Allgemeine und Biologische Psychologie

Frequently Asked Questions

What is white noise?

Noise is a sound with an irregular, random waveform. Unlike a musical or speech sound, it contains a lot of different frequencies. It is called “white noise” if all audible sound frequencies are represented with the same strength. This designation is in analogy to vision: white light contains all visible frequencies of light.

Digital white noise is a very easy-to-generate signal: One can take any sequence of random numbers and convert it at a certain sample rate into a waveform. Did you ever hear the number ? I don't mean hearing someone reading “Three point one four one...” Did you ever hear the number itself? Here you can. Ten seconds of the 20-kHz waveform of this noise correspond to 200,000 samples, and these samples were chosen to be 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7... 5, 9, 9, 2, i.e. the first 200,000 digits of .
Please note that a zero sound amplitude corresponds to 0x80 in WAV files, so the actual bytes stored in the WAV file are 0x83 0x81 0x84 0x81....

The digits of  are assumed to be distributed uniformly in a random fashion. Hence, this is “uniformly distributed noise”. Most natural noise is “Gaussian distributed noise”, that is the amplitude values follow a Gaussian distribution. The difference is not perceivable. Even a bivalued distribution of amplitude values (0, 1, 1, 0, 0, 0, 1, 0...) sounds perfectly noisy. All these random noises are “white”, i.e. they contain all frequencies that can be produced by the converter. The upper limit is in general roughly the half of the sample rate, i.e. 10 kHz for the demos on this web page.

What is periodic noise?

Let us assume I have to generate 10 seconds of digital 20-kHz white noise (see above). Again, I want to use a list of the digits of . However, my list contains only 20,000 digits (i.e. 1 s). Therefore, I start to recycle: 3, 1, 4, 1, 5, 9, ... 5, 5, 1, 7, 3, 1, 4, 1... I must do so ten times to fill 10 seconds. This is then periodic noise.

Usually, if one does cut-and-paste operations with sound signals, one has to be especially careful about where to cut or paste in order to avoid audible artifacts (clicks) at the “joints”. Not so with digital white noise. The waveform of noise is already as irregular as it could be, so cut-and-paste operations will not add to its irregularity. Let us consider the numbers that represent the amplitude values. The first number of the second cycle (the 3) is not more “surprising” than any other random digit would be. A cyclical sequence of random number does not have a marked-out start. If one would write random numbers on a ring (and if one would not choose the well-known digit sequence of ), no mathematical expert could tell where the sequence starts and ends. Hence, it should be expected that periodic noise sounds just as nonperiodic, ongoing noise does. And it does so, for cycles longer than, say, two or three seconds. But for shorter cycles (or longer cycles and trained listeners) periodic noise sounds different. The example of the main page had a 500-ms cycle, i.e. the random number sequence becomes cyclical after the first 10,000 digits. With such short a cycle, the difference to ongoing white noise is quite audible.

Why does periodic noise sound so structured?

If one looks at a visual random display one will notice structures such as lines and edges. Our perceptual system is eager to see structures even in displays that are not intended to convey any structured information. This is the reason why 19th-century astronomers found channels on Mars and speculated that there might by life on Mars.

Actually, their drawings are not that bad. If one compares these drawings with corresponding photomosaic maps of Mars, one finds many details on the photomosaic map that are well reproduced. Given the atmospheric blur (both on Earth and on Mars) such drawings represent a very good achievement. The “channels” are a perception-induced surplus to a fine observation performance.

In audition, the same Gestalt mechanism would try to identify “lines” and “edges” in sounds. However, while in vision one can take one's time and look carefully again and again on the visual display in order to detect such features, with auditory noise this is not possible. One gets a single chance to listen to the sound, and then the sound proceeds...

With periodic noise, the perceptual system has the possibility for a “second (third ...) look” ... if it can still remember what was presented earlier. This kind of memory is called echoic memory. Echoic memory stores sensory sound information in a quasi-literal fashion. It does so for a second or two, but listeners can easily be trained to extend this to about ten seconds. The fascinating thing is that one can remember a feature that one did not hear consciously.

A common question concerns the physical nature of the “lines” and “edges” of sound. It is often suggested that one should look at the spectrogram of the noise and try to identify features in the spectrogram that correspond to the perceived features in the sound of that noise sample. However, the spectrogram of white noise looks pretty much like a visual random display: it is full of possible features, and it is not clear which of them evoke the perceived events. There is an answer to this question, but it involves complicated mathematics and hours of experimentation time. Maybe a short account will be presented here soon...

