Signal and Noise Model. The received signal is assumed to follow the model. x ( t) = s ( t) + n ( t) where s (t) is the signal and n (t) is the noise. Without losing the generality, we assume that the signal power is equal to 1 watt and the noise power is determined accordingly based on the signal to noise ratio (SNR). Since the autocorrelation function of a wide-sense-stationary discrete-time random process is defined as R X ( k) = E [ X i X i + k], we have that the white-noise process has an autocorrelation function given by σ 2 δ [ k] where δ [ k] is the unit pulse (a.k.a. discrete-time impulse) function. Share. Improve this answer. a zero-mean Gaussian Process: v t ˘GP(0;k(t;t0)): (5) This formulation has a good deal of expressive power, as This flexibility suggests that GPs can accurately model noise for a wide variety of sensor configurations and perception algorithms. Furthermore, the GP noise model generalizes both the common independent Gaussian noise model and The modulated signal passes through an additive white Gaussian noise channel. The top receiver performs hard decision demodulation in conjunction with a Viterbi decoder that is set up to perform hard decision decoding. The second receiver has the demodulator configured to compute log-likelihood ratios (LLRs) that are then quantized using a 3 Compare: BACKGROUND NOISE, RUSTLE NOISE. Sound Example: Gaussian noise produced with about 4000 pulses/sec. Gaussian distribution showing the probability y of finding a deviation x from the mean (x = 0), according to the equation stated, where e is the base of natural logarithms, and s is the standard deviation. The probability of larger and The term "red noise" comes from the "white noise"/"white light" analogy; red noise is strong in longer wavelengths, similar to the red end of the visible spectrum. Strictly, Brownian motion has a Gaussian probability distribution, but "red noise" could apply to any signal with the 1/f 2 frequency spectrum. Power spectrum a squared white noise term as white noise. In this paper we show that under a suitable renormalization, integral powers of Gaussian white noise viewed as the limit of a band-limited Gaussian process with flat spectral density is indeed Gaussian white noise, a non-trivial fact given that non-linear transformations of Gaussian random An alrernative way to think about instance noise vs. label noise is via graphical models. The following three graphical models define joint distributions, parametrised by $\theta$. We used additive Gaussian white noise whose variance parameter $\sigma$ we annealed linearly during training. The figure below shows that the discriminator's Estimate the noise power if needed. If none is provided, the noise profile is estimated as the mean of the output of (2). Take the input image and remove the mean so that the image is centred at 0. Scale the output of (4) by (1 - noise) / (output of (2)). Add the mean back to (5). The scaling ensures the removal of the variation due to the noise. Yes, many DSP and statistics texts (as well as Wikipedia's definition of a discrete-time white noise process) and many people with much higher reputation than me on dsp.SE and stats.SE say that uncorrelatedness suffices for defining a white noise process, and in the case of white Gaussian noise it does because Gaussianity brings in the jointly pyvPc.