As an expert in the field of acoustics and signal processing, I can provide you with a comprehensive understanding of what violet noise is. Noise, in general, refers to a random signal or a combination of frequencies that is not musically coherent and can be considered unwanted or disruptive. There are various types of noise, each with its own characteristics and applications. Violet noise is a less commonly discussed type compared to white, pink, or brown noise, but it has its unique properties and uses.
Violet noise, also known as purple noise, is a specific type of noise that has a distinct spectral characteristic. The power density of violet noise increases with frequency, which means that as the frequency goes up, the power density of the noise increases. This increase is not linear but follows a quadratic relationship, which is to say, the power density is proportional to the square of the frequency (\(f^2\)). This characteristic differentiates it from white noise, where the power density is flat across all frequencies, and from pink noise, where the power density decreases with an increase in frequency following a power law that is inversely proportional to the frequency.
The term "violet noise" is derived from the color spectrum analogy used to describe different types of noise. Just as white light contains all colors, white noise contains all frequencies with equal power. As you move through the spectrum towards violet, the frequency increases, and this is reflected in the increasing power density of violet noise.
One of the interesting aspects of violet noise is that it can be thought of as the result of differentiating a white noise signal. Differentiation in signal processing is an operation that highlights the high-frequency components of a signal. When you differentiate white noise, you effectively create a signal where the higher frequencies are more prominent, which aligns with the definition of violet noise.
In practical terms, violet noise can be used in various applications where a signal with an increasing power density with frequency is desired. It can be useful in audio processing for creating a specific type of sound texture or in testing and calibration of audio equipment to ensure that they respond correctly to a wide range of frequencies, especially in the higher ranges.
It's important to note that the term "violet noise" is not as widely recognized or used as other noise types, and some sources may refer to it as "blue noise" or "pink noise" with a misunderstanding of the spectral characteristics. The correct identification of violet noise is crucial for accurate signal analysis and application in various fields.
In conclusion, violet noise is a unique type of noise with a power density that increases quadratically with frequency. It is an interesting and less commonly explored area within the study of noise and signal processing. Understanding its properties and applications can provide valuable insights for professionals working in audio engineering, telecommunications, and other related fields.
read more >>

Violet noise is also called purple noise. Violet noise's power density increases 6 dB per octave with increasing frequency (density proportional to f 2) over a finite frequency range. It is also known as differentiated white noise, due to its being the result of the differentiation of a white noise signal.read more >>