Y=AX^B) to a series of user selected points, as shown in the graphic below. Uses a matrix inversion technique to solve a linear regression equation for the function coefficients. For the exp, log, and power functions, a linear fit is used. This is done by first linearizing the chosen equation using a natural log transformation.
To find the coefficients of the fitted function |
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Let  |
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where:
N = the number of coefficients = the degree of the polynomial + 1
m = the number of data points (peaks) being fitted
xi = the X coordinates of the selected points
yi = the Y values of the selected points
(in this case, the shifts in the X coordinates at the selected peaks)
ai = the coefficients of the fitted function
The coefficients are then given by: 
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Computationally, the terms are given by the following:
 
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so that 
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Baseline Correction, GIFTS (Auto-Leveling Method) |
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This method removes the baseline slope and offset by an iterative fitting process which discards points above a threshold and fits the remaining points with a straight line. The algorithm used is commonly employed in the industry for pre-correcting data in IR spectral searching. A least squares line is fit through all the points in the trace. The number of points above and below the line is counted. If there are fewer points above the line than below, they are considered peaks and discarded. The process is then repeated until the number of points above the line is less than or equal to those below the line. The calculated line is then used as the baseline and subtracted from the trace.
NOTE: This algorithm does not work well with data that includes both positive and negative going peaks, and baselines that are severely skewed. |
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