"White noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density."
A sequence of uncorrelated random variables.
Stationarity: A stationary time series is one whose statistical properties, such as mean and variance, do not change over time. This is an important concept in time series analysis and can affect the selection of appropriate models.
Autocorrelation: The correlation between observations within a time series based on a lagged time difference. This can be used to identify patterns and dependencies within the series.
Power Spectral Density: This represents the distribution of power in a time series over different frequencies. It can be used to analyze the frequency components of non-stationary time series and detect periodicity.
Autoregressive (AR) Models: These are statistical models that use past values of a time series to predict future values. AR models assume a linear relationship between lagged variables.
Moving Average (MA) Models: These are statistical models where each value in a time series is a weighted average of past values, and the weights decrease exponentially as the distance from the present increases.
Autoregressive Integrated Moving Average (ARIMA) Models: These models combine the features of AR and MA models, as well as incorporate differencing to remove trends and seasonality.
White Noise: A series of random data points with a constant mean and variance that are uncorrelated and independent of each other. White noise is often used as a baseline comparison for the analysis of other time series.
Gaussian White Noise: A type of white noise where the values follow a normal distribution. Gaussian white noise is often used as a theoretical construct in statistical analysis.
Non-Parametric Methods: An approach to modeling time series without assuming a specific probability distribution. Non-parametric methods are often useful when the underlying data distribution is unknown.
Wavelet Analysis: This is a technique for time-frequency analysis that decomposes a time series into different frequency components. Wavelet analysis can be useful for detecting and characterizing non-stationary features in time series.
Singular Spectrum Analysis (SSA): This is a method for decomposing a time series into basic components and identifying trends, seasonality, and other patterns. SSA can be used for forecasting and anomaly detection.
Kalman Filters: These are mathematical models that use a series of measurements to estimate the state of a system. Kalman filters can be used for tracking and prediction of time series.
State Space Models: A statistical model that represents a time series as a set of mathematical equations that describe the evolution of its underlying state variables. State space models provide a flexible framework for modeling complex time series.
Machine Learning: Techniques such as neural networks, support vector machines, and random forests can be used for time series prediction and classification. Machine learning can be more flexible than traditional statistical methods but may require more data and computational resources.
Bayesian Analysis: A statistical framework that accounts for uncertainty and prior beliefs in the modeling process. Bayesian methods can be used for time series modeling and forecasting.
Deep Learning: This is a subset of machine learning that uses artificial neural networks with multiple layers to learn complex features in data. Deep learning has shown promising results for time series prediction and classification.
Standard White Noise: This is the most common type of white noise. It's a stationary random process with a normal distribution.
Gaussian White Noise: This type of white noise is also stationary and has a normal probability distribution.
Poisson White Noise: Poisson white noise is a random process that follows a Poisson distribution. This type of white noise is often used in applications where the number of events occurring in a certain timeframe needs to be modeled.
Uniform White Noise: This type of white noise is uniform distributed, with all the values having the same probability of appearing within a given range.
Brownian Noise: Brownian noise is a type of white noise in which the power spectral density is proportional to the frequency.
Pink Noise: This type of noise is similar to brownian noise, with a spectral density that decreases by 3dB per octave as the frequency increases.
Red Noise: The spectral density of red noise is inversely proportional to the frequency.
Blue Noise: Blue noise has a spectral density proportional to the frequency.
Violet Noise: This type of noise has a spectral density proportional to the square of the frequency.
Gray Noise: Gray noise is a type of noise that has a spectral density that is flat across all frequencies.
"The term is used, with this or similar meanings, in many scientific and technical disciplines, including physics, acoustical engineering, telecommunications, and statistical forecasting."
"White noise draws its name from white light, although light that appears white generally does not have a flat power spectral density over the visible band."
"In discrete time, white noise is a discrete signal whose samples are regarded as a sequence of serially uncorrelated random variables with zero mean and finite variance."
"One may also require that the samples be independent and have an identical probability distribution."
"If each sample has a normal distribution with zero mean, the signal is said to be additive white Gaussian noise."
"The pixels of a white noise image are typically arranged in a rectangular grid and are assumed to be independent random variables with a uniform probability distribution."
"Yes, the concept can be defined for signals spread over more complicated domains, such as a sphere or a torus."
"The bandwidth of white noise is limited in practice by the mechanism of noise generation, by the transmission medium, and by finite observation capabilities."
"For an audio signal, the relevant range is the band of audible sound frequencies (between 20 and 20,000 Hz)."
"Such a signal is heard by the human ear as a hissing sound, resembling the /h/ sound in a sustained aspiration."
"The 'sh' sound /ʃ/ in 'ash' is a colored noise because it has a formant structure."
"The term white noise is sometimes used in the context of phylogenetically based statistical methods to refer to a lack of phylogenetic pattern in comparative data."
"Yes, it is sometimes used analogously in nontechnical contexts to mean 'random talk without meaningful contents'."
"White noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density."
"In digital image processing, the pixels of a white noise image are typically arranged in a rectangular grid, and are assumed to be independent random variables with a uniform probability distribution."
"If each sample has a normal distribution with zero mean, the signal is said to be additive white Gaussian noise."
"For an audio signal, the relevant range is the band of audible sound frequencies (between 20 and 20,000 Hz)."
"Such a signal is heard by the human ear as a hissing sound, resembling the /h/ sound in a sustained aspiration."
"The term white noise is sometimes used in the context of phylogenetically based statistical methods to refer to a lack of phylogenetic pattern in comparative data."