﻿ Noise Statistics details - EN

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# Noise Statistics details

The Noise Statistics calculates the Signal/Noise ratio and some other statistic values of one or more data objects available in the current data view. The Signal/Noise ratio can be calculated for a particular spectral region or the whole data range.

The Noise Statistics command is available in the Mathematics menu.

## Noise Calculation Algorithms

Some characteristic values are calculated for the noise statistics result:

### Mean Value

The mean value M calculates the mean of all intensities Si  in a user defined spectral range of interest. The following equation is applied:

Where

M: Mean intensity value

N: Number of data points in range

Si: Intensity values

### Peak-to-peak Deviation

The peak-to-peak deviation is calculated from a linear least squares fit among a spectral windows. Calculation considers the baseline respectively. The following equation is used:

Where

Dp-p: Peak-to-peak deviation (baseline corrected)

(Fcenter-Fwing .. Fcenter+Fwing): Specifies start and end point of the range of interest

Yi: Linear function determined from a linear least squares fit among data points.

Si: Intensity values

### Standard Deviation

The standard deviation for baseline-corrected data is calculated from the following equation:

Where

Dst: Standard deviation

N: Number of data points in range

Si: Intensity values

Yi: Linear function determined from a linear least squares fit among data points.

### Signal to Noise Ratio Peak-to-Peak

The signal to noise ratio peak-to-peak is calculated using the following equation:

Where

SNRp-p: Peak-to-peak Signal to Noise Ratio

M: Mean intensity value

Dp-p: Peak-to-peak deviation (baseline corrected)

### Signal to Noise Ratio Root Mean Square Error

The root mean square error (RMS) for the signal to noise ratio is calculated using the following equation:

Where

SNRRMS: Signal to Noise Ratio Root Mean Square Error

M: Mean intensity value

Dst: Standard deviation