Hi everyone,

I was recently wondering about how different programs present waveform displays to the user.
For example, Audacity simply connects samples via a straight line due to efficiency, meanwhile iZotope RX among others show the mathematically correct curve as seen below.


The thing is, I refuse to believe that when played through a speaker the cone moves as is displayed via the blue line.
Assuming that the speaker has some amount of resonance, some post-ringing is possible. But since hardware has no way of seeing into the future, pre-ringing like that should technically be non-existent.

Therefore I have been wondering if there is a program, that displays the waveform exactly as a physical speaker would move when playing back a single-sample spike (forgot the specific name of it) for instance.

Thanks in advance

 

The correct digital waveform representation looks like this https://en.wikipedia.org/wiki/Digital_signal#/media/File:Digital.signal.discret.svg (red lines).

The curve is (will be) the analogue result.

And in the digital domain the pre-ringing can of course be shown and therefore also put out and be audible.

 

Not to mention overs/Intersample Peaks.

 

You need to look up the sinc function, which is the plot you've posted. Also the sampling theorem which @No Avenger alluded to.

The only way really is to use an oscilloscope to see how your DAC makes it go. You can then try to measure your speakers to see how well they do the representation, but then you have a lot of things on your desk: the speakers, the measuring mics and the room acoustics.

You can take a look for instance this whitepaper from Texas Instruments on how DACs work.

 

Thanks for the info. I guess one more way to get a representation of what the waveform would look like would be oversampling the band-limited signal (by say x16) and then drawing the curve assuming a maximum speed as well as a specific weight of the driver playing it back.
That way there is possible post-ringing due to intertia, but no pre-ringing.

Actually, taking a second look at the Resample module in RX there is a pre-ringing parameter which appears to create just about the waveform I would expect to occur IRL. Probably the thing I was searching for in the first place.

 

it is not even what is created by the DAC.

but, otoh, it is probably more close to what you hear than a straight line between samples - or steps.

personally i prefer to look at samples as they are, i.e. stepped.

spike is the correct term.

a bandlimited spike, when i look at your picture.

but for full spectrum - and for a useful speaker measurement - you would use a bipolar click.

i dont think you can visualize what a speaker does, because every speaker does something different. just as every room, every listening position, and every DAC.

if you want to get an idea about these realms, play a sinewave of 22 khz at 44khz sr over your speakers, which is identically to a tri wave or square wave, then turn the volume up and tell me what you hear.

...

 

why do you think a DAC or a speaker would ignore these 130 samples?

 

Blue line shows what is really your output, from digital steps to analog wave, approximately, but way closer to it.

"Analogue" is not synonymous with "continuous".
"Digital" is not synonymous with "discrete". (c) FabienTDR

 

Yes that's the ultimate proof.
In case you can borrow one, high impedance probe (1Mohm) should suffice to have a good approximation of the real speaker voltage waveform.

Here a scheme to check speaker power, use VM1 (2th pic), just neglect the VM2 scope on 100mOhm current shunt.
You should provide a continuous burst of spikes to trigger them unless the scope has single shot persistance memory (most DSO will do).
Measure AC power consumed by a loudspeaker

 

The ultimate proof is: for EQing, all you need is the Fast Fourier Transformation representing the spectrum adequately enough so that you are actually cutting resonances at the right frequency position – the rest is irrelevant.

 

Because there is no way for a DAC or speaker cone to look into the future.
Assuming that all samples before the spike are at 0, any system playing back the spike would start moving or reacting when the spike hits, not before.
There is after all no way to tell if the stream of 0s is going to continue or if and when a different value is going to happen at all.

From a "perfect" system without inertia, resonances, ringing etc., I would expect something like this to occur (disregarding intersample peaks for a moment):

The moment the spike occurs the output voltage is being ramped up to the value of the input sample, reaching it at the latest when the next sample gets read out.

As to measuring voltages with an oscilloscope, I would like to do that if I had easy access to one.
Maybe there are models that can even plot the measured signal back to a .wav file (with the maximum possible sampling rate able to be provided by the scope)..?

 

I don't know about saving the input signal to .wav directly, but modern scopes can save the measurement for sure, and years ago in a physics lab the things we used could go up to MHz range so matching the source sample rate should be possible.

 

that does not make sense at all. a DAC converts what comes in, not what a humans intention was when he made the waveform^^

does that look like zeros to you?

there is no nonbandlimited spike in a bandlimited spike.

which does not exist.

and "perfect" will not be when a bandlimited waveform would be suddenly no longer badlimited in the analog output.

perfect would mean that the waveform does not change. but do we really want that? however, it does not matter, both is not what a DAC does.^^


i suggest this simple test:

create a bandlimited impulse and a nonbandlimited inversed impulse, play them synchronized via 2 DACs and sum then in the analog domain.

it will be fun, i promise.


and i wonder what the display mode in fig 1 should be good for.

 

Well in late 90's I used professional Lecroy DSOs to diagnose electrical transients.
It saved raw waveform data on floppy, and you wouldn't believe: I could import it on PC with Cool Edit!!!
With new ones is even easier because many DSOs have embedded OSs like Windows, etc.

 

Speakers by themselves they can produce post ringing only (as artefacts). But if they are being fed with digitally produced pre ringing, they will reproduce it, of course.

 

Which is fine, totally agree with that. DACs don't know intentions. But in case of the spike, with all 0s before, electronics should logically not react until they receive the spike. Everything else physically doesn't make sense.

In fact it does, my mistake for taking a screenshot of a single-sample spike at 48kHz and resampling it to 192kHz. In the original post it is more clear that the calculated pre-ringing is in fact all 0s.

That already fails at creating a non-bandlimited spike, infinite resolution is not something we have access to.

No practical application except for eliminating the visual pre-ringing when viewing the waveform.

That, there are occasions where pre-ringing is audible (say, heavy processing on a kick drum).

 

dude, i just figured that your additional photos also show such a "corrected" a diplay of samples, didnt see that before, i thought it is actually blits.

so forget about that part, that was my fault.

however, this form of displaying waves does not make much sense to me.

you need that kind of "correction" and displaying only in certain contexts, such as generating (I)IRs in matlab and the like, or when changing samplingrates or creating wavetables - i have no idea what it has to do in an audio app for musicians. (?)

especially since you are right, that this is not what a DAC will produce from a simple spike.


i think you should forget about that "mathematically correct". mathematically correct is a single sample of 1. what the highpass filter in the DAC will do with that, we dont know yet.

the izotope trio probably explain the purpose somewhere, but i generally dont read manuals.

yeah the other photos, which were the only ones i was looking at, dont even show the actual samples.


sorry if i also dont have the answer to the original question, but it is an interesting idea.

measuring the sound of a speaker by recording it in 384khz and then comparing it against the "input" is theoretically easy. unfortunately... there is a microphone, filters, and jitter involved, haha.