Pink Noise Flicker Noise or 1f Noise

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What is noise ? The simple meaning, noise is unwanted sound. Let's talk about noise in electrical meaning. The term noise stems from the perception a person has when electrical jitter effects in the audio frequency range are amplified sufficiently and then are passed to a loudspeaker. This phenomenon is generally known from a broadcast receiver, for example. Later, the term noise was extended to frequencies outside the audible range. In general, the electrical noise originates from current or voltage fluctuations in electronic circuits. One disturbing effect of noise is that it limits the sensitivity of receivers of communication systems or reduces their transfer capacity. Furthermore, it limits the accuracy of measurement systems. Without noise the transmitter power could be reduced down to a limit set by interference from communication channels. As a consequence the electrical noise has a large influence on the system design and thus on the costs.

What is the difference between sinusoidal signal and noise signal in electronic? Signal can be represented by mathematical description in time domain or in frequency domain. In the frequency domain, the power of a sinusoidal signal is concentrated at a single frequency. In contrast, for a noise signal the power at a single frequency is always zero. Power can only be measured for a non-zero bandwidth. This offers the possibility of a measurement to discriminate between sinusoidal signals and noise signals. The time-dependent behavior of noise signals cannot be predicted in general. In contrast to sinusoidal signals, the description of noise signals is thus restricted to different mean values, then it is only possible to characterize their properties with the help of mean values, as for example the mean square value, i.e the mean power. The noise power per unit bandwidth, the so-called spectrum, will turn out to be a particularly important quantity for the description of noise signals.

Pink noise or flicker noise or 1/f noise is electronic noise with pink spectrum. It occurs in almost all electronic devices, and results from a variety of effects, such as impurities in a conductive channel, generation and recombination noise in a transistor due to base current, and so on. It is always related to a direct current.

Then what is pink spectrum?
Pink spectrum is the frequency spectrum of noise that is flat in logarithmic space; it has equal power in bands that are proportionally wide. This means that pink noise would have equal power in the frequency range from 10 to 20 Hz as in the band from 1000 to 2000 Hz. Since humans hear in such a proportional space, where a doubling of frequency is perceived the same regardless of actual frequency (1020 Hz is heard as the same interval and distance as 10002000 Hz), every octave contains the same amount of energy and thus pink noise is often used as a reference signal in audio engineering. That is, the human auditory system perceives approximately equal magnitude on all frequencies. The power density, compared with white noise, decreases by 3 dB per octave (density proportional to 1/f). For this reason, pink noise is often called "1/f noise".

Since there are an infinite number of logarithmic bands at both the low frequency (DC) and high frequency ends of the spectrum, any finite energy spectrum must have less energy than pink noise at both ends. Pink noise is the only power-law spectral density that has this property: all steeper power-law spectra are infinite if integrated to the DC, low frequency end, and all flatter power-law spectra are infinite if integrated to the high-frequency limit.

What is the purpose of studying pink noise?
Pink noise occurs in many physical, biological and economic systems. Some researchers describe it as being ubiquitous. In physical systems it is present in some meteorological data series, the electromagnetic radiation output of some astronomical bodies, and in almost all electronic devices (referred to as flicker noise). In biological systems, it is present in heart beat rhythms and the statistics of DNA sequences. In financial systems it is often referred to as a long memory effect. Also, it is the statistical structure of all natural images (images from the natural environment).

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