Gaussian noise is a statistical noise having a probability density function equal to that of the normal distribution, often used in signal processing to simulate real-world random variations. It is characterized by its mean and variance, and is commonly assumed in many algorithms due to the central limit theorem, which suggests that the sum of many independent random variables tends toward a Gaussian distribution.

Gaussian Noise

Gaussian noise

Statistical noise refers to the random variability or 'error' in data that cannot be attributed to any specific cause and can obscure the true underlying patterns or signals. It is crucial to account for statistical noise in data analysis to ensure accurate interpretation and to avoid misleading conclusions.

statistical noise

A Probability Density Function (PDF) is a function that describes the likelihood of a continuous random variable taking on a particular value, where the area under the curve represents the probability of the variable falling within a given range. The total area under the PDF curve equals one, ensuring that it accounts for all possible outcomes of the variable.

probability density function

The normal distribution, also known as the Gaussian distribution, is a continuous probability distribution characterized by its symmetrical bell-shaped curve, where the mean, median, and mode are all equal. It is fundamental in statistics because many natural phenomena and measurement errors are approximately normally distributed, making it a cornerstone for statistical inference and hypothesis testing.

normal distribution

Signal processing involves the analysis, manipulation, and synthesis of signals such as sound, images, and scientific measurements to improve transmission, storage, and quality. It is fundamental in various applications, including telecommunications, audio engineering, and biomedical engineering, where it enhances signal clarity and extracts useful information.

signal processing

real-world random variations

Mean and variance are fundamental statistical measures used to describe the central tendency and dispersion of a dataset, respectively. While the mean provides a single value representing the average, the variance quantifies the degree to which each data point differs from the mean, offering insights into the data's spread and variability.

mean and variance

Algorithms are step-by-step procedures or formulas for solving problems or performing tasks, and are fundamental to computer science and artificial intelligence. They optimize processes by providing clear instructions that can be executed by machines to achieve desired outcomes efficiently and effectively.

algorithms

The Central Limit Theorem (CLT) states that the distribution of sample means approximates a normal distribution as the sample size becomes larger, regardless of the population's original distribution. This theorem is foundational in statistics because it allows for the application of inferential techniques to make predictions and decisions based on sample data.

central limit theorem

independent random variables

The Gaussian distribution, also known as the normal distribution, is a continuous probability distribution characterized by its bell-shaped curve, where the mean, median, and mode are equal, and it is defined by its mean and standard deviation. It is fundamental in statistics and natural sciences due to the Central Limit Theorem, which states that the distribution of the sum of a large number of independent, identically distributed variables tends towards a Gaussian distribution, regardless of the original distribution of the variables.

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