Sine waves

This video lesson is part of a complete course on neuroscience time series analyses.
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[milosradulovic]

Absolutely amazing! First explaining the basics instead of just rushing in is a genius move!

[SunnyJerai]

I've been trying to understand what Time/Frequency domain and Fourier Transform are. Every video on Youtube felt confusing. Finally I stumbelled on your Videos and they are so intuitive. Thank you Mike.

[dakynshew]

wooow sir ..you r the teacher ive search for a long really need conceptual teacher like you n everyone does now your whole youtube videos is my mission to watch n i will be sharing to my frinds

[igorcruz]

Brilliant series of lectures Mike! Btw, where can I find that GUI example you used in the video? Thanks.

[williammartin]

In the Matlab example, I would have thought that when you put the mouse on 0, 1 in the polar plot, it would look like a "sine" wave, but it seems to look like a "cosine" wave. What am I missing?

[QUIXU]

OK, so I am now here, (or am I hare, hair or hear, although I maybe just an heir)?

Never mind as a sound isn't always easily written, or spoken off, which is also why I am hear...
OK lets forget about them's.

As we all know (or are taught to know) Sine waves can be written on a flat piece of paper, to denote a 2D image of what these are

However, I suspect these are 3D representations of a memory of a pinpoint in tie, passing along a spiral route, from inception to final decay.
&
Understaning sine waves in this context, I believe that NONE truely interferre with another (in the exact same planetary sense) unless the opposing pinpoint eats backwards/forwards (dependant upon phase angle), along the same exact path, destroying to zero any former content along that line, thus a signal that is exact and at the same time 180degrees OUT of phase, can and does, annyhilate any previous image of that initial signal.

To this point, many refer to a sound from one speaker destroying to zero, the exact same sound out of another, if they are 180 opposed.

This (in my mind) creates some confusion with others, as to how far "out of phase" any signal can be, other than immediately 180 degrees at the same latent potential (power level), as two slightly different power levels on the same fault line, opposing each other, will lleave a faint (audible) trace, and anything NOT in the same phase, cannot alter another, simply because they are at the same power level.
BOTH have to try and occupy the exact same positions during every passing of a waveform.

Otherwise, they are NOT anti-phasing, but merely accidentally crossing.

I am referring to two such waves, of exactly the se physical content, that (by the simplest of options) are NOT on the exact same phase angle, so neither the positive or the negative versions of either, can have any impact on the other's two impulse directions.

I was told many years ago to NEVER face two speakers at each other, as one would completely suck the diaphragm out of the other, if they were NOT "in phase".
Yet a stereo audio signal is exactly NOT an exact image of the other, but merely "similar" such that neither is the same for most of the tiime.
So what happens is this, some sounds appear to disapear, some appear louder, some not at all, yet as a stereo signal is also a multiple mix of different frequencies, all won't impact another, unless exactly the same versed or inversed.
Yeah yeah I know versed isn't a word, but (for me) it fits as the opposite to inversed.!!!

Now, getting back as it were to a sine wave, an audio "file" sound wave, if the LEFT CHANNEL IS MERELY 60* TO THE LEFT OF CENTER (and the R the same on the other side), pushing both the L&R into each other across a single speaker will either?
1/- Do nothing,
2/- Slightly reduce the total loudness,
3/- Slightly increase the total loudness,
Or
4/- Blow the diaphram completely off the cone of that speaker.

However I doubt the first or the last as neither is a mirror image signal to the other.
What I would suspect as happening is this, for all (total) frequencies, there will be a common increase and decrease in total loudness depending on how many different frequencies go through 100% at any one time, as well as how many o through the 180* degree opposite value, while most "frequency" signals will be so far out /in phase with any other, there will be a general perceived loudness.
I do feel, that there may be some HUMMING and fuzziness of signals, but I seriously doubt any listener would notice, unless told to listen for?
I do think however, that at no point will the (output) audio signal fade to zero, or double in value.

Which brings me to another quizical situation.

That of the alternate phase, exactly the same angle towards and away from any of the other two.

After all, most situations with phases - there are THOSE that all have THREE balanced phases, operating around a neutral core.
It's been used commercialy for many, many years and is commonly known sinply as
3ph
or 3ph N & E (= 50hz or 60 hz 110/220 or 230/400 Mains power)

IF anyone connects any other PHASE onto itself (by reversing the poles), or reverses the connection onto another phase/line, the fuses blow as the current flow becomes horrendously huge.

YET each and every 3ph supply line CAN AND DOES support the notion of interconnection between all three.
So long a something is using the excess power between any two poles.

ie:
If a step-ladder connection is made (looks like three monkey arms) between all three phases, such that there is a transformation action occurring, one can (and does) get yet another THREE equally powerful phases, to gain 6phase ppower, with all phases equidistant from the next or the previous phase.

It's not unusual to see this effect in an audio signal path, nor is it (for me) all that unfamiliar - to get NINE such phases all with a set angle of separation, such that NONE are the mirror image of any other, yet all are derived from the same initial 3 phases, or, in the definition of a single 3ph supply line, one installation. (grouned or not).
If these three are grounded at the incoming termination point, then all three become grid-tied to ground.

If you were to REMOVE one of the incoming line (phase) fuses, and tried to run the installation on the other two lines, you WOULD NOT SEE any main difference except that "one circuit" of lights would fail to illuminate, and some three phase machines wouldn't start, or would judder until able to sustain rotation by being turned one way or the other..

Yet you would NOT have three phases, just TWO
Just like a stereo sound system eh?

But unlike a stereo sound system, instead of speakers on the lines or phases, you need the machines connected that way, to provide a twisting/rotational power force, that does "turn" until it strikes the missing line/phase whereupon it stops turning.
It then vibrtes at 50/60hz until it is powered off, by it's fuses blowing on overload, or the power is switched off.

Hoever a (normal 2ch) stereo sound system has none of those features, and simply continues to express noise (called music and talking etc).

I have (since 1965) played WITH music in the sense of playing it across and via all three master channels, which, happily grant me NINE direct play channels and a summated "10th" which is formed not from a L&R - but from a FRONT & BACK (diametrically opposed) channels, which (funnily enough) are NOT 180 degrees opposed as one may think, but merely 90 degrees (or less) opposed.

It means neither adds nor depletes the other, yet I get way more than a 50% increase in loudness, as I get the increase and decrease of each signal loudness, before the sine waves cross the zero point, at which time the summated speaker's cone goes negative and powers it's diaphragm movement the other way.

I thus get all summated sounds AND all differentials as well, meaning, I get every available phase angle obtainable, from ANY (and I do mean ANY) original 2ch stereo ANALOGUE format (of standard L&R audio outputs), from ANY audio amplifier.

That means that I can instantly get an immediate NINE channels direct, without adding another amplifier, or, with a "simple" 2ch to one channel summation device, gain a 10th "center of room" summated channel, which I normally feed from the front center and the rear center channels.
The 10th central channel tends to have a fairly flat "medium power" band, of hum notes, floating between all the other channels, never increasing too loudly, and never depleteing either, until the actual sound fades in & out at the two ends of each sound track.

Thus, to the listener, inside of AND OUTSIDE OF, the immediate listening environment, the entire content is able to be clearly heard, as if one was NOT enclosed in a small room, but wandering around in a huge outdoor concert event.

In other words, an audiophiles true heaven, without needing to be there (years beforehand with recorded music) nor overseas, without airfares and tickets to be bought, all done in the comfort of one's own premises, either in the home, or ouy on the farm somewhere, miles away from neighbours, where one can truly "crank it up bro"