I wasn't going to bring up Bessel functions because then I'd have to exmplain them. But glad someone did.
But once the OP's got the feedback he wanted / needed, does it really matter what happens to the thread afterwords?
Nope. The Purefi page says, "he carrier frequency is 1.38kHz, the modulation frequency is 43Hz." Where are the harmonics?
I see the 43Hz quite clearly modulating the envelope.
And since the resultin AM and FM spectrums are NOT the same, and neither is the waveform or peak value, thus there's no question as to an audibple difference, I suggest the Purefi site article be...um...amended. A bit.
Strong opinion, however like my wife, completely wrong.
Read Bruce Hofer's work;
https://hifisonix.com/wordpress/wp-content/uploads/2017/11/Designing_for_Ultra-Low_THD_N-1.pdf
1% Vishay RN60D thin metal film are good resistors and will not break the bank. Even the standard 1/4 and 1/2 Watt thin metal film resistors are not bad at a few cents each.
Vishay PTF series low ppm TCR thin metal film resistors measure better but cost 5 or 6 dollars each.
Z Metal-foil resistors stink at least when I measure them with the AP analyzer on my bench.
Thanks DT
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We have found in hi end audio an audible difference in resistors, even between 1% or better thin film types. Vishay seems to make some pretty practical ones that sound good. Older Holco resistors have a slightly 'forgiving' sound so we once used them primarily for feedback resistors. Older Roderstein resistors sounded very 'balanced' and were used as the primary resistors in the Vendetta Research SCP-2 phono stage, and in the CTC Blowtorch preamp. Old Holco and older Vishay (original resistors) were sometimes used to improve the sonic balance, especially in the CTC Blowtorch. I still maintain a lot of older Roderstein resistors in my inventory, but for new products we usually Vishay DALE branded (brown color) resistors, that don't look real pretty, but both measure and sound good. Thanks to Ed Simon for his measurements of these devices.
I think you answered a different question from that asked. most people would interpret 'warm' wrt audio as a frequency change, although a big jump in H2 might also give that. IMHO a resistor would have to be in the pathalogical category to cause either.
FM modulated by a pure 43Hz sine. The AM counterpart has some harmonics (because of your Bessel functions)
good
Waveforms are of course different. However the magnitude spectra are the same within 0.005dB unless you want to question Matlab. What is your point?
Looking at the Purifi article, it appears to be commentary on the common overreliance on typical phase-free spectral analysis to judge audio equipment performance and quality, estimate audibility of distortion products, etc. IIRC Scott Wurcer made the same point regarding overreliance.
Perhaps comfort with the measurements arises from the assumption that humans are insensitive to phase. Maybe not exactly true for every person under all conditions. For one type of example, IIRC 1audio remarked that humans can be very sensitive to phase that is changing. Similarly ESS noted in their slide deck they believe changing excess phase may be audible to some people. Of course the ESS comment is in reference to very low distortion and very low noise level dacs, not something as imperfect as loudspeakers.
Is there too much reliance on that type of spectral analysis or not?
Perhaps comfort with the measurements arises from the assumption that humans are insensitive to phase. Maybe not exactly true for every person under all conditions. For one type of example, IIRC 1audio remarked that humans can be very sensitive to phase that is changing. Similarly ESS noted in their slide deck they believe changing excess phase may be audible to some people. Of course the ESS comment is in reference to very low distortion and very low noise level dacs, not something as imperfect as loudspeakers.
Is there too much reliance on that type of spectral analysis or not?
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I would say too much reliance on a belief that ears and brains are infallible on this forum.
WHERE does he talk about "warm sounding" resistors?
Which can be clearly detected just by ear?
Are you answering to this thread?
Dear John.
You are a respected designer with a lot of good products in your History.
Sadly lately you seem to be drifting bit by bit into the subjective/fairy dust area of Audio.
Pity.
Far left side of the Bonsai 360-review personality-type related graphic below?
Attachments
My point is that the waveforms are different, so the auditory stimulus MUST be different, opening a possibility of audible difference. Your magnatude spectra is wrong. I've run several actual FFTs. Must be an error in the setup of Matlab. Peak values are very different.
I believe your point is that the spectrums are identical (they aren't), so its somehow amazing that the two are audibly different (it isn't), and you attribute that to sideband phase shift. And from that, you're somehow trying to push some form of magic audio theory on the unsuspecting public.
The waveforms and spectra are different. Provable. They are audibly different. Provable. Big deal, and no magic.
We're done here.
Hey, you're the reference expert here. Why don't you go off and do your thing now, and find the papers that show how relatively insensitive humans are to in-band phase shift? Come on now, this goes both ways. Oh, and no manufactureres propaganda, we need real papers, like AES papers etc.
Again I suggest, since you summarily dismiss any information given you here, that you honestly try to answer your own questions with Google. You seem to be good at it. But be honest, and do NOT just try to validate your own opinions. You will learn nothing doing that.
if you consider 0.005dB a difference to be audible then you have a point and that would be spectacular if the difference was attributable to 0.005dB. Otherwise, not. You claim my amplitude spectra to be wrong - that is a very strong claim without shred of evidence and I have posted the exact Matlab script running in double precision). I have tried to explain to you that spectral windows as normally used prior to FFT analysis is spreading the signal energy into neighboring FFT bins including into other sidebands which means that the peak spectral values are not exact. Your spectra showed characteristic skirts from a window. Without knowing the exact algorithm behind your plot it is of course hard to get any closer to an explanation.
it's surprising that two signals with identical spectra (proved) sound so different. Its up to others to theorize about why
at least one thing to agree on
I don't consider 0.005dB an audible difference. The two samples are much more different than that in peak value.
I posted my FFT results. Sorry if you missed them. .005dB? Of what? RMS? Sure. Peak? Heck no, they are 3dB apart. Matlab isn't making the mistake here.
Still valid, window or not. And my amplitude figures are correct too, the two are not the same.
I don't agree that it's surprising because the spectra are different, which I did prove and post, and the peak amplitude is different. And the envelope is different. And....geez man, if you can't see the obvious, I can't help you. Not a surprise at all. Different waveforms, different auditory stimulli.