# White noise energy vs. frequency components energy.

• Low-Q
In summary: White noise is a mixture of all possible frequency components at the same time, occurring at the same levels. It can be found in resistors where an electric current flows through. When filtering white noise through a band pass filter, the bandwidth determines the width of the frequency band, with a narrower bandwidth filtering out more frequencies. However, the level of the filtered signal decreases as the bandwidth gets narrower. This is due to the specifics of how the filter is modeled, not an inherent trait of frequency filtering. Additionally, the power in the noise signal decreases as the filter bandwidth decreases. This is because white noise is zero mean and the probability of the noise matching the filter bandwidth decreases as the bandwidth gets smaller. It is important to look at noise power rather than

#### Low-Q

Gold Member
"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

Low-Q said:
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.

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## What is white noise energy?

White noise energy is a type of sound energy that contains all frequencies at equal intensities, resulting in a constant and steady sound. It is often referred to as "static" or "static noise."

## What are frequency components energy?

Frequency components energy refers to the individual frequencies present in a sound. It is the measure of energy at each frequency and can be visualized as a graph with frequency on the x-axis and energy on the y-axis.

## How are white noise energy and frequency components energy related?

White noise energy contains all frequencies at equal intensities, so its frequency components energy graph would appear as a flat line. This means that all frequencies have the same amount of energy, resulting in a constant and steady sound.

## What are the benefits of using white noise energy?

White noise energy has been shown to have a calming effect on the brain and can help improve focus and concentration. It is also commonly used in sound masking to drown out other noises and promote better sleep.

## How is white noise energy used in scientific research?

White noise energy is often used in scientific studies as a control for background noise. It is also used in signal processing and engineering to filter out unwanted frequencies and improve the quality of audio signals.