Talk:Heterodyne

Brain behavior

Could someone include a reference for the stuff (ahem) on brain behavior? At best it isn't well written (not clear which wave phenomenon in the brain is being referred to, e.g. the electrical pulses? If so, what is with the comment on low frequency as it relates to the ear?) At worst, it seems like unsupported pseudoscience. Thanks —The preceding unsigned comment was added by Al Biglan (talk • contribs) 18:17, 3 June 2005 (UTC)

• In addition to what you said, I must say that even the introduction is pretty mushy: what happens when two instruments are playing out of tune is that their sounds get linearly mixed, and thus the sum of two sines at close frequencies is equal to the product of a "beating" sine at a low frequency and an "average" sine at the average frequency. Given that it is a product and not a sum, this does not mean that any new frequencies have been created: for example, if you high-pass it at a frequency higher than the "beating" frequency, the signal will be kept unchanged and the beating will be preserved... Which makes me wonder about the general correctness of Gary D and Foobar's contributions, and their extrapolation to "brain waves". --Ma Baker 18:02, 11 Jun 2005 (UTC)

While I agree the intro is mushy, the article is close to correct in its interpretation of the mixed frequencies:

if you mix a frequency: f1=(a+h)

and a frequency: f2=(a-h)

you get a new sound which can be expressed as the product of the

mixed frequency: a

and the

beat frequency: f1-f2

The difference refered in the article is no doubt refering to the difference in the beat frequency formula. --Anuran 00:41, 23 October 2005 (UTC)

I'm very skeptical about this audio brain stuff - the brain does not receive sine waves but rather what is roughly a narrow-window time-average of the discrete audio power spectrum (at sampling frequencies defined by the lengths of various hairs). Because this destroys things such as phase information, etc, there is no way for two audio signals beyond the hearing range of the human ear to get information into the brain (I doubt the human brain can perceive being shook at audio frequencies). Is there a *REAL* reference on this floating around somewhere, because this is pretty ridiculous stuff.

From what little I know about the auditory beat effect, this interpretation seems to be right. The ear is basically a frequency domain sampler, so any beat frequency would have to be produced outside of the brain. If someone could varify this, I'd bet that parts of ear basically behave nonlinearly, so you get a difference frequency out. This would mean that some ear component has a non-constant acoustic impedance, which is not hard to imagine. The eardrum, for instance, could very well be the source, as it is a circular membrane, which I believe has a non-linear stress-strain relationship. In any case, I think there's enough ambiguity to not mention the human auditory system at all. --Jschultz 03:07, 27 October 2006 (UTC)

Yes, this article does seem to be confusing two concepts. Searching for "binaural beats" on Google, I found that almost all of the references were pseudoscientific, but right at the bottom of page 5 I found a reference [1] from a credible institution, the Life Sciences Department of Sussex University (England). A bit later on I found another one [2] from Rutgers University, if you prefer the other side of the pond. These suggest that binaural beats are real, but belief in a connection between these and "brainwaves" takes us into quack territory. The only serious investigation that I can find into a link between binaural beats and EEG output is a report from Penn University[3] on an experiment that produced a negative result (no link). --Heron 20:56, 22 August 2005 (UTC)

Heyyy!!

This article has to de: links, that legal? Thanx 69.142.2.68 00:22, 19 September 2005 (UTC)

Cleanup

My fellow wikipedians - I've added sections to this article (as it is in quite a mess!) however I still think it could use some more reorganization. An image or two wouldn't hurt either. Maybe also more uses for electronic heterodynes?

formula contradicts other sources

This article says that the beat frequency is equal to the difference of the the frequencies divided by 2. Nearly every other source says it is merely the difference (f1 - f2). Does someone want to set this straight?

