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# Headphone CSD waterfall plots - Page 57

I'm not quite sure if any one of us knows what the others are discussing exactly. I certainly don't anyway. Is this still related to testing individual frequency pulses to form a map of ringing per frequency?

I'm not doubting that one gets problems cutting off a wave with one's window. Though I still don't (even after reading that article) see where the abrupt start or stop to a physical sine waves comes from if not from trying to represent it as individual samples? (Not that it matters, since we're treating our measurements digitally anyway.)

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The difference between a pixelated image and the output of FFT is that you can inverse the latter and get exactly the same signal as the original input signal. With pixelation information is lost, but that's not the case with FFT.

The harmonics created are part of the abrupt start and stop of a sine wave. Actually, the harmonics would stretch into infinity, but since we're using sampled audio those harmonics are limited to Fs/2. If you want energy at exactly one frequency only you need a continuous sine wave.

Quote:
What you could do is record a x kHz sine wave that stops abruptly and look at the last cycle and post-ringing in the time domain.

?

Edited by xnor - 10/15/12 at 8:19am

Fair enough, my porn-influenced analogy fell short somewhat. Where do these harmonics come from in sine waves, speaking of physical sound waves, and how does a physical sine wave start or stop abruptly? Trying to go to basics here.

From the abrupt start/stop. In reality things aren't perfect so there's always some smoothing involved.

Quote:
Originally Posted by vid

I'm not quite sure if any one of us knows what the others are discussing exactly. I certainly don't anyway. Is this still related to testing individual frequency pulses to form a map of ringing per frequency?

I'm not doubting that one gets problems cutting off a wave with one's window. Though I still don't (even after reading that article) see where the abrupt start or stop to a physical sine waves comes from if not from trying to represent it as individual samples? (Not that it matters, since we're treating our measurements digitally anyway.)

I (and by now everyone else) assumed that by a "frequency pulse" you meant putting a single cycle of a sine wave through a pair of headphones and measuring the decay.  The point I wanted to make was best stated by arnaud:

Quote:
Vid, it does not matter if we look at a discrete fourier transform or not. The fact remains that a single sine period is composed of non only that frequency but also a bunch of others that describe the discontinuity at the end of the period. Just like a square wave and saw tooth shape can be decomposed into fundamental plus harmonics...

ie if a headphone is to "start" and "stop" playing a sine wave cleanly it needs to be able to reproduce many frequencies apart from the frequency of the sine wave in question--and if the headphone doesn't stop the sine cleanly, it may be because of poor frequency response rather than any acoustical problems.

Put it this way: let there be a hypothetical pair of headphones that can perfectly reproduce 1kHz tones and is perfectly incapable of reproducing any other frequency.  What you'd get from playing a single cycle of 1kHz sine through it would be the phones ringing like a bell at 1kHz *forever*--except to start the ringing requires response outside of 1kHz--the phones can't stop ringing but they can't even start either.

This is an approximation of the effect:

On the left, a single cycle of a 441Hz sine wave (chosen because it neatly fits in 100 samples).  On the right, a very narrow filter letting through only 441Hz, constructed using several Butterworth low pass and high pass filters.

The resulting waveform.  Note the post "ringing" and even pre "ringing".  Yet this is a minimum phase system, there are no echoes responsible for this "ringing".  It is just a result of the "phones" not being able to reproduce other frequencies apart from 441Hz.

edit: I tried the same experiment using the steepest filters from RS-MET EngineersFilter: a 20th order Elliptic lowpass followed by a 20th order Elliptic highpass at 441Hz with maximum rejection.  The resulting waveform is more 441Hz "ringing" with roughly the same envelope as above, but "ringing" for a good 1.5s (!) It's also at -47.5dB whereas the original pulse was 0dBFS.

Edited by Joe Bloggs - 10/15/12 at 10:05am

Nope, didn't mean to suggest a specific way to go about measuring single frequencies individually. I was rather trying to get to the core of CSD, i.e. what (if any) difference there is between measuring the decay of individual pulses (x cycle[s]) vs measuring the decay of frequencies in an MLS signal.

Of the experiment I can only say that I'm not quite sure what you've tested. To start with, why do the phones need to be able to produce many frequencies in order to produce a clean signal at a certain frequency?

Quote:
Originally Posted by vid

Nope, didn't mean to suggest a specific way to go about measuring single frequencies individually. I was rather trying to get to the core of CSD, i.e. what (if any) difference there is between measuring the decay of individual pulses (x cycle[s]) vs measuring the decay of frequencies in an MLS signal.