Why does nonperiodic noise sound so homogenous?

This is a very good question. In other words: I don't know the answer. Why do listeners need a “second look”? After all, noise is full of potential features that could serve to evoke specific events, and that do elicit specific events if reoccurring. But why do they elicit nothing special at their first occurrence?

With training, listeners need less and less cycles to perceive the periodicity of periodic noise. But even after a tremendous amount of training, and under optimal conditions (not-too-long cycles, e.g. 0.6 s) listeners will never perceive specific features of a noise sample during the first cycle. That is, if they are presented with a 2.4-s noise, consisting of four 0.6-s cycles, they will hear one homogenous cycle and three structured cycles. This hints to a kind of threshold process in conscious perception: If the activation of the feature detectors by the sound signal is too low, consciousness is not attenuated but annihilated. The first occurrence of a feature in a noise signal seems always to evoke subthreshold activation, the repeated occurrence seems to evoke much higher activations. But this is speculation...

Do other people hear the same sounds in periodic noise as I do?

This question is often asked when periodic noise stimuli are presented to an audience, say in a lecture. Let me add a similar but more basic question: Do you hear the same sounds in periodic noise as you do? I mean: If you listen to the same sample of periodic noise today and tomorrow, will you perceive the same features in it? If we know how to answer this question we can proceed to the inter-listener comparison.

How should we study these questions? You could try to remember the sound by verbalizing. However, this does not work very well. In spite of your verbal description you will probably not recall the exact sound of the sample the next day. It is even more problematic if you try to communicate to others what you heard in order to see whether they hear the same sounds.

We could, however, measure your tapping to the periodic noise sample, and do this today and tomorrow. And we could measure your tapping and that of a friend of yours, and compare those tapping patterns. In general, one finds that listeners tend to find again the tapping point of yesterday with a high probability. For most samples, listeners find one or at most two preferred tapping points per cycle and noise sample. The tapping patterns of two different listeners are significantly correlated, but to a lesser degree. There are differences as well as similarities in the tapping patterns of different listeners. However, it is not clear whether different tapping patterns prove different perception: It could be the rhythmical organization of the perceived features that differ. On the other hand, similar tapping patterns could be elicited by quite different perceptions. So these results are only a hint that there is some but not perfect similarity between the perceptions of different listeners.

A part of the variation between listeners is due to the variety of different features present in a single periodic noise sample. If there is need to reduce this variety, one can apply semiperiodic noise...

What is semiperiodic noise, and how does it decrease the variance?

In order to reduce the amount of information that could serve as clue for the detection of the periodicity, one can keep constant a part of the cycle and vary the remaining part. A typical example would be a 0.6-s cycle, where only a 0.2-s segment of the cycle is kept constant, and 0.4 s are converted from newly generated random numbers. Let us call the constant 0.2-s segment “A”, and designate other 0.2-s segments of noise by other capital letters (B, C, D...). Please remember that white noise can be cut and pasted ad lib. A semiperiodic noise could then be built as follows: ABCADEAFGA... A “classical” periodic noise would have to repeat all three segments that build the 0.6-s cycle: ABCABCABCA...

It is much harder to detect the periodicity of semiperiodic noise. It takes much more cycles. But once one has got the feature, it gets clearer and clearer, until finally one ask oneself why one did not hear it at once. Some samples of semiperiodic noise are more difficult to detect and pursue than others, and there are again certain differences between listeners. But there is evidence that once two listeners can cope with the same semiperiodic noise sample they actually listen to the same auditory feature in this noise.

What is the difference between periodic noise and frozen noise?

In masking studies, researchers for various reasons often apply “frozen noise”. This designation indicates that they have used the same noise sample in successive trials. In general, however, such trials are separated by silence. This situation is different from the sound that we are talking about. “Periodic noise” is a single ongoing noise stimulus, with no major amplitude fluctuations in it, of how many cycles ever it may be constituted. The term “frozen noise”, however, is applied to a series of noise stimuli, with silent gaps in-between.

There are other designations that have been chosen for periodic noise. It has been called:

repeated noise

recycled noise

recycling frozen noise

repetition of frozen noise

periodic random waveforms

infratonal periodic sound

...

While some of these designations are quite close to the term “frozen noise” and might cause confusion, other are legitimate and precise. The term “periodic noise” does, however, also appears to be precise, and then... let's face it: would you have ever clicked on a URL called www.repeated-segments-of-frozen-noise-presented-periodically-as-a-single-ongoing-stimulus.de?