Odd Waveform

It's the nature of digital audio.  The curves are not really there, but neither are the straight lines - only the samples.  To make the sequence of samples more natural to work with, the program displays lines between the points; some programs fit a curve to the points, which is closer to the effect of playing back.  For lower frequencies this looks perfectly natural, but at frequencies closer to the sampling frequency you can get this strange-looking effect - but once you understand it, you realise it can be ignored.

One way to look at this is to remember that no frequency that is higher than half the sampling frequency can be represented by sampling (for the sampling to work, you must actually filter them out as a part of the process); if you play back the jagged wave formed by joining the dots there will be lots of higher frequencies, but then you filter them out (because they can't have been there originally) and you are left with the smooth waveform you expect.

I knew the sample rate because it's listed in the details to the left of the waveform!  Note how the dots (indicating the actual sample values) are much closer in the central wave, which is sampled at 44.1kHz.

Paul

Ok, Lol, guess I should have read the rate as it's written right in plain view- duh-) and- I see what you mean as to samples being shown as the something like 'connecting dots' between the next  sample; the higher the sample rate, the closer the dots; so the 44.1khz has closer dots than the 22.05khz sample rate. Because there's such a big change between each of the 22.05khz 'odd' wave, it looked like the sample rate wasn't the same as the voice; but- it is. There are about 41 samples in each of the .002 second sections.

SteveG, what do you mean by 'big'? amplitude?

Judging from the way the sample you posted is scaled, it looks to be normalised to a +/- value of 1, and the amplitude uses all of it. So that would be pretty much a full amplitude signal - ie, pretty loud.

It's the nature of digital audio.  The curves are not really there, but neither are the straight lines - only the samples.  To make the sequence of samples more natural to work with, the program displays lines between the points; some programs fit a curve to the points, which is closer to the effect of playing back. 

yes, the 'click' IS loud; and seems louder where I was talking louder too; which again makes some sense that the 'click' has some relation to the recorded audio, vs. an electromechanical plug/unplugging.

Generally very close! Thing about real-world waveforms is that they can't change their levels instantaneously, and all the samples represent is 'steering points' towards a final analogue waveform that can be realised in a physical sense. So if you looked at the output from your sound device on an analogue oscilloscope you would see the curves, and you wouldn't (or shouldn't!) see any samples.

so, when a speaker or driver even in an earphone tries to reproduce the sound; it's attempting to move with the signal, in amplitude and speed;(?) to recreate the recorded sound directly...an o-scope would allow you to see not a sampling, but the analog signal; not sure how that correlates to something like a voice or sound, vs. an oscillating frequency like from a multivibrator; uh-oh, complicated.

how did you figure that out?

Sample rate 22.5K, 6 samples per wave. 22.5/6=3.75. Voila!

so, are we in agreement that the odd wave is about 3.75khz? which means it's easily in the audible range?

Hmm... when I checked it along the whole wave, it wasn't exactly consistent - and I would have expected a sample interference pattern to be rather more regular than this one - which is why I think it's interference.

Steve, what would you think could cause 'interference' like this?
and, you mean that because the sound is kind of 'jerky'; like not a smooth consistent wave?

WELL, my audio-friends, if I didn't know better, I'd be saying the 'oddwave' sound doesn't matter;
except I know where it happens;
at the places where MY OWN words were removed from the recording.
so.... (fill in the blank________________)

So can you show us a larger chunk of the waveform on either side of the "odd wave" so we can see it in context? We might then be able to make a better guess as to what it is. If it is, as you suspect, an indication of audio editing then it is possible that poorly edited audio using inferior software might show a click at edit points. Opening one of these audio files in Audition and viewing it in Spectral view could be very enlightening.