Of the experiment I can only say that I'm not quite sure what you've tested. To start with, why do the phones need to be able to produce many frequencies in order to produce a clean signal at a certain frequency?

CSDs are visualizations of the Impulse Response. One may be able to tell some ringing and frequency response issues from the IR, but it's much easier to visualize these issues using CSD and FR plots.

One can derive the Impulse Response using MLS or frequency sweeps. Just two different methodologies which should yield similar results.

Edited by ultrabike - 10/15/12 at 1:28pm

Thanks for the clarification, super.

Two vintage orthos. Graphs are on raw data, so the frequency response is not going to be totally spot on.

KWH HOK 80-1 (modded)

Yamaha HP-50S (unmodded)

(My software didn't spot the long ridge for some reason and so it's not annotated on the graph, but it's more or less in the same place as the smaller ridge in the modded version below.)

Yamaha HP-50S (modded)

Yamaha HP-50S (ortho bass hump modded out via EQ, i.e. no physical modding)

Convolution test.

KWH HOK 80-1 convolved with the difference between its response and the response of the physically modded Yamaha HP-50S. Or rather, the MLS test tone was convolved with that difference, then fed into the HOK and measured in the normal way

The modded HP-50S, for reference

The convolution has some noise issues, but I think it's partly because I don't know what I'm doing. The sound was good (convolving a song to test it out), but had some pre-echo.

Seems you may have issues with the phase, which may explain pre-echo... Dunno. Your results look pretty good, however, AFAIK convolution in the time domain is multiplication in the frequency domain.

How about doing the KWH HOK 80-1 convolved with the ratio between the FR response of the physically modded Yamaha HP-50S and its FR response. That is, you'll need the ratio of the FR magnitudes and the difference of the FR phase responses. Then obtain the IR of that, and convolve it with the KWH HOK 80-1...

Edited by ultrabike - 10/16/12 at 10:20am

Convolution test 2.

Taking the difference between the quite bad response of some cheap Creative stock buds and the relatively good response of the AKG K 314. Convolving the Creative response by that difference (i.e. measuring them with a convolved MLS signal).

Creative stock buds, stock response:

AKG K 314:

Creative stock buds convolved:

The noise issues from the first test were solved to some degree.

Based on doing a few minutes of direct comparisons on one song (so not very thorough), the sound is similar between the K 314 and the convolved Creative. The biggest difference comes from adjusting the physical fit on the Creatives, since their bud shape isn't exactly the same as that of the AKG.

Edited by vid - 10/16/12 at 5:06pm

LOL! If you took the difference in the dB scale that is already a multiplication in linear scale... Sorry about that, and your results with the Creative buds are impressive. Very good job!

Quote:
Originally Posted by Joe Bloggs

I'm still hoping to see more CSD graphs of impulse response convolved with their minimum phase inverse filter, such as posted by xnor.  As has been pointed out before much of the "ringing" we see is just a consequence of the frequency magnitude response.  A CSD graph of the impulse response with the magnitude corrected to flat would let us separate actual non-minimum phase ringing from the FR-induced "ringing" that can just be EQed out.

Remember you asked for a guide on how to do this vid? What you are doing now is already close to what I was suggesting. You are convolving phone A with the FR difference between phone A and B. What I want to see is just phone A convolved with the FR difference between phone A itself and a flat response. And this convolution filter should be minimum phase rather than linear phase. You can re-measure the phones with the filter in place like you are doing now, or (what I'd prefer) convolve the filter directly with the impulse response of the original measurement and plot a CSD of the result.
Quote:
Originally Posted by Joe Bloggs

What I want to see is just phone A convolved with the FR difference between phone A itself and a flat response.

AKG K 314 convolved with its inverse. The convolution was applied to the MLS test tone, fed into the phones and measured. I created the conv filter from an earlier measurement, thus you see some effects of positioning. (Ignore the ridge markers at the bottom, forgot to take them off the template.)

Can't say whether it's minimum phase or not, but the sound is curious in a neat way.

Edited by vid - 10/16/12 at 8:26pm
Quote:
Originally Posted by vid

AKG K 314 convolved with its inverse. The convolution was applied to the MLS test tone, fed into the phones and measured. I created the conv filter from an earlier measurement, thus you see some effects of positioning. (Ignore the ridge markers at the bottom, forgot to take them off the template.)

Can't say whether it's minimum phase or not, but the sound is curious in a neat way.

Seems like the ridge around 10k is difficult, but obviously the CSD cleaned up a bit!

Edited by ultrabike - 10/16/12 at 10:12pm
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