Smoothing

The signal to noise ratio (S/N) of a spectrum can be enhanced by smoothing (or filtering) technique. The noise contains high-frequency (compared to the spectral features) fluctuations of the signal. Smoothing applies a low-pass filter to the spectral data to remove the noise while having the informative spectral signals preserved.

Mnova ElViS incorporates some of the most used signal smoothing algorithms.

You can select a desired smoothing algorithm from the Method drop-down list: Nonlocal Means, Modified Median Wiener, Exponential Smoothing and Savitzky-Golay.

'Savitzky-Golay algorithm': This approach performs a least squares fit of a set of consecutive data points to a polynomial and takes the calculated central point of the fitted polynomial curve as the new smoothed data point.

Savitzky and Golay has shown that a set of integers (A-n, A-(n-1) …, An-1, An) could be derived and used as weighting coefficients to carry out the smoothing operation. The use of these weighting coefficients, known as convolution integers, turns out to be exactly equivalent to fitting the data to a polynomial, as just described, and it is computationally more effective and much faster. Therefore, the smoothed data point (yk)s by the Savitzky-Golay algorithm is given by the following equation:

Sets of convolution integers, instead of the smoothed signal, can be used to obtain directly, instead, its 1st, 2nd, …, mth order derivative, therefore the Savitzky-Golay algorithm is very useful for calculation of the derivatives of noisy signals consisting of discrete and equidistant points.