Root-mean-square noise

The value should be that of single polymer chain elasticity caused by entropic contribution. At first glance, the force data fluctuated a great deal. However, this fluctuation was due to the thermal noise imposed on the cantilever. A simple estimation told us that the root-mean-square (RMS) noise in the force signal (AF-lS-b pN) for an extension length from 300 to 350 nm was almost comparable with the thermal noise, AF= -21.6 pN. 

Signal-to-noise ratio Ratio of signal intensity to the root-mean-square noise level. 

Because sensitivity depends on so many different experimental factors, NMR spectroscopists generally use the signal-to-noise ratio, SIN, as a figure of merit for sensitivity comparisons. For example, in a comparison between NMR probes or spectrometers from two vendors, the spectral SIN measured for a standard sample acquired with specified acquisition parameters and probe geometry would provide a direct indication of relative sensitivity. The SIN is calculated for an NMR experiment as the peak signal divided by the root mean square (RMS) noise, given by Equation 7.6, and is directly related to the performance of the radiofrequency coil [3,6]... 

Tests. Air is scanned in the absorbance mode for 10 min. peak-to-peak noise is recorded at 500 nm. The root mean square (RMS) noise is then calculated. The RMS noise measurement is a measure of the standard deviation of the background signals. Modem spectrophotometers are usually equipped with the noise estimation function. For older spectrophotometers, the RMS noise can be estimated by multiplying the highest peak-to-peak noise level by a factor of 0.7 (Figure 10.8). 

A more common measurement of noise, which requires a digitized signal and a computer, is the root-mean-square (rms) noise, defined as... 

A better measure of noise is the root-mean-square noise (Equation 20-14), which is —5 times less than the peak-to-peak noise. Therefore 2 times the peak to-peak noise level is —10 times the root-mean-square noise. The detection limit that is 2 times the peak-to-peak noise level is close to the limit of quantitation in Equation 5-6. The lesson is that you should define how you express a detection limit when you report one. 

It is important to specify detectors independent of column parameters and of sample size. One parameter that does this is minimum detectable level, MDL. It is the "level" of sample in the detector at the maximum of the peak, when the signal-to-noise ratio is two. The term detectability is sometimes used for MDL. Variations of this definition are sometimes given which require the signal-to-noise ratio to be either one, three, or five. The parameter is also defined sometimes in terms of root-mean square (rms) noise. Peak-to-peak noise can be taken as six times rms noise. 

Following the discussion in Bennett ( [Bennett, 1948]), we define the Signal to Noise Ratio (SNR) for a signal with zero mean and a quantization error with zero mean as follows first, we assume that the input is a sine wave. Next, we define the root mean square (RMS) value of the input as... 

The root mean square (r.m.s.) noise voltage AFj for unit bandwidth is A/j/ Y, where A/j is the r.m.s. noise current for unit bandwidth and Y is the admittance. Therefore... 

S/N = (maximum peak height)/(root-mean-square of noise) (10.2)... 

Statistical methods are the most popular techniques for EN analysis. The potential difference and coupling current signals are monitored with time. The signals are then treated as statistical fluctuations about a mean level. Amplitudes are calculated as the standard deviations root-mean-square (rms) of the variance according to (for the potential noise)... 

Thermal noise — originates from the thermal agitation of charge carriers (- electrons, -> ions, etc.) in a - resistor. It exists even in the absence of current flow and can be described by the formula (/thermal = (4kB TRAf)1/2. [/thermal is the average amplitude of this noise (also denoted [/rms (or Vrms), see also - root mean square), k is the -> Boltzmann constant, R is the resistance, and A/ is the bandwidth of measurement frequencies. 

Shot noise — originates from the movement of charge carriers when they cross n-p junctions or arrive at an electrode interface. It is much smaller than thermal noise and depends on the signal as follows C/shot = R(2IeA/) /2. [/shot is the -> root mean square amplitude... 

Flicker noise — is common to all solid-state devices and predominates in measurements at frequencies, / < 300 Hz. Although the physical origin of this noise is not well understood, it can be described by the following empirical equation [/fiicker = (KI2If)1/2, [/flicker is the - root mean square amplitude of this noise, K is a constant depending on factors such as resistor materials and geometry, and I is the DC current [i]. 

Is this a physically sensible number This depends on the original units of measurement and what the instrumental noise characteristics are. If it is known that the root mean square noise is about 0.05 units, then it seems sensible. If the noise level, however, is substantially lower, then not enough PCs have been calculated. In fact, most modem chromatographic instruments can determine peak intensities much more accurately than 0.05 AU, so this would suggest a second PC is required. Many statisticians do not like these approaches, but in most areas of instrumentally based measurements it is possible to measure noise levels. In psychology or economics we cannot easily consider performing experiments in the absence of signals. 

Average root-mean-square (RMS) noise level at high light flux... 

Spectrophotometric noise tests include measuring spectra of high- and low-reflectance (or transmittance) reference materials. Peak-to-peak noise and root-mean-square (RMS) noise levels are acceptable parameters for evaluation. The preferable measurement involves tabulating the RMS noise in successive 100-nm spectral segments. Instrument noise is usually evaluated as a function of wavelength by using a reference standard as the sample and the background reference. 

---