Gaussian noise

Consider a plant that is subjeet to a Gaussian sequenee of disturbanees w(kT) with disturbanee transition matrix Cd(r). Measurements z(/c+ )T eontain a Gaussian noise sequenee v(/c + )T as shown in Figure 9.6. 

Additive Gaussian Noise Charmed.17 An example of the use of these bounds will now be helpful. Consider a channel for which tire input is an arbitrary real number and the output is the sum of the input and an independent gaussian random variable of variance a3. Thus,... 

We now apply Eqs. (4-194) to (4-201) to the frequency limited, power limited, additive white gaussian noise channel. If N is the block length of a code in samples, then T = N/2W is the block length in time. Furthermore if is the available signal power and if N0 is the noise power per unit bandwidth, then the signal to noise ratio, A, is 8/N0W. Finally we let JRT> the rate in nats per second, be 2 WB. Substituting these relations into Eqs. (4-194) and (4-197), we get... 

Abstract Hilbert space, 426 Accuracy of computed root, 78 Acharga, R., 498,539,560 Additive Gaussian noise channel, 242 Adjoint spinor transformation under Lorentz transformation, 533 Admissible wave function, 552 Aitkin s method, 79 Akhiezer, A., 723 Algebra, Clifford, 520 Algebraic problem, 52 linear, 53... 

A remarkable properties of very noisy channel with Gaussian noise distribution is that the channel capacity can be increased by discarding samples in... 

Owing to the constraints, no direct solution exists and we must use iterative methods to obtain the solution. It is possible to use bound constrained version of optimization algorithms such as conjugate gradients or limited memory variable metric methods (Schwartz and Polak, 1997 Thiebaut, 2002) but multiplicative methods have also been derived to enforce non-negativity and deserve particular mention because they are widely used RLA (Richardson, 1972 Lucy, 1974) for Poissonian noise and ISRA (Daube-Witherspoon and Muehllehner, 1986) for Gaussian noise. 

Image Space Reconstruction Algorithm. ISRA (Daube-Witherspoon and MuehUehner, 1986) is a multiplicative and iterative method which yields the constrained maximum likelihood in the case of Gaussian noise. The ISRA solution is obtained using the recursion ... 

If the exact statistics of the noise is unknown, assuming stationary Gaussian noise is however more robust than Poissonian (Lane, 1996). 

Assuming Gaussian noise and if the calibration data is given by an image of a point-like source, the MAP criterion writes ... 

Transform) the content of a given column ( vector) can be mathematically modified in various ways, the result being deposited in the (N + 1) column. The available operators are addition of and multiplication with a constant, square and square root, reciprocal, log(w), Infn), 10 , exp(M), clipping of digits, adding Gaussian noise, normalization of the column, and transposition of the table. More complicated data work-up is best done in a spreadsheet and then imported. 

Since only 20 data records were collected from the system during the execution of the designed experiments conducted by Reece et al. (1989), we used their response surface models, deliberately contaminated with small Gaussian noise terms, to generate a total of 500 (x, z) pairs (assuming that the three variables, jCj, Xj, Xj, have independent and uniform... 

It can be shown [4] that the innovations of a correct filter model applied on data with Gaussian noise follows a Gaussian distribution with a mean value equal to zero and a standard deviation equal to the experimental error. A model error means that the design vector h in the measurement equation is not adequate. If, for instance, in the calibration example the model was quadratic, should be [1 c(j) c(j) ] instead of [1 c(j)]. In the MCA example h (/) is wrong if the absorptivities of some absorbing species are not included. Any error in the design vector appears by a non-zero mean for the innovation [4]. One also expects the sequence of the innovation to be random and uncorrelated. This can be checked by an investigation of the autocorrelation function (see Section 20.3) of the innovation. 

Gaussian noise has been added onto the structure factor amplitudes squared as computed from the L-alanine model density for each datum, the amount of noise added was proportional to the experimental esd for the corresponding intensity measurement ... 

Measurements for both state variables, A and T, and both input variables, Aq and To, were simulated at time steps of 2.5 s by adding Gaussian noise to the true values obtained through numerical integration of the dynamic equations. A measurement error with a standard deviation of 5% of the correspoding reference value was considered and the reconciliation of all measured variables (two states and two inputs) was carried out. 

Using the model, a set of base case data is generated by adding Gaussian noise to the calculated measurements, using the same variance as the physical measurement. 

Fig. 1 depicts a block diagram of blind watermark commnnication, where the attacker introduces additive white Gaussian noise (AWGN) V. The depicted scenario can be considered coimnnnication with side information about the host data at the encoder. ... 

The image data were formed by adding 4% (of peak image value) Gaussian noise to the signal image. Sampling was at one-half the Nyquist interval so as to permit superresolution of the central dip in the object. 

Fig. 2 Deconvolution of a single Gaussian peak, (a) Noise-free Gaussian peak, (b) Inverse filtering of the peak in (a) with another Gaussian function. The resulting peak is also Gaussian in form, (c) Peak in (a) with Gaussian noise of rms amplitude of the amplitude of the Gaussian peak superimposed.

Fig. 19 Interferogram of Fig. 13(a) with Gaussian noise of rms amplitude 0.1 added, (a) Cosine interferogram of unity amplitude with random noise of rms amplitude 0.1 superimposed. (b) Single spectral line with the oscillatory artifacts. 

Fig. 27 Finite interferogram of the four monochromatic sources of Fig. 26 with Gaussian noise of rms amplitude 0.1 superimposed and the resulting degraded spectral lines, (a) Interferogram of 30 data points, (b) Merged and distorted spectral lines.

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