RMS noise

The rms noise is measured in a noise bandwidth, The D is called D star lambda when the spectral band is limited to a given interval, and D blackbody when the total blackbody incident power density is used in the calculation. 

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. 

We can measure the peak-to-peak noise, Np p, rather easily and calculate the equivalent in rms noise. 

Detection limit is the minimum amount of signal that can be observed with some certainty that there is a signal at all. This requires that the signal be at least three times the rms noise of the experiment. 

The figure below represents the noise of a spectrometer detector. Estimate the peak-to-peak noise, and the rms noise of this detector. If an analyte produces a signal of 6.3 pA, will it be above or below the limit of detection ... 

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]... 

It is assumed that the noise voltage n(t) is the result of a real stationary process (Davenport and Root, 1958) with zero mean. Because it can be shown that the spectral density function S(f) is the Fourier transform of the autocorrelation function of the noise, it follows that the rms noise is given by... 

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). 

Acceptance. The RMS noise should typically be less than 0.001 AU. 

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

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. 

It is evidently insufficient to consider only the response of a detector when analysing its usefulness for a particular application. It is generally necessary to analyse both intrinsic and extrinsic noise signals and compare them with the response. The result of this comparison can be expressed in many different ways. One of the most useful is the noise-equivalent power nep which is the power of an rms signal input (in watts) required to give a response equal to the total rms noise voltage AVN. Then ... 

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. 

This equation should be recognized as equating rms noise with the standard deviation of the noise signal, ct. S/N can, therefore, be defined as x/tr. 

Since we can equate rms noise with standard deviation then,... 

Regression coefficients, partial, 172 standardized, 168 Regression, linear, 156 multivariate, 171 polynomial, 163 through origin, 162 Residuals, 13 Residuals analysis, 159 Ridge regression, 203 RMS noise, 31 Roots, characteristic, 73... 

SIT. ISIT. Under the definition of dynamic range as the ratio of the largest readable signal to the rms noise of the detection system, there are actually at least four kinds of dynamic range values. We will confine our discussion to the following three types of dynamic range. 

For a numerical description of the voltage or charge-noise performance of an electronic circuit, two values are often used the signal-to-noise ratio (SNR) and the dynamic range (DR). SNR is defined by comparing an actual signal level V with its rms noise AV, according to... 

DR compares the maximum signal level AVmax with the minimum rms noise level (AVmin) in an image sensor typically obtained in the dark... 

---