Ratio signal-to-noise

The signal-to-noise ratio (S/N) describes the uncertainty of an intensity measurement and provides a quantitative measure of a signal s quality by quantifying the ratio of the intensity of a signal relative to noise. 

Noise results from the electronics of an instrument, and thus noise is not only present between the signals but also on the signals. Consequently, intensity measurements are influenced by noise. Real and very numerous bacl ound signals of various origin, e.g., FAB or MALDI matrices, GC column bleed and impurities, can appear as if they were electronic noise, so-called chemical noise. In the strict sense, this should be distinct from electronic noise and should be reported as signal-to-background ratio (S/B) [31]. In practice, this can be difficult to do. 

Example A signal may be regarded to be clearly visible at S/N 10, a value often stated with detection limits. A mass spectrometer in good condition yields S/N 10 which means in turn that even isotopic peaks of low relative intensity can be reliably measured, provided there is no interference with background signals (Fig. 1.7). 

As stated earlier, the spectral width of the frequencies is determined by the rate at which the data are collected so in order to have a spectral width of WHz, the data must be sampled at 2WHz. In other words, to collect data over wider spectral widths, we must collect data more slowly. However, because the accuracy with which the frequencies are measured depends on the length of time spent in collecting data points in each FID, to obtain a high resolution spectrum we need to collect data points for a 

A serious problem associated with quadrature detection is that we rely on the cancellation of unwanted components from two signals that have been detected through different parts of the hardware. This cancellation works properly only if the signals from the two channels are exactly equal and their phases differ from each other by exactly 90°. Since this is practically impossible with absolute efficiency, some so-called image peaks occasionally appear in the center of the spectrum. How can you differentiate between genuine signals and image peaks that arise as artifacts of quadrature detection  

The relaxation rates of the individual nuclei can be either measured or estimated by comparison with other related molecules. If a molecule has a very slow-relaxing proton, then it may be convenient not to adjust the delay time with reference to that proton and to tolerate the resulting inaccuracy in its intensity but adjust it according to the average relaxation rates of the other protons. In 2D spectra, where 90° pulses are often used, the delay between pulses is typically adjusted to 37j or 4Ti (where T, is the spin-lattice relaxation time) to ensure no residual transverse magnetization from the previous pulse that could yield artifact signals. In ID proton NMR spectra, on the other hand, the tip angle 0 is usually kept at 30°-40°. 

What is signal-to-noise (S/N) ratio, and how can it be improved by acquiring a large number of FIDs  

In GC-MS, choosing one kind of measure over another is difficult because under the average oscillation level of the base line, the detected current corresponds primarily to ions that should be considered when determining the SNR. To be rigorous, 

FIGURE 5.1 Two ways of considering the signal (S and S ) and two ways of considering the noise (N and N ) for a chromatographic peak. 

A few portions of (metastable) ions dissociate in the analyzer. The resulting lighter daughter ions are ejected from the quadrupole. However, the neutrals thus generated continue more or less along the initial trajectory of the parent ion. Some of them may reach the detector. The impacts then recorded are correlated to the U and V values applied to the electrodes of the quadrupole and converted in a peak in the mass spectrum. In reality, these impacts are not correlated to the arrival of ions. 

The different GC-MS programs therefore do not measure the SNR in the same way. This concept becomes problematic only when one wants to compare the performances of different mass spectrometers on a specific analysis. During method development, it is only important for the user to determine this ratio in the same way at each optimization step of the method to establish the influences of all parameters on the SNR. Logically, an inaease in the SNR will generally translate as a decrease in the LOD values of the method. 

Numerous independent scans of a substance under the same conditions give numerous peaks with an average height S, The difference between the highest and lowest peak height is the noise N (Fig. 4-26). 

Having a constant amplification, the noise is independent of the signal height of two different peaks and, consequently, the SNR is directly proportional to the peak height according to 

If only a single scan is possible, the noise must be estimated, as shown in Sec. 4.5.3.I. If many spectra are available, it is better to take the arithmetic mean of the maxima. The plus-minus mean-error deviation is then a useful value for characterizing the noise. 

In one sense the signal is out of our control, it will depend entirely on what the true treatment difference is. Similarly there is little we can do about the patient-to-patient variability, although we can reduce this by having, for example, precise measures of outcome or a more homogeneous group of patients. The sample size however is very much under our control and common sense tells us that increasing this will provide a more reliable comparison and make it easier for us to detect treatment differences when they exist. 

in Chapter 8, we will discuss power and sample size and see how to choose sample size in order to meet our objectives. We will also see in Section 3.3 how, in many circumstances, the calculation of the p-value is directly based on the signal-to-noise ratio. 

