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In signal processing theory, Gaussian noise, named after Carl Friedrich Gauss, is a kind of signal noise that has a probability density function (pdf) equal to that of the normal distribution (which is also known as the Gaussian distribution). [1] [2] In other words, the values that the noise can take are Gaussian-distributed.
An example of a random vector that is Gaussian white noise in the weak but not in the strong sense is = [,] where is a normal random variable with zero mean, and is equal to + or to , with equal probability. These two variables are uncorrelated and individually normally distributed, but they are not jointly normally distributed and are not ...
Gaussian because it has a normal distribution in the time domain with an average time domain value of zero (Gaussian process). Wideband noise comes from many natural noise sources, such as the thermal vibrations of atoms in conductors (referred to as thermal noise or Johnson–Nyquist noise ), shot noise , black-body radiation from the earth ...
The regularization parameter plays a critical role in the denoising process. When =, there is no smoothing and the result is the same as minimizing the sum of squares.As , however, the total variation term plays an increasingly strong role, which forces the result to have smaller total variation, at the expense of being less like the input (noisy) signal.
Gaussian noise requires a higher level of added noise for full elimination of audible distortion than noise with rectangular or triangular distribution. Triangular distributed noise also minimizes noise modulation – audible changes in the volume level of residual noise behind quiet music that draw attention to the noise.
He conducted research on the S-transform by encompassing the characterization of its range through properties like analyticity and growth, with subsequent applications in white noise analysis extending the Gaussian L2-space. The research also featured examples of the generalized functions and the introduction of new distribution classes marked ...
In the simple version above, the signal and noise are fully uncorrelated, in which case + is the total power of the received signal and noise together. A generalization of the above equation for the case where the additive noise is not white (or that the / is not constant with frequency over the bandwidth) is obtained by treating the channel as many narrow, independent Gaussian ...
Thus, the concept of noise prediction for stationary Gaussian noise sources developed in [2] [6] can be naturally extended to the case where noise characteristics depend highly on local data patterns. [1] [10] [11] [12] By modeling the data-dependent noise as a finite-order Markov process, the optimum MLSE for channels with ISI has been derived ...