In this article, we will teach you What is the difference between white and Gaussian noise?, What is white noise Gaussian white noise?, What is the difference between Gaussian noise and random noise?

## What is the difference between white and Gaussian noise?

White noise and Gaussian noise are distinct types of stochastic processes used to model random variations in signals or data:

White noise is characterized by a flat-power spectral density, meaning that it has equal power at all frequencies within a specified bandwidth.

In other words, each frequency component of white noise carries an equal amount of energy. It is a purely random signal with no correlation between its values at different times or frequencies. White noise is often used in signal processing and statistics as a reference or baseline to analyze the behavior of systems in the presence of random fluctuations.

### What is white noise Gaussian white noise?

Gaussian noise, on the other hand, refers to noise that follows a Gaussian or normal distribution.

This distribution is characterized by a bell-shaped curve with a mean of zero and a certain standard deviation. Gaussian noise is not necessarily flat across all frequencies like white noise; It may exhibit frequency-dependent characteristics.

However, in many practical applications, Gaussian noise is added to signals or data because it accurately models the random variability observed in natural and engineered systems due to its statistical properties.

White noise and Gaussian white noise are often used interchangeably to refer to both white (flat power spectral density) and Gaussian (normally distributed) noise. This means that each noise sample follows a Gaussian distribution with a constant average variance, and successive samples are statistically independent of each other.

Gaussian white noise is commonly used in simulations, experiments and theoretical models where random variability with these specific statistical properties is desired or assumed.

### What is the difference between Gaussian noise and random noise?

The difference between Gaussian noise and random noise lies in their underlying probability distributions and statistical properties:

Gaussian noise specifically follows a Gaussian distribution, meaning that its probability distribution function is characterized by a bell-shaped curve with specific mathematical properties such as zero mean and a variance that determines the spread or width of the noise.

curve. Gaussian noise is widely used because of the central limit theorem, which states that the sum of many independent random variables tends to follow a Gaussian distribution regardless of the original distributions of those variables.

Random noise, on the other hand, is a broader term that encompasses any form of unpredictable or random variation in signals or data. This does not imply a specific distribution like Gaussian noise does. Random noise can exhibit various statistical properties depending on its origin and characteristics.

It can include Gaussian noise, but it can also refer to other types of noise such as uniform noise, exponential noise or colored noise, each with their own distinct statistical properties and applications.

White noise and additive white Gaussian noise (AWGN) are related concepts commonly encountered in signal processing and communications:

White noise, as described previously, is a random signal with a flat power spectral density across all frequencies.

It represents random fluctuations that are equally distributed across the frequency spectrum, making it valuable for modeling and analyzing the behavior of systems under random disturbances.

AWGN, on the other hand, refers specifically to white noise that has been added to a signal during transmission or processing. It is characterized by a Gaussian distribution with zero mean and some variance, representing the additive nature of noise in communication channels or electronic systems.

AWGN is a standard model used in communication theory to simulate the effects of noise interference on signal quality, transmission efficiency, and error rates. By adding AWGN to signals, engineers can evaluate the performance of communications systems under realistic noise conditions and optimize system parameters to achieve reliable data transmission.

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