Dear Pranjali,

The calculations of the mean (signal) and standard deviation (noise) for multiple measurements at each wavenumber can be done in Matlab or Excel or without any of those. In power terms, you will need to calculate a square of that ratio.

The S/N definitions can vary depending on the expected type of signal. Some basics can be found at the attached link.-Slava

http://infohost.nmt.edu/~jaltig/Noise.pdf

 Most FTIR spectrometers have the facility for averaging technique.  The more the number of averages, the S/N ratio is improved. Modern electronics does this automatically and gives you a smooth spectra, that can be collected at the highest resolution, ( with highest no. of averages), and the inbuilt computer display the result directly. 

If you want to do this you have to collect all the raw signals collected straight from the transducer inside, and can figure out the S/N ratio. How to do this you have to consult the FTIR instrument designers.

IN case you the raw data, figure out the Signal intensity (occurring at the peaks) as they are strong enough, and the random noise variation in the background.

Collect data with different averaging cycles (as they correspond to varying S/N ratio 

In this way you will know how the S/N ratio is really affecting the refinement in your data. (You can do this in the time domain mode, or the frequency domain mode.

K. Sreenivas

My advice on the noise measurements originated from common sense and personal experience. Frankly, I never looked how to do this "in theory".

That is, two consecutive measurements without the sample and taking a "ratio" of these two is the simplest possible way to see the noise distribution. As you will notice, this distribution will be very different when measured with vs. without sample, because the IR flux will be much lower under the strong lines, and therefore the noise under those will be much higher. 

Raman, unlike the (absorbance) FTIR, is more like "fluorescence". Therefore, taking two consecutive  RAMAN signals, and "rationing" them should show the noise in a similar way. However, I have not done too much Raman myself, and somebody with more experience might come up with a simpler way.  

A significant issue is that of the Fellgett's advantage at the signal-to-noise ratio. The following references may certainly help:

A.G. Marshall, "Advantages of Transform Methods in Chemistry", in: Alan G. Marshall (Ed.), "Fourier, Hadamard, and Hilbert Transforms in Chemistry", Plenum Press / Springer Science, 1982, pp. 1-43.

J.A. de Haseth, "Fourier Transform Infrared Spectrometry", Ibidem, pp. 387-420.

W.D. Perkins, "Fourier Transform Infrared Spectroscopy ─ Part II. Advantages of FT-IR", J. Chem. Educ., 64(11) 1987, A269-A271.

http://link.springer.com/chapter/10.1007/978-1-4899-0336-5_1

http://link.springer.com/chapter/10.1007/978-1-4899-0336-5_13

http://pubs.acs.org/doi/abs/10.1021/ed064pA269

Mr./Miss/Mrs Priyadarshini,

Via Eqs. 1 and 2 (attachment)

S/N is the signal-to-noise ratio, Signal is the average signal, and Noise rms is the root-mean-square value of the noise. Since the root-mean-square value of a quantity is associated with the standard deviation of the quantity, the signal-to-ratio can be considered to be the reciprocal of the relative standard deviation of the measurement equal to X¯/S, where S is the standard deviation of a series of measurements and X¯ is the average value.

If the output of an instrument is steady and in a digital format, the signal-to-ratio can be estimated

conveniently by collecting a number of observations of the signal. From this sample of data, the average value can be computed by summing the observations and dividing by n, the number of samples collected. An estimate of the standard deviation can then be calculated from

S=∑(Xi−X¯)2n−1

where s is an estimate of the standard deviation, Xi is an individual observation, and X¯ is the average of the observations.

S/N= SIGNAL/NOISE RMS