White Noise Generator: How Does it Work?

[Beer-monster]

Hi guys

I'm currently working on a university experiment trying top create acoustic crystals. We're using a white noise generator to generate sounds at all frequencies.

However I'm unsure exactly how a white noise generator creates the random signal. Can anyone explain how the an analogue (and/or computer) white noise generator works? In particularly I need to know if the generator really does play all frequencies at once, or rather randomly plays sevral from its range at high speed and changing rapidly?

Being a physicist this sort of circuitry is a bit beyond me, and I can find nothing on the web expect schematics. Any help would be greatly appreciated.

Thanks

Beery

 

[Cliff_J]

You don't get exactly all frequencies at all times. So if you measured for only say a .05 sec window you would have a subset of the spectrum, but the signal would change and the next .05 sec window you include a different subset of the spectrum. So in the end you do get a signal that averages out to include the full frequency bandwidth over a moderate time window but depending on how its generated it may take a second or two.

From:
http://rane.com/par-w.html"

white noise 1. Physics. Analogous to white light containing equal amounts of all visible frequencies, white noise contains equal amounts of all audible frequencies (technically the bandwidth of noise is infinite, but for audio purposes it is limited to just the audio frequencies). From an energy standpoint white noise has constant power per hertz (also referred to as unit bandwidth), i.e., at every frequency there is the same amount of power (while pink noise, for instance, has constant power per octave band of frequency). A plot of white noise power vs. frequency is flat if the measuring device uses the same width filter for all measurements. This is known as a fixed bandwidth filter. For instance, a fixed bandwidth of 5 Hz is common, i.e., the test equipment measures the amplitude at each frequency using a filter that is 5 Hz wide. It is 5 Hz wide when measuring 50 Hz or 2 kHz or 9.4 kHz, etc. A plot of white noise power vs. frequency change is not flat if the measuring device uses a variable width filter. This is known as a fixed percentage bandwidth filter. A common example of which is 1/3-octave wide, which equals a bandwidth of 23%. This means that for every frequency measured the bandwidth of the measuring filter changes to 23% of that new center frequency. For example the measuring bandwidth at 100 Hz is 23 Hz wide, then changes to 230 Hz wide when measuring 1 kHz, and so on. Therefore the plot of noise power vs. frequency is not flat, but shows a 3 dB rise in amplitude per octave of frequency change. Due to this rising frequency characteristic, white noise sounds very bright and lacking in low frequencies. [Here's the technical details: noise power is actually its power density spectrum - a measure of how the noise power contributed by individual frequency components is distributed over the frequency spectrum. It should be measured in watts/Hz; however it isn't. The accepted practice in noise theory is to use amplitude-squared as the unit of power (purists justify this by assuming a one-ohm resistor load). For electrical signals this gives units of volts-squared/Hz, or more commonly expressed as volts/root-Hertz. Note that the denominator gets bigger by the square root of the increase in frequency. Therefore, for an octave increase (doubling) of frequency, the denominator increases by the square root of two, which equals 1.414, or 3 dB. In order for the energy to remain constant (as it must if it is to remain white noise) there has to be an offsetting increase in amplitude (the numerator term) of 3 dB to exactly cancel the 3 dB increase in the denominator term. Thus the upward 3 dB/octave sloping characteristic of white noise amplitude when measured in constant percentage increments like 1/3-octave.] See noise color. 2. Music. Slang term for music that is discordant with no melody; disagreeable, harsh or dissonant.

