Signal weighting

A summation operator of input signals, weighted by the respective synapses of the neuron. 

Considering for example the simultaneous effects of a T filter from partial saturation when using short recycle delays, o, and the signal attenuation by T2 relaxation during a Hahn echo with echo time t, a signal weight is introduced by which the acquired signal (Equation 5.13) needs to be multiplied with,... 

According to some remarks concerning the physical interaction between the incident ultrasonic wavelet and the defects [4-6], we consider that an Ascan signal, may be described as a weighted sum of few delayed and phase-shifted replicas of the ultrasonic incident wavelet j(r). We can express this mathematically as ... 

In all spent researches the received ratio signal / noise and sensitivity for revealed defects, distribution of material density and the weights of high density components (tungsten, lead, uranium) are well agreed with results of alternate physics-chemical methods of analyses... 

Figure Bl.14.13. Derivation of the droplet size distribution in a cream layer of a decane/water emulsion from PGSE data. The inset shows the signal attenuation as a fiinction of the gradient strength for diflfiision weighting recorded at each position (top trace = bottom of cream). A Stokes-based velocity model (solid lines) was fitted to the experimental data (solid circles). The curious horizontal trace in the centre of the plot is due to partial volume filling at the water/cream interface. The droplet size distribution of the emulsion was calculated as a fiinction of height from these NMR data. The most intense narrowest distribution occurs at the base of the cream and the curves proceed logically up tlirough the cream in steps of 0.041 cm. It is concluded from these data that the biggest droplets are found at the top and the smallest at the bottom of tlie cream.

A simple, non-selective pulse starts the experiment. This rotates the equilibrium z magnetization onto the v axis. Note that neither the equilibrium state nor the effect of the pulse depend on the dynamics or the details of the spin Hamiltonian (chemical shifts and coupling constants). The equilibrium density matrix is proportional to F. After the pulse the density matrix is therefore given by and it will evolve as in equation (B2.4.27). If (B2.4.28) is substituted into (B2.4.30), the NMR signal as a fimction of time t, is given by (B2.4.32). In this equation there is a distinction between the sum of the operators weighted by the equilibrium populations, F, from the unweighted sum, 7. The detector sees each spin (but not each coherence ) equally well. 

Figure 9-13. Artificial neuron the signals x, are weighted (with weights IV,) and summed to produce a net signal Net. This net signal is then modified by a transfer function and sent as an output to other neurons,...

Analytical chemists make a distinction between calibration and standardization. Calibration ensures that the equipment or instrument used to measure the signal is operating correctly by using a standard known to produce an exact signal. Balances, for example, are calibrated using a standard weight whose mass can be traced to the internationally accepted platinum-iridium prototype kilogram. 

Once again, as you work through this example, remember that x represents the concentration of analyte in the standards (Cs), and y corresponds to the average signal (Smeas)- We begin by setting up a table to aid in the calculation of the weighting factor. ... 

Weighted normal calibration curve for the data in Example 5.13. The lines through the data points show the standard deviation of the signal for the standards. These lines have been scaled by a factor of 50 so that they can be seen on the same scale as the calibration curve. 

To ensure that S eas is determined accurately, we calibrate the equipment or instrument used to obtain the signal. Balances are calibrated using standard weights. When necessary, we can also correct for the buoyancy of air. Volumetric glassware can be calibrated by measuring the mass of water contained or delivered and using the density of water to calculate the true volume. Most instruments have calibration standards suggested by the manufacturer. 

In an indirect volatilization gravimetric analysis, the change in the sample s weight is proportional to the amount of analyte. Note that in the following example it is not necessary to apply the conservation of mass to relate the analytical signal to the analyte. 

The purity of ferrous ammonium sulfate is determined by a redox titration with K2Gt207, using the weight of the reagents as the signal in place of volume. 

The use of weight instead of volume as a signal for titrimetry is reviewed in the following paper. 

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