1/f Noise Description

The focus of this project is to study 1/f or 1/f2 noise of thin metal films due to electromigration.
1/f0, 1/f2 and 1/f fluctuations

The diagram on the left shows the relation between the frequency and power (dB level) of various noise types. the 1/f0  white noise, the top horizontal line, shows a fluctuation in which the power changes at random, irrespective of wave frequency. the 1/f2 Brownian noise, the bottom curve, shows  waves which change in very strict conformity with a certain fluctuation pattern. The 1/f, the middle line, indicates a pattern in which the power change is inversely proportional to the frequency. (Both power and frequency have been converted into Fourier values)

 

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Classical music and 1/f fluctuation

Analysis of wave pattern in classical music, as well as popular songs, are shown in this diagram. Frequency is inversely proportional to the power, a relationship which creates 1/f fluctuations. The constant, rusty noise of a TV after broadcasting ends is displeasing. On the contrary, wave patterns which are most soothing conform to the 1/f fluctuation. The sounds created by classical music following a 1/f fluctuation patterns are especially soothing to our ears.

 

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Waves of electroencephalogram and 1/f function

Analysis of the relation between the alpha rhythm and electrically stimulated pain relief is shown by the electroencephalogram on the right coincides with 1/f fluctuation patterns seen when relaxed, listening to music. Introduction of noise or pain while in this state reduces the alpha rhythms, while decreasing the beta rhythms, thus causing a shift from the 1/f fluctuation pattern to the 1/f0 fluctuation or white noise.

 

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Pain relief by 1/f stimulation

The results of electrical treatment centering on the removal of intense pains caused by cancer and other diseases are shown above. Thirteen males and eight females were initially treated by ordinary electric stimulation. It's effectiveness was less than 50%. When 1/f electrical stimulation was administered to five cases which had not responded to the initial treatment, effective relief of pain occurred in four cases.

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Effectiveness of 1/f stimulation treatment.

The result of treatment by ordinary electric stimulation and the 1/f electric stimulation are shown on the table on the right. The electric stimulation was applied for about 30 minutes, and the degree of pain reduction attributed to the treatment was evaluated. The original pain level was established as a reference level of 10. In 7% cases, pain almost entirely disappeared (i.e. Pain level reduced to 0-3), by ordinary electric stimulation. In addition, 28% reported some relief of pain. The combined results shows about 35% of patients were satisfied with the ordinary electric treatment. When treated by 1.f electrical stimulation, 30% of the patients reported their pain was almost entirely gone, while about 40% felt their pain was reduced in half. A total of 70% of patients were thus satisfied with 1/f electrical stimulation treatment.

 

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*Portion of the text above are extracted from Nihon Medix catalogue*

 

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