So can you show us a larger chunk of the waveform on either side of the "odd wave" so we can see it in context? We might then be able to make a better guess as to what it is. If it is, as you suspect, an indication of audio editing then it is possible that poorly edited audio using inferior software might show a click at edit points. Opening one of these audio files in Audition and viewing it in Spectral view could be very enlightening.

hmmmm...that sounds interestingly hopeful...)
wouldn't that be a nice surprise...?
how big a chunk would you need to see? i have a five minute section, zipped...actually, can put a link to the online download here...hmmm...in the morning then-)

so, when a speaker or driver even in an earphone tries to reproduce the sound; it's attempting to move with the signal, in amplitude and speed;(?) to recreate the recorded sound directly...an o-scope would allow you to see not a sampling, but the analog signal; not sure how that correlates to something like a voice or sound, vs. an oscillating frequency like from a multivibrator; uh-oh, complicated.

They are all the same thing as far as signals are concerned - changes of amplitude happening over a period of time. None of them can change instantaneously; even the multivibrator that appears to has a finite risetime. And that's what Nyquist and sample rate is all about - the highest frequency you can represent at any given sample rate is the equivalent of half of that rate. What it comes down to in simple terms is that it takes two samples (in the right place) to steer the output up and down again as fast as it's possible for them to do so - hence the ultimate speed of output movement being limited to half of the rate the samples occur.

There was, in the early days of digital audio, a widespread belief that somehow, it was the samples themselves that were being 'listened to' as a sort of stepped waveform - this was caused by several pundits (who should have known better) spreading a very poor explanation of how it works, which unfortunately seems to have stuck, despite having no foundation in physical reality at all. The truth of the matter is that the samples steer the electrical output of the D-A converter towards its next value at the next sample point, and it's simply not possible for this output to change instantaneously - the Laws of Physics dictate this absolutely. So the waveform passes through the sample point, certainly - but the rate at which this happens depends just as much on the other samples near it as anything - there's nothing absolutely fixed about this at all.

There are quite a few issues with samples though - it's quite possible to get them to provide more output than the 'digital ceiling' might lead you to think. I created a demonstration of this years ago and put it in a pdf which you can look at here. Gives you a much better idea of how the output relates to sample positions.

so, when a speaker or driver even in an earphone tries to reproduce the sound; it's attempting to move with the signal, in amplitude and speed;(?) to recreate the recorded sound directly...an o-scope would allow you to see not a sampling, but the analog signal; not sure how that correlates to something like a voice or sound, vs. an oscillating frequency like from a multivibrator; uh-oh, complicated.

They are all the same thing as far as signals are concerned - changes of amplitude happening over a period of time. None of them can change instantaneously; even the multivibrator that appears to has a finite risetime. And that's what Nyquist and sample rate is all about - the highest frequency you can represent at any given sample rate is the equivalent of half of that rate. What it comes down to in simple terms is that it takes two samples (in the right place) to steer the output up and down again as fast as it's possible for them to do so - hence the ultimate speed of output movement being limited to half of the rate the samples occur.

There was, in the early days of digital audio, a widespread belief that somehow, it was the samples themselves that were being 'listened to' as a sort of stepped waveform - this was caused by several pundits (who should have known better) spreading a very poor explanation of how it works, which unfortunately seems to have stuck, despite having no foundation in physical reality at all. The truth of the matter is that the samples steer the electrical output of the D-A converter towards its next value at the next sample point, and it's simply not possible for this output to change instantaneously - the Laws of Physics dictate this absolutely. So the waveform passes through the sample point, certainly - but the rate at which this happens depends just as much on the other samples near it as anything - there's nothing absolutely fixed about this at all.

There are quite a few issues with samples though - it's quite possible to get them to provide more output than the 'digital ceiling' might lead you to think. I created a demonstration of this years ago and put it in a pdf which you can look at here. Gives you a much better idea of how the output relates to sample positions.

Steve, I get what you're saying here- but didn't get what you meant by 'rearranging samples' in the .pdf... samples always occur with perfect timing, right? so the rearranging was of amplitude at the sample points (?); which then changes what- the wave? and overshoot,etc? honestly, i'm not sure how it relates to the 'odd waveform', except to explain (well) ho actual curves and overshoots look between samples ....that does make sense....thanks-) I'll get a file up tomorrow- what's the best way to get it here? is there a limit on size? thanks again!!!

