# White noise energy vs. frequency components energy.

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"White noise" energy vs. frequency components energy.

White noise, I have learned that is a mixdure of all possible frequency components at the same time. All at the same levels. White noise can for example occour in resistors where an electric current flows through.

If I filter it through a band pass filter that filters out everything except one frequency range, the bandwidth of the filter will determine how narrow or wide the frequency band will be. The narrower the bandwidth is the more of the frequencies below and above the center frequency is filtered out. However, at the same time, the level of the filtered signal will decrease as the bandwidth gets narrower. At least seen in audio simulations on my computer.

This let me think that if I am left with one single "coherent" frequency, that frequency will have no amplitude at all because I assume that this particular frequency is one of an infinite numbers of frequencies. Is this a correct guess? Please help me understand the nature of white noise, and why it is measurable.

Vidar

## Answers and Replies

White noise, I have learned that is a mixdure of all possible frequency components at the same time. All at the same levels. White noise can for example occour in resistors where an electric current flows through.

If I filter it through a band pass filter that filters out everything except one frequency range, the bandwidth of the filter will determine how narrow or wide the frequency band will be. The narrower the bandwidth is the more of the frequencies below and above the center frequency is filtered out. However, at the same time, the level of the filtered signal will decrease as the bandwidth gets narrower. At least seen in audio simulations on my computer.

This let me think that if I am left with one single "coherent" frequency, that frequency will have no amplitude at all because I assume that this particular frequency is one of an infinite numbers of frequencies. Is this a correct guess? Please help me understand the nature of white noise, and why it is measurable.

Vidar

I think the level of the signal gets lower after the filter because of the specifics of how the filter is modeled, it is not inherent to the concept of frequency filtering.

That said, if your "signal" is in fact just noise, then yeah, it will of course decrease as you narrow the filter. The power in the noise signal is sigma^2 * B where B is your filter bandwidth. If you make B small, the power goes down. Note you have to look at noise power and not voltage because white noise is zero mean. Think of it this way, in the limit your B goes to zero and the probability the brownian motion of the resistor at a given instance matches your filter bandwidth also goes to zero so your signal goes to zero.

Also, resistors don't need a current to generate white noise. The thermal noise power of a resistor is proportional to the temperature, regardless of the current. Some devices (not resistors) have what is called "Shot" noise and that is proportional to current.

skeptic2
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