There's a difference between the beat frequency and the difference frequency. If you create sin(100Hz)*cos(2Hz), you will hear four beats of 100Hz per second, and not 2. The reason is that cos flips between +1 and negative 1, but the amplitude of the signal you are hearing is really the absolute value of it, thus the beating of amplitude is really |cos(2Hz)|, which has a wavelength of 4Hz (but is not shaped like a cosine). - Rainwarrior 17:52, 16 August 2006 (UTC)

Brain wave stuff $\neq$ good

As someone who works on how the brain processes sound, I found this section pretty unbelievable, and hence added a "Disputed" tag. For example, you would not hear a mix of 100 Hz and 102 Hz as "101 Hz", because your brain effectively performs a Fourier transform on the sound you hear. Now, it is true that you could not properly distinguish the tones; they would probably just sound slightly out-of-tune.

While the article gets it right that epilepsy can be temporarily induced by a periodic stimulus (which is one of the things my research group works on), virtually the entire rest of the article is based on pseudoscience or misunderstandings.

I vote that the whole section be axed.

And yes, the beat frequency is $f_{1}-f_{2}$. (This was a question on an exam I was marking last semester!)

I very much disagree with: "your brain effectively performs a Fourier transform on the sound you hear". There is much, much more going on than a Fourier decomposition in the brain. If you work with computer sound recognition (you may, you didn't say exactly), you should know just how inadequate Fourier analysis is on its own for that purpose. Now, I don't know what this bit about "brain wave frequencies" is all about, perhaps it should be removed, but binaural beats are a well known and easily demonstratable process. I would agree that the language is inaccurate, though. The heterodyning principle is that the signal produced by mixing 100Hz and 102Hz is equivalent to the amplitude modulation of 101Hz with 1Hz (percieved as a 2Hz beating). It is not so much that the brain will percieve one or the other, but that the perception of it is ambiguous between the two, mostly (but not entirely) resolved by which parts of the signal lie in the audible range. - Rainwarrior 17:04, 16 August 2006 (UTC)

Also, binaural beating is generally a quieter effect than the beating of a mixed signal. So, 100 in one hear with 102 in the other ear is going to have a stronger perception as an unmixed signal than as as the 101Hz * 1Hz idea. Quickly doing the experiment on myself, I would say that I hear a tone that is wavering in pitch (up and down) with slight amplitude changes, rather than two distinct pitches. If actually mixed, I definiftely hear is as 101Hz with a 1Hz amplitude modulation. But, if I take two tones that are more distinct, and gradually slide them into 100 and 102Hz, they are felt as more distinct (in the binaural test), but in the mixed test the distinction seems to be lost at some point. - Rainwarrior 17:49, 16 August 2006 (UTC)

An Oscilloscope and spectrum analyzer show it all.

My experience with audio and using an oscilloscope leads me to these conclusions on heterodyning. Any one with a waveform generator and oscilloscope can do the experiments and prove it to themselves.

When 2 audio (or r.f.) signals are added together, the higher frequency "rides" on top of the lower frequency. The peak to peak amplitude of the higher frequency does not change, however it's amplitude in reference to 0v. rises and falls at the frequency of the lower signals frequency. A speaker would produce this rising and falling at the frequency of the lower frequency signal. A frequency spectrum analyzer will show only the 2 original signals. There is no mysterious beat frequency...only the rising and falling of the higher frequency at the lower frequency's rate. .........I assume that when 2 independently created audio signal come into the ear, the results are the same. What the brain does with them I do not know.

If signals are mixed nonlinearly 4 signals result: The 2 original and the sum and difference of those originals. The trignometric product of 2 sine waves verifies this...hence nonlinear mixing is often referred to as the "multipling" the 2 original sine wave signals together. To produce this multiplication effect with 2 original sine waves, the higher frequency is usually modulated with the lower frequency. This process, done electronically, involves changing the peak to peak amplitude of the higher frequency at the lower frequency rate. The peak to peak amplitude of the higher frequecy is never higher then the original peak to peak value, but it varies at the rate of the lower frequency. An oscilliscope very clearly shows this waveform, and a spectrum analyzer will show 4 frequencies present in the waveform.