The spectral information used in an analysis is encoded as an electrical signal from the spectrometer. In addition to desirable analytical information, such 

The rms (room mean square) noise is the square root of the average deviation of the signal, from the mean noise value, i.e. 

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. 

as well as affecting the appearance of a spectrum, influences the sensitivity of an analytical technique and for quantitative analysis the S/N ratio 

The spectral information used in an analysis is encoded as an electrical signal from the spectrometer. In addition to desirable analytical information, such signals contain an undesirable component termed noise which can interfere with the accurate extraction and interpretation of the required analytical data. 

There are numerous sources of noise that arise from instrumentation, but briefly the noise will comprise flicker noise, interference noise, and white noise. These classes of noise signals are characterized by their frequency distribution. Flicker noise is characterized by a frequency power spectrum that is more pronounced at low frequencies than at high frequencies. This is minimized in instrumentation by modulating the carrier signal and using a.c. detection and 

An FT-IR spectrometer is used optimally when detector noise exceeds all other noise sources and is independent of the signal level. This is the usual case for mid-infrared spectrometry but may not be so for shorter wavelengths. The sensitivity of mid-infrared detectors is commonly expressed in terms of the noise equivalent power (NEP) of the detector, which is the ratio of the root mean square (rms) noise voltage, P , in V Hz to the voltage responsivity, R, of the detector, in V W . It is effectively a measure of the optical power that gives a signal equal to the noise level thus, the smaller the NEP, the more sensitive is the detector. The NEP is proportional to the square of the detector area, Ao, with the constant of proportionality being known as the specific detectivity, D that is. 

To determine the signal-to-noise ratio (SNR) obtainable in any measurement, we must know not only the noise power but also the power of the signal. The spectral brightness i.e., the power flow per unit area per wavenumber per steradian at wavenumber v from a blackbody source at temperature T is given by the Planck equation  

Fourier Transform Infrared Spectrometry, Second Edition, by Peter R. Griffiths and James A. de Haseth Copyright 2007 John Wiley Sons, Inc. 

the SNR of a spectrum measured with a two-beam interferometer is given by 

When the solid angle of the beam through the interferometer is determined by the maximum wavenumber of interest in the spectmm, v ax, and the desired resolution, Av, the solid angle of the beam through the interferometer, fi/, is given by 

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For the case of noise presence (4, 0) the signal to noise ratio [Pg.125]

The detectability of critical defects with CT depends on the final image quality and the skill of the operator, see figure 2. The basic concepts of image quality are resolution, contrast, and noise. Image quality are generally described by the signal-to-noise ratio SNR), the modulation transfer function (MTF) and the noise power spectrum (NFS). SNR is the quotient of a signal and its variance, MTF describes the contrast as a function of spatial frequency and NFS in turn describes the noise power at various spatial frequencies [1, 3]. 

Sandborg, M. and G. Alm-Carlsson, Influence of x-ray energy spectrum, contrasting detail and detector on the signal-to-noise ratio (SNR) and detective quantum efficiency (DQE) in projection radiography. Phys. Med. Biol., 1992. 37(6) p. 1245-1263. 

In order to maximize the excitation, precautions have to be taken to avoid cross-talk between excitation and signal. Therefore differential probes are commonly used with a SQUID system Nevertheless, for the discussed defects the SQUID system has a lower excitation field by a factor of about 100 compared with the commereial system This we must keep in mind, when we compare measured signal to noise ratios. There is a potential to improve for small defeets, when eross-talk is managed very well. 

The combination of contrast and granularity produces a signal to noise ratio which allows for direct comparison of various films. The classes have minimum values for eontrast and maximum values for graininess. The ASTM classification system employs the same parameters as the European Standard EN584-1 and ISO CD (see Table 1). 

The obtained image has decreased signal to noise ratio and a very good quality which helps for interpretation. 

In fig. 2 an ideal profile across a pipe is simulated. The unsharpness of the exposure rounds the edges. To detect these edges normally a differentiation is used. Edges are extrema in the second derivative. But a twofold numerical differentiation reduces the signal to noise ratio (SNR) of experimental data considerably. To avoid this a special filter procedure is used as known from Computerised Tomography (CT) /4/. This filter based on Fast Fourier transforms (1 dimensional FFT s) calculates a function like a second derivative based on the first derivative of the profile P (r) ... 

