White noise refers to noise whose power spectral density is uniformly distributed over the entire frequency domain.
Random noise with the same energy density at all frequencies is called white noise.
White noise refers to the noise in which the noise energy contained in each frequency band of equal bandwidth is equal in a wide frequency range.
White noise or white noise is a random signal or random process with a constant power spectral density .
In other words, the power of this signal is the same in each frequency band. Since white light is composed of monochromatic light of various frequencies (colors), the property of this signal with a flat power spectrum is called "White", this signal is also called white noise.
In contrast, other noise signals that do not have this property are called colored noise .
Ideal white noise has infinite bandwidth, so its energy is infinite , which is impossible in the real world. In practice, we often treat a flat signal with limited bandwidth as white noise because it makes our mathematical analysis more convenient. However, white noise is more convenient to deal with mathematically, so it is a powerful tool for system analysis. Generally, as long as the spectral width of a noise process is much larger than the bandwidth of the system it acts on, and its spectral density can basically be considered as a constant in the bandwidth, it can be treated as white noise. For example, thermal noise and shot noise have uniform power spectral densities over a wide frequency range and can generally be considered white noise.
When you need to concentrate on your work and there are always complex sounds around you, you can use these two sounds to cover up. In general, you can use white noise for normal situations , while pink noise is a masking material specifically for speech.
Pink noise is also known as inverse frequency (1/f) noise because its energy distribution is inversely proportional to frequency, or 3 dB per octave.
Gaussian white noise
Gaussian white noise: If a noise, its amplitude distribution obeys Gaussian distribution , and its power spectral density is uniformly distributed, then it is called Gaussian white noise.
Thermal noise and shot noise are white Gaussian noise.
The so-called Gaussian in white Gaussian noise 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 a constant, which refers to the correlation of successive signals in time. This is a question of examining two different aspects of a signal.
White Gaussian noise means that the signal contains all 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 comes from. Its amplitude at any time is random, but it satisfies the Gaussian distribution function as a whole. For the knowledge of time-varying signals, refer to " Signals and Systems ", and Gaussian White Noise to " Communication Principles " books.
It is an infinite-dimensional Schwartz extensive function theory newly created internationally in the mid-1970s. Researcher Yan Jiaan of the Institute of Applied Sciences is one of the main contributors to the establishment and improvement of the mathematical framework of the theory. The framework he proposed with Professor Meyer, a corresponding academician of the French Academy of Sciences, is called Meyer-Yan space. He established a well-established mathematical framework for infinite-dimensional non-Gaussian analysis with recently published papers by Kondratiev et al. Pioneering research in this area is planned in the future. Because white noise analysis has a profound physical background, it has more and more profound applications in quantum physics.
白噪声的应用领域之一是建筑声学，为了减弱内部空间中分散人注意力并且不希望出现的噪声（如人的交谈)，使用持续的低强度噪声作为背景声音。一些紧急车辆的警报器也使用白噪声，因为白噪声能够穿过如城市中交通噪声这样的背景噪声并且不会引起反射，所以更加容易引起人们的注意。
在电子音乐中也有白噪声的应用，它被直接或者作为滤波器的输入信号以产生其它类型的噪声信号，尤其是在音频合成中，经常用来重现类似于铙钹这样在频域有很高噪声成分的打击乐器。
白噪声也用来产生冲击响应。为了在一个演出地点保证音乐会或者其它演出的均衡效果，从P A 系统发出一个瞬间的白噪声或者粉红噪声，并且在不同的地方监测噪声信号，这样工程师就能够建筑物的声学效应能够自动地放大或者削减某些频率，从而就可以调整总体的均衡效果以得到一个平衡的和声。
白噪声可以用于放大器或者电子滤波器的频率响应测试，有时它与响应平坦的话筒或和自动均衡器一起使用。这个设计的思路是系统会产生白噪声，话筒接收到扬声器产生的白噪声，然后在每个频率段进行自动均衡从而得到一个平坦的响应。这种系统用在专业级的设备、高端的家庭立体声系统或者一些高端的汽车收音机上。
白噪声也作为一些随机数字生成器的基础使用。
白噪声也可以用于审讯前使人迷惑，并且可能用于感觉剥夺技术的一部分。上市销售的白噪声机器产品有私密性增强器、睡眠辅助器以及掩饰耳鸣。
白噪声有什么用？
其主要用途之一是用来考核一个系统，
有限带宽“白噪声”做为未来的随机信号，它拥有各平权的频率信号，
It's a good idea to use this to initially assess the entire frequency band of the system!
If a system or structure fails to withstand the "white noise" test, it is difficult to say what it does!
The power spectral density is constant: S(ω)=S0
Signal autocorrelation: R(τ)=S0δ(τ)
Mathematical expectation: E(X(t)]=0
Mean square value : E[X(t)^2]=∞
where δ(τ) is the Dirac function.
It is the power spectrum of the random signal in the same unit . This is a good signal frequency and is a theoretical construct, just like the spectrum of light in full color white color, white noise fills the entire human ear with vibrational frequencies that can help a person relax or sleep. Life is full of sounds and noise disturbances, such as honking cars, barking dogs, snoring neighbors, sirens, yelling. White noise does not add to loud noise white noise , but contains all sounds of equal frequency. Research shows , a steady, peaceful sound as well as flow monotonous, such as white noise, can filter and disperse noise to help reduce noise distraction, which is why it is used to help people relax and sleep.