I do not know how this nonlinear mixing takes place in nature, but if it does then 4 distinct signals should result. GregFiore 19:08, 16 August 2006 (UTC) Greg Fiore

I'm not sure what you're calling nonlinear mixing... but because of the trig identity you've discussed, the amplitude modulation (nonlinear mixing?) of two sine waves is indistinguishable from the addition (linear mixing?) of two corresponding sine waves. If doing amplitude modulation, it doesn't matter which is the "modulator" and which is the "carrier", because the result either way is identical. Whether or not you get 4 frequencies in your analysis usually depends on whether the outer two tones are withing the detectable range (frequently they are not), though the two original "additive" tones usuall come up stronger, and the two heterodyned frequencies may have additional harmonics. - Rainwarrior 03:55, 17 August 2006 (UTC)

Heterodyne Harmonics

I think missing here is the acknowledgment that mixing can occur through any non-linear device/function. So we're not generalizing enough to say that there are x number of frequencies generated, frequency y is here, frequency z is here, etc. The implication in most of these examples, I think, is that a quadratic is used, but this is only a commonly used approximation for some mixers, notably diode mixers. I think it would be more appropriate to indicate that the harmonics that are generated are determined by the function that governs the device's behavior, and that generally at least a difference term is produced. To some degree the method of mixing is also important to the harmonic production. Bolometric mixers, for instance, act like capacitive envelope detectors and inherently filter out higher harmonics. I know it's a fine point because it's only briefly discussed in the first paragraph, but the topic seems to be causing confusion in the discussion.--Jschultz 01:42, 23 October 2006 (UTC)

Modifying Example in Header

I'm making a tweak in the example in the header that cites a 3000 Hz and a 3001 Hz frequency to produce an "audible beat frequency of 1 hertz" (emphasis added) and changing it to a 3000Hz/3100Hz/100Hz example because 1Hz is not audible to humans (see Human_hearing#Localization_of_sound_by_humans:_a_brain_circuit).

If anyone disagrees, please discuss.

--KNHaw 22:56, 20 December 2006 (UTC)

Need different definition

The definition is not consistent with "beating", which is the article's favorite example. If beating is truly an example of heterodyning, then the definition is wrong. For example: 1) The definition says "...in a nonlinear device". However, beating is a linear phenomenon that occurs in linear devices and mediums (it's just addition!). The definition should be expanded to include linear phenomenon also... if beating is to be included. 2) "...the generation of new frequencies..." - beating doesn't really create new frequencies. A spectrum of the beating signal would actually show the original two frequencies unchanged. The beating frequency wouldn't show up anywhere. By contrast, multiplication actually creates REAL signals at the sum and difference frequencies. Instead of saying "new frequencies" maybe "new frequencies (real or apparent)" 3) "mixing of two frequencies". Using the word "mixing" would be ok in general usage, but in this field it has a technical meaning which would exclude beating (for example, see wikipedia for "Frequency Mixer"). I suggest using a word that doesn't have the same technical association for example: "combining" instead of "mixing". It's great to use the word mixing elsewhere in the article as an example, but not in the definition where it excludes other types of heterodyning. Catapultsam 22:59, 14 April 2007 (UTC)

Mathematical Treatment/Derivation?

I *believe* I once read a mathematical derivation of how heterodyning works in a book by Donald Wehner.. it may have been the 2nd Ed. of "High Resolution Radar", but my point is that heterodyning made ALL THE SENSE IN THE WORLD to me at the time I read that derivation. When I read this Wiki article, heterodyning seems very vague and mysterious. Perhaps a mathematical treatment could illuminate things... I recall it being a very simple derivation. —Preceding unsigned comment added by 69.183.146.246 (talk) 04:38, 7 February 2008 (UTC)

Important reference

Please see the section on Frequency Counter, and Prescaler.