Signal and noise

Interference from external sources due to inductive and capacitive coupling 

Heavy electrical equipment can cause interference through the creation of multiple earths where there are leakages to earth at different points of the measuring device circuit. These earth points will be at different potentials due to the existence of the ground current which produces common and series mode interference voltages in the measurement circuit. 

Clearly, such interference can be reduced by increasing the distance between the source and the measurement circuit—mutual inductance and capacitance both being inversely proportional to the distance. Inductive coupling can also be much reduced by the use of twisted pair cable (Fig. 6.65). If adjacent loops in the circuit have the same area (e.g. loops 1 and 2) and are coupled with the same magnetic field, then the induced voltages between points A and B and between B and C will cancel each other out, and this will be repeated along the whole section of twisted pairs. 

Capacitive coupling can be suppressed by enclosing the entire measurement circuit within an earthed metal screen which provides a low impedance path to earth for the interfering currents. This is called electrostatic screening. 

A/D conversion is of increasing importance as, in many instances, the analog outputs of various measuring elements are now frequently connected to microcom- 

Instrumental analysis uses electronic equipment to provide chemical information about the sample. Older instruments used vacuum tubes and output devices like strip chart recorders, while modem instmments use semiconductor technology and computers to control the 

All instruments measure some chemical or physical characteristic of the sample, such as how much light is absorbed by the sample at a given wavelength, the mass-to-charge ratio of an ion produced from the sample, or the change in conductivity of a wire as the sample passes over it. A detector of some type makes the measurement and the detector response is converted to an electrical 

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Information of the energy imparted to the entrance screen is then transferred through a number of conversions in the detector chain, which introduce pixel-to-pixel correlation, before it is stored as digital data. This correlation has to be considered to be able to predict absolute signal and noise levels in the stored, data the noise would otherwise be overestimated. 

Fig. 13. Expected signal and noise levels for RE-TM alloys and Pt/Co multilayers (schematic). The total noise entering the SNR is the sum of the system noise, disk noise, and write noise. The system noise is electronic noise and photon shot noise and is comparable for disks with the same reflectivity.

His solution required that both the signal and noise be modelled as random proeess with known statistieal properties. 

W. B. Davenport, Jr., and W. L. Root, An Introduction to the Theory of Random Signals and Noise, McGraw-Hill Book Co., New York, 1958 P. M. Woodward, Probability and Information Theory with Applications to Radar, Pergamon Press, New York, 1957. 

Davenport and Boot, Random Signals and Noise, Chapter 6, McGraw-Hill, New York, 1968. 

The phase spectrum 0(n) is defined as 0(n) = arctan(A(n)/B(n)). One can prove that for a symmetrical peak the ratio of the real and imaginary coefficients is constant, which means that all cosine and sine functions are in phase. It is important to note that the Fourier coefficients A(n) and B(n) can be regenerated from the power spectrum P(n) using the phase information. Phase information can be applied to distinguish frequencies corresponding to the signal and noise, because the phases of the noise frequencies randomly oscillate. 

The applicability of these techniques depends on the type and form of the power spectra of both signal and noise. The only method that can be universally applied, is signal averaging. If the signal function is measured n times, the S/N ratio increases by Jn. 

Signal and noise as a function of working electrode surface area... 

Describe two ways to distinguish between an analytical signal and noise in the output of an instrument. 

Pierce, J.R. An Introduction to Information Theory, Symbols, Signals and Noise, Dover Publications, New York, 1980. 

The connection between noise in the time and in the frequency domain is given by the linearity property of the Fourier transform (see, e.g., Ref. 31). Let s(t) and n(t) be the signal and noise in the time domain and S(a>) and N((u) their corresponding Fourier transforms, then... 

Davenport, W.B., Root, W. An Introduction to the Theory of Random Signals and Noise. New York McGraw Hill Book Comp. 1958. 

The sources of signal and noise in virus diffraction data... 

Figure 5.17 An illustration of signal and noise. Detection limit is defined as the concentration that produces a signal that is double the noise level. 

Nevertheless, certain types of prior knowledge can be introduced within the context of a linear method. Probabilities, signal and noise statistics, power spectra, and the like may be incorporated. Often this type of prior knowledge is difficult to obtain. In any case, it rarely exerts an influence nearly so profound as that of simple bounds on the amplitude of the solution. If the observing spread function obliterates all frequencies beyond the cutoff Q, they are forever lost to the linear restoration methods. No linear filter s... 

All an illusion, you say That was a false awakening that didn t really occur. You have no objective evidence of it. Rubbish I reply. You are again forced back to the wall of absurdity. I know I (sometimes) have false awakenings (from REM) and I know what they are like, just as I know I sometimes have confusional, confabulatory awakenings (from NREM) and I know what they are like. These problematical exceptions must be acknowledged and they must be explained, but they must not be allowed to confound signal and noise (or baby and bath water). ... 

FIDs in general are composed of NMR signals and noise. The decay of the NMR... 

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