The base of this estimation is the signal to noise ratio. The lowest signal to noise ratio S/N which is necessary as a minimum to discern a signal from noise is S/N = 2 1 (4). Referring to the limiting values for the granularity Oj, of the film system classes the smallest density difference AD of an defect which would just be visible should be at least two times greater than On. 

Flaws under this dimension will be under the critical signal-to-noise ratio of 2 1 for a given film system class and for instance for the borderline film of class C5 a flaw must be already -21 % deeper for perception than for the film of class C4. 

A corresponding composite probe with the same frequency and crystal size, however, detects the test flaw much better the echo has a 12 dB higher amplitude (see Fig. 4) and in addition, the noise level is much lower, resulting in an improved signal to noise ratio. This effect is especially observed at high sound attenuation. However, in materials with low attenuation or in case of shorter sound paths the standard probe yields a comparable good signal to noise ratio. 

The second example shows results obtained with an angle beam probe for transverse waves in coarse grained grey cast iron. Two commercially available probes are compared the composite design SWK 60-2 and the standard design SWB 60-2. The reflector in this example is a side-drilled hole of 5 mm diameter. The A-scans displayed below in Fig. 5 and 6 show that the composite probe has a higher sensitivity by 12 dB and that the signal to noise ratio is improved by more than 6 dB. 

Composite transducers will replace conventional transducers in applications where the improvement of test sensitivity, signal to noise ratio and axial resolution are mandatory. It must nevertheless also be noted in connection with the broadband feature that though composite probes have a specified nominal frequency, the echo signals allow no echo amplitude... 

As any conventional probe, acoustic beam pattern of ultrasound array probes can be characterized either in water tank with reflector tip, hydrophone receiver, or using steel blocks with side-drilled holes or spherical holes, etc. Nevertheless, in case of longitudinal waves probes, we prefer acoustic beam evaluation in water tank because of the great versatility of equipment. Also, the use of an hydrophone receiver, when it is possible, yields a great sensitivity and a large signal to noise ratio. 

Signal processing in mechanical impedance analysis (MIA) pulse flaw detectors by means of cross correlation function (CCF) is described. Calculations are carried out for two types of signals, used in operation with single contact and twin contact probes. It is shown that thi.s processing can increase the sensitivity and signal to noise ratio. 

Fig.5 shows the noise influence on CCF for both types of pulses and different b values. This influence is weak, especially for q(t) type of signals. For s(t) signals growth of 2-factor critically increases the signal to noise ratio. For q(t) signals this effect is much weaker and depends on quantity of periods in pulses. 

Correlative signal processing in MIA pulse flaw detectors is an effective way to increase the sensitivity and signal to noise ratio. Instruments with such processing system should be provided with a device for adjusting and sustaining initial phases of both current and reference pulses. 

Based upon a piezoelectric 1-3-composite material, air-bome ultrasonic probes for frequencies up to 2 MHz were developped. These probes are characterized by a bandwidth larger than 50 % as well as a signal-to-noise ratio higher than 100 dB. Applications are the thickness measurement of thin powder layers, the inspection of sandwich structures, the detection of surface near cracks in metals or ceramics by generation/reception of Rayleigh waves and the inspection of plates by Lamb waves. 

In order to obtain a high signal-to-noise ratio sufficient acoustical power is necessary. For special applications a programmable pulser (transmitter) is required in order to optimize the frequency spectrum. 

The VMOS-pulser with a rise time lower than 6 ns provides high axial resolution and high-frequency inspections above 10 MHz with an excellent signal-to-noise ratio. The output voltage amounts to about 228 V without load, and 194 V with a load of 75 H, A damping control from 75 Q to 360 Q matches the impedance to the transducer. 

In testing materials with high sound damping, the burst transmitter increases the signal-to-noise ratio to, typically, 12 dB. Typical applications honeycomb and concrete components, and air-coupled testing. 

Fig. 5, also an A-scan, shows the possibility of the echo-technique for concrete. The interface and backwall-echo of a 20 cm thick concrete specimen are displayed (RF-display). A HILL-SCAN 3041NF board and a broadband transducer (40mm element 0) are used which enable optimal pulse parameters in a range of 50 to 150 kHz. Remarkable for concrete inspections is the high signal-to-noise ratio of about 18 dB. 

The HILL-SCAN 30XX boards enable ultrasonic inspections from 50 kHz (concrete inspections) to 35 MHz (inspection of thin layers) with a signal to noise ratio up to 60 dB. The gain setting range of the receiver is 106 dB. High- and low pass filters in the receiver can be combined to band-passes, so that optimal A-scans are displayed. 

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