noise color People working in pro audio know the terms white noise and pink noise, but few recognize the terms "azure noise" or "red noise," but they are real terms. Noise that is not white is called colored noise and will have more energy at some frequencies than others, analogous to colored light.
White noise and pink noise are well defined and known; much less so are the others.
White noise is so named because it is analogous to white light in that it contains all audible frequencies distributed uniformly throughout the spectrum. Passing white light through a prism (a form of filtering) breaks it down into a range of colors. Examination shows that red light is characterized by the longer wavelengths of light, i.e., the lower frequency region. Similarly, "pink noise" has higher energy in the low frequencies, hence the somewhat tongue-in-cheek term.
The Federal Standard 1037C Telecommunications: Glossary of Telecommunication Terms defines four noise colors (white, pink, blue & black) and is considered the official source. No official standard could be found for the others.
The following list of noise colors is loosely based on a rainbow-prism light analogy, where a prism creates a rainbow effect by separating white light passed through it into a visible spectrum labeled red, orange, yellow, green, blue, indigo, and violet from lowest to highest frequencies. Also shown is the approximate slope of the power density spectrum relative to white noise used as the reference:

red noise also called brown noise: -6 dB/oct decreasing density (most amount of low frequency energy or power; used in oceanography; power proportional to 1/frequency-squared); popcorn noise.

pink noise: -3 dB/oct decreasing noise density (but, equal power per octave; 1/f noise or flicker noise; power proportional to 1/frequency).

white noise: 0 dB/oct reference noise with equal power density (equal power per hertz; Johnson noise).

blue (or azure) noise: +3 dB/oct increasing noise density (power proportional to frequency).

purple (or violet) noise: +6 dB/oct increasing noise density (power proportional to frequency-squared; most amount of high frequency energy or power).

black noise: silence (zero power density with a few random spikes allowed).

Other noise colors exist for specialized fields like video/photographic/image processing, communications, mathematical chaos theory, etc., but are not found in pro audio circles. Definitions for the noise colors orange, green, gray, and brown are found many times on the Web, but all appear to be from the same document (whose true origin I could not detect), e.g. see Bob Paddock at Circuit Cellar Online. Definitions without supporting documentation are suspect.

 

[Beer-monster]

Okay so does that mean that a 1 to 10 second sample of white noise isn't representative of the entire audio spectrum?

That might explain why previous students have not acquired particularly good results from using our white noise generator, and even using the noise software.

Is there anyway to calculate how long it'd take the generator to cycle through all the frequencies in its bandwidth?

Cheers

Beery

 

[Cliff_J]

Once past maybe a half second, there should be a pretty accurate representation of the entire audio spectrum. And the low-frequency parts are the ones most affected since they have such a long period for their waveform.

If you have access to a reasonably flat microphone, record in a few seconds and software like Cool Edit (now Adobe Audition) can do a frequency analysis.

There are also many other RTA (real-time analyser) solutions although most setup for audio are going to be setup for pink noise - so with white noise they will show a gently sloping up line as the frequency gets higher (as above, white noise is equal power per freq, pink is equal power per octave which means less power at high freq to mimic human hearing).

Cool edit can also generate the white noise and you could analyse it right in the software. Now whether or not the transducer you're using can reproduce it is another matter, low frequencies require very large amounts of air to be moved and are a challenge for all drivers at some SPL. High frequencies require very low mass and the coil of wire used in most speakers has an inductance that will really limit the uppper frequency range they can reproduce.

Your problem may not be with the generation but the reproduction. You may be better off band-limiting your noise input to avoid causing unnecessary reproduction problems, or re-examine the transducers used.

 

[Beer-monster]

Well I've tried measuring the with the microphone and analysing with a Fourier transform on MATLAB, we get a reasonably flat signature mid way (with a very slight slope towards) high frequencies, except we are getting noise at low frequencies high amplitude spike at lower frequencies (my guess is this is mains hum and its harmonics with some DC) noise.

However previous experiments have hardly detected a bandgap in the crsystals (just zones of small attenutaion) and so we're trying to isolate any problem in the set up before moving to the crystals. It was considered that the generators might not have been producing a reliable frequency pattern. Since a sound sample of over a second was used it was probably something else.

Any idea where I can find some more exact info on the white noise generator and its sampling method so I can check it out and unclude it as a reference?

 

[Cliff_J]

Maybe someone else will have more info, but I don't have any more sources other than some interesting ones that came up in a google search on "white noise algorithm" that had a few examples.