🐴 White Noise Vs Gaussian Noise

for Gaussian noise, the whole image is affected in the same way by the noise, for Poisson noise, the lighter parts are noisier than the dark parts, for impulse noise, only a few pixels are modified and they are replaced by black or white pixels. Fig. 74 Example of different types of noise (with almost the same power). # Fundamentally, the benefit of pink noise is that it tends to get softer and less abrasive as the pitch gets higher. The lower frequencies are louder, and the higher frequencies become easier on the ears. Pink noise shows up in many different places in nature, which makes it seem a bit more natural to most people's ears than white noise. What I mean by generating is sampling, I should have said that instead. I want to sample say $\hat{X}_{i}\sim WN(0,\sigma^2)$ and $\tilde{X}_{i}\sim IID(0,\sigma^2)$, where WN and IID denote White Noise and Independent and Identically Distributed (noise). In the Gaussian case these two overlap, but in other cases? Can we actually see from data For white noise, it's more complicated. The FFT of a chunk of white noise does NOT have constant spectrum, it's actually white noise as well (the real part and the imaginary part). It only becomes constant if you average every over a large enough number of chunks (or a long enough period of time) or if you apply some sort of spectral smoothing. Assuming both white noise, and salt and pepper, which filter should I apply 1st - Gaussian, or median? Median is nonlinear, thus order does matter. image-processing; opencv; python; Should I choose mean or median filter for gaussian noise. 2 Ideas to process challenging image. 11 median filter for color images. Lastly, What the information we glean-out of the model (intuitively) if we are informed about noise that besides being zero mean, white and Gaussian, it is circular symmetric complex as well? (I do know white noise has impulse auto-correlation but confused with circular-symmetric term). 1. I know the white noise is uncorrelated. So a perfectly white signal has an autocorrelation equal to an impulse at zero. This implies that the corresponding signal in the time domain is any function with no correlation whatsoever between the different samples. And I know that any colored noise can be thought of as filtered white noise, so Gaussian Noise. Thermal vibration of atoms. Depends on the standard deviation of the noise amplitude. White noise (thermal or Johnson-Nyquist noise) has a constant spectral density across all frequencies, which means that its energy is distributed uniformly across the frequency spectrum. It is characterized by a flat noise density plot. Now they call a generalized Gaussian stochastic process with expectation and covariance given by $(1)$ and $(2)$ a Gaussian white noise. Thus, the generalized derivative $W'$ of the generalized Brownian motion $W$ is a Gaussian white noise. Pink noise is characterized by a spectrum that rolls off inversely by frequency, or 1/frequency in strength. The greater the frequency, the less energy is present, such that each octave higher represents a halving of acoustic energy. Pink noise sounds more balanced to us because of the way we weight frequency content and sounds less loud than Consider the opposite case if the I and Q components of a Gaussian Noise process were dependent such as I = kQ, the resulting noise would stay on a fixed angle passing through the origin (such as staying on the 45° line if I = Q) rather than adding a random magnitude and phase to each sample. Ideally Lowpass-filtered White Gaussian Noise 1) Strong Sense White Noise: A process ǫt is strong sense white noise if ǫtis iid with mean 0 and finite variance σ2. 2) Weak Sense (or second order or wide sense) White Noise: ǫt is second order sta-tionary with E(ǫt) = 0 and Cov(ǫt,ǫs) = σ2 s= t 0 s6= t In this course: ǫt denotes white noise; σ2 de-notes variance of ǫt. Use 8wKT.

white noise vs gaussian noise