Steve, I get what you're saying here- but didn't get what you meant by 'rearranging samples' in the .pdf... samples always occur with perfect timing, right? so the rearranging was of amplitude at the sample points (?); which then changes what- the wave? and overshoot,etc? honestly, i'm not sure how it relates to the 'odd waveform', except to explain (well) ho actual curves and overshoots look between samples ....that does make sense....thanks-)

I should have said not to take too much notice of the actual rearrangement (you can't do this in the present version) - the file was meant to illustrate the considerable potential for overload of D-A converters. But it does show how the waveform can alter in ways you might not expect. Sample timing is never 'perfect' - there's always room for error whenever electrical signals are generated, and sample clocks are no exception, but generally these days the errors are so small that you can effectively ignore them for most practical purposes; clock generators have improved.

There are limits on uploads to the site, but a short sample of noise shouldn't exceed them!

Steve, I get what you're saying here- but didn't get what you meant by 'rearranging samples' in the .pdf... samples always occur with perfect timing, right? so the rearranging was of amplitude at the sample points (?); which then changes what- the wave? and overshoot,etc? honestly, i'm not sure how it relates to the 'odd waveform', except to explain (well) ho actual curves and overshoots look between samples ....that does make sense....thanks-)

I should have said not to take too much notice of the actual rearrangement (you can't do this in the present version) - the file was meant to illustrate the considerable potential for overload of D-A converters. But it does show how the waveform can alter in ways you might not expect. Sample timing is never 'perfect' - there's always room for error whenever electrical signals are generated, and sample clocks are no exception, but generally these days the errors are so small that you can effectively ignore them for most practical purposes; clock generators have improved.

There are limits on uploads to the site, but a short sample of noise shouldn't exceed them!

Ok, great- can you explain just once again (maybe i'll get it) what you mean by 'rearranging' the samples? how can samples be rearranged?

Ok, great- can you explain just once again (maybe i'll get it) what you mean by 'rearranging' the samples? how can samples be rearranged?

Like I said - you can't do this in the present version. What you could do in earlier incarnations was to alter (by dragging) the position of individual samples in the amplitude direction. You couldn't alter their positions in time though (fairly obviously...)

Ok, great- can you explain just once again (maybe i'll get it) what you mean by 'rearranging' the samples? how can samples be rearranged?

Like I said - you can't do this in the present version. What you could do in earlier incarnations was to alter (by dragging) the position of individual samples in the amplitude direction. You couldn't alter their positions in time though (fairly obviously...)

oh, you could alter sample's amplitude, but not time (yep) in what software? Adobe Audition? (or was it CoolWave?)

here's one place where the 'click' or 'screech' or whatever it is exists; it's always in one channel our of four; it might not be in the specific channel that was edited, but i believe it's where editing was; in this example, it's possible that MY words were edited out while the judge (who is talking) is speaking;  another theory is that the click is 'near' the location of the edit; since there was tons of editing in this proceeding, throughout the proceeding. btw, the court stopped me from using my own personal recorder, my palm treo 650 cellphone to record; if i had that recording, these edits would have been clearly known to have been done. thus their re4ason for confiscating my phone at every proceeding.

i do have an audacity project this was made from; btw i'm rushing here, busy with other tasks....selling my house losing it now; this recording MIGHT be a composite of all four channels; i don't remember; nonetheless, the click is loud here, and with a longer section of time.

I can't see or hear any evidence of an edit at that point - removing the noise alone leaves the judge's cadence sounding natural (though I can't make out the word), and the same frequencies can be seen continuing before and after the place it is at.

Are you saying that your speech was recorded in a different channel, and removed from that without altering the time of the recording as a whole?  If so, I would expect to hear at least a trace of it through the judge's microphone, which I can't.

Paul