What are the two representations of Gaussian white noise?

Gaussian white noise refers to a class of noise in which the probability density function of the noise satisfies the statistical characteristics of normal distribution, and its power spectral density function is constant. In the theoretical analysis of communication systems, especially in the analysis and calculation of the anti-noise performance of the system, it is often assumed that the channel noise in the system (i.e., the above-mentioned undulating noise) is Gaussian white noise. Here's why:

1.Gaussian white noise can be expressed by specific mathematical expressions, which is convenient for derivation, analysis and operation.

2.Gaussian white noise does reflect the additive noise in the actual channel and is more realistically represented. the characteristics of the channel noise.

Gaussian white noise: If the amplitude distribution of a noise obeys the Gaussian distribution, and its power spectral density is uniformly distributed, it is called Gaussian white noise.

Thermal noise and shot noise are Gaussian white noise.

The so-called Gaussian white noise in Gaussian means that the probability distribution is a normal function, while white noise means that its second-order moment is uncorrelated, and the first-order moment is constant, which refers to the correlation of successive signals in time. This is a question of examining two different aspects of a signal.

Gaussian white noise refers to the fact that the signal contains all the frequency components from negative infinity to positive infinity, and each frequency component has the same weight in the signal. White light contains light of various frequency components, from which the name white noise is derived. Its amplitude at any moment in time is random, but satisfies the Gaussian distribution function as a whole.

For the knowledge of time-varying signals, please refer to "Signals and Systems", and for Gaussian white noise, please refer to "Principles of Communication".

The one-dimensional probability density function of the bilateral power spectral density I n0 2, the mean value of zero stationary Gaussian white noise is to be honest, this is more difficult to know, not many people understand it, and people don't want to tell you.

White noise, that is, the spectrum is a constant; That is, its covariance function is not 0 when delay=0, and the value is zero when delay is not equal to 0; In other words, the sample points are not correlated with each other. Therefore, "white" and "not white" have nothing to do with distribution. When the sampling values are randomly obtained from the Gaussian distribution, the stochastic process composed of the sampling points is "Gaussian white noise". In the same way, when the sample values are randomly obtained from a uniform distribution, the random process composed of the sampling points is called "uniform white noise".

So, is there "non-white Gaussian" noise? The answer is yes, it's "Gaussian color noise".

The distribution of this noise is Gaussian, but its spectrum is not a constant, or in other words, the Gaussian signal is not sampled randomly, but according to a certain law.

White noise should be an autocorrelation function that is not 0 when delay=0 and zero when delay is not equal to 0. If you want to talk about the covariance function, then you should add a condition: zero mean.

Follow-up question: If the two signals are s1=1, s2=-1, and the noise variance is 2=4, and the cost is c00=c11=0, c01=1, and c10=2, the optimization criterion for the decision is determined, and then two likelihood functions are obtained. How do you do this?

Gaussian noise means that the probability density function of the noise obeys the Gaussian distribution, and white noise means that any two sampled samples of the noise are not correlated with each other, and the two describe different angles.

Strictly speaking, white noise is only an idealized model, because the power spectral density of the actual noise cannot have an infinitely wide bandwidth, otherwise its average power would be infinite and physically unrealizable. However, white noise.

It is more convenient in mathematical processing, so it is a powerful tool for system analysis. In general, as long as a noisy process has a spectral width that is much larger than the bandwidth of the system on which it operates, and its spectral density is basic in that bandwidth.

can be considered as a constant, and it can be treated as white noise. For example, thermal noise and scattering noise have uniform power spectral densities over a wide frequency range and can generally be considered white noise.

How to make standard white noise with MATLAB:

To generate random numbers of Gaussian distributions, use randn();

y=randn(1,2500);

y=y/std(y);

y=y-mean(y);

a=;b=sqrt(;

y=a+b*y;%a is the expectation and b is the standard deviation.

2.WGN: Produces white Gaussian noise: y = wgn(m,n,p) A matrix that produces a white Gaussian noise in n rows of m, where p specifies the intensity of the output noise in dbw.

3.To noise a given signal, use awgn().