Signal-Averaging

The process of signal averaging is conducted by repetitively scanning and co-adding individual spectra. Assuming the noise is randomly distributed, then 

To consider the effect of signal averaging on the noise level we must refer to the propagation of errors. The variance associated with the sum of independent errors is equal to the sum of their variances, i.e. 

Since we can equate rms noise with standard deviation then, 

Thus the average magnitude of random noise increases at a rate proportional to the square root of the number of scans. 

For signal averaging to be effective, each scan must start at the same place in the spectrum otherwise analytical signals and useful information will also cancel and be removed. The technique is widely used but is most common in fast scanning spectrometers, particularly Fourier transform instruments such as NMR and IR. Co-adding one hundred scans is common in infrared 

000 scans and aim to achieve a 100-fold improvement in signal-to-noise ratio may be unacceptable. In addition, computer memory constraints on storing the accumulated spectra may limit the maximum number of scans permitted. 

The main advantage of rapid scanning instruments is the ability to increase the signal-to-noise ratio (SNR) by signal averaging, which leads to an increase of signal-to-noise proportional to the square root of the time. It follows that in a rapid-scan interferometer the SNR is related to the number of scans by the following relationship  

JI Consider a typical FT-IR spectrometer which scans from 4000 to 400cm i at a resolution of 1 cm . This has an advantage over the equivalent dispersive spectrometer in that all of the information is measured at the same time, rather than by recording the information concerning the resolution intervals (lcm ) which falls on the exit slit sequentially. If it is assumed that the noise is independent of the signal, then the 3600 cm i resolution intervals are equivalent to 3600 separate scans by the FT-IR spectrometer. What then is the improvement in the SNR  

JJ Suppose we scanned in one second and signal averaged by repeat scanning 3600 times. What now is the further improvement in the SNR  

NMR experiments usually pertain to long (many hours) recording of the radiowave radiation coming from a Kquid specimen. Therefore, we obtain a static (time-averaged) record, which involves various kinds of averaging  

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Effect of signal averaging on a spectrum s signal-to-noise ratio (a) spectrum for a single scan ... 

It is essential, however, to follow a r rous experimental protocol for such applications. To maintain the quantitadve character of NMR spectroscopy, the reped-tion rate of signal averaging experiments has to be at least five times the longest spin-latdce relaxadon dme present in the sample. This waiting period is necessary to ensure that the magnetizadon is probed in a reproducible state, corresponding to thermodynamic equilibrium. 

Z. Fiu and J. B. Phillips, Farge-volume sample introduction into narrow-hore gas chromatography columns using thermal desorption modulation and signal averaging , /. Microcolumn Sep. 2 33-40 (1990). 

Averaging All machine-trains are subject to random, non-recurring vibration as well as periodic vibration. Therefore, it is advisable to acquire several sets of data and average them to eliminate the spurious signals. Averaging also improves the repeatability of the data since only the continuous signals are retained. 

In some ways, it s surprising that carbon NMR is even possible. After all, 12Q the most abundant carbon isotope, has no nuclear spin and can t be seen b> NMR. Carbon-13 is the only naturally occurring carbon isotope with a nucleai spin, but its natural abundance is only 1.1%. Thus, only about 1 of ever) 100 carbons in an organic sample is observable by NMR. The problem of low abundance has been overcome, however, by the use of signal averaging anc Fourier-transfonn NMR (FT-NMR). Signal averaging increases instrument sensitivity, and FT-NMR increases instrument speed. 

Another technique for improving the signal-to-noise ratio is to repeat scans over a frequency interval and signal averaging with a computer. In general, the signal-to-noise ratio is enhanced by the square root of the... 

J/cm2. As previously reported (1), excitation at 532 nm resulted in a shorter lifetime (86 4 microseconds) even at the lowest fluence used (0.1 J/cm2), where, with extensive signal averaging, a final signal-to-noise ratio of about 20 was obtained. As noted above the observed fluorescence decays at 532 nm became increasing non-exponential with increasing laser fluence. 

The "add-to-memory" signal averaging method currently available to us distorts fluorescence intensity versus time plots when the fluorescence intensity is a non-linear function of incident laser energy and the laser energy varies from shot to shot. For this reason we have not attempted detailed kinetic modelling of the observed fluorescence intensity decay curves recorded at high 532 nm laser fluence. 

The quality of data recorded from weak, high-mass-ion beams can usually be improved by the use of signal averaging. The computer software necessary is now available from the mass spectrometer manufacturers. Although signal averaging has not yet been applied to high-mass-carbohy-... 

X 10- torr. The magnetic field strength was 1.16 T and 10 scans were signal averaged. 

Figure 5. X-ray photoelectron survey spectrum (a) of an o-phenylenedlamlne derlvatlzed glassy carbon surface. High resolution C Is and N Is spectra of a derlvatlzed surface (b) and surface which was derlvatlzed following reduction with lilAlH to destroy surface o-qulnone functional groups (c). The spectrum were signal averaged for 90 min (a) and 20 min (b and c) and smoothed prior to display.

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