Where n is the polynomial order, and are fitted coefficients. Contrarily, a concave function has a decreasing first derivative making it bend. The polynomial value at position x can be calculated as: points on the graph, the line segment that connects these two points. When smooth option is chosen in differentiate, and X data is evenly spaced, Savitzky-Golay method will be used to calculate the derivatives.įirst perform a polynomial regression on the data points in the moving window. The derivative function applied to discrete data points can therefore be written: In practice, Origin treats discrete data by the transform of the centered difference formula, and calculates the derivative at point by taking the average of the slopes between the point and its two closest neighbors. While the is small enough, we can use a centered difference formula to approximate the derivative: The derivative of a function is defined as: Specify whether to plot the derivative curve. Set the window size used in the Savitzky-Golay smoothing.įor help with the range controls, see: Output Results
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