Questions about White noise

Short answers, pulled from the story.

What is white noise in signal processing?

White noise is a statistical model that describes a random signal having equal intensity at different frequencies, giving it a constant power spectral density. This theoretical construct 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 the physical world, an ideal white noise signal is a purely theoretical construction because the bandwidth is limited in practice by the mechanism of noise generation, by the transmission medium, and by finite observation capabilities.

How does white noise affect cognitive function in students?

A small study published in 2007 found that white noise background stimulation improves cognitive functioning among secondary students with attention deficit hyperactivity disorder while decreasing performance of non-ADHD students. Rausch, V. H. published a study in 2014 titled White noise improves learning by modulating activity in dopaminergic midbrain regions and right superior temporal sulcus, which provides a scientific basis for the cognitive effects of white noise. Overall the experiment showed that white noise does in fact have benefits in relation to learning, and the experiments showed that white noise improved the participants' learning abilities and their recognition memory slightly.

What is the audible frequency range for white noise in audio signals?

For an audio signal, the relevant range is the band of audible sound frequencies between 20 and 20,000 Hz, and such a signal is heard by the human ear as a hissing sound resembling the /h/ sound in a sustained aspiration. The term is used with this or similar meanings in many scientific and technical disciplines, including physics, acoustical engineering, telecommunications, and statistical forecasting. Any distribution of values is possible for white noise, although it must have zero DC component, and even a binary signal which can only take on the values 1 or -1 will be white if the sequence is statistically uncorrelated.

What is the mathematical definition of a Gaussian white noise vector?

If, in addition to being independent, every variable in the vector also has a normal distribution with zero mean and the same variance, the vector is said to be a Gaussian white noise vector, and in that case, the joint distribution of the vector is a multivariate normal distribution. The power spectrum of a random vector can be defined as the expected value of the squared modulus of each coefficient of its Fourier transform, and under that definition, a Gaussian white noise vector will have a perfectly flat power spectrum, with the power spectrum equal to the variance for all frequencies. The independence between the variables then implies that the distribution has spherical symmetry in n-dimensional space, and therefore any orthogonal transformation of the vector will result in a Gaussian white random vector.

How is white noise defined in discrete-time stochastic processes?

A discrete-time stochastic process is called white noise if its mean is equal to zero for all time points and if the autocorrelation function has a nonzero value only for time zero. Such a process is said to be white noise in the strongest sense if the value for any time is a random variable that is statistically independent of its entire history before that time, and a weaker definition requires independence only between the values at every pair of distinct times. An even weaker definition requires only that such pairs be uncorrelated, and some authors adopt the weaker definition for white noise, and use the qualifier independent to refer to either of the stronger definitions.

Read the full story about White noise →