You get the spectrum by applying the well known mathematical operation known as the Fourier transform on the signal. this gives one complex number per frequency point which gives is the magnitude and phase.
You are right in a way that the Fourier Transform has the nature of an average since the Fourier transform is defined as an integral from time minus infinity to infinity. That is how the spectrum is defined never the less.
A spectrum analyzer has a finite integration time and has setting to trade off frequency resolution with time resolution. A spectrum analyzer can be used to give an approximation of the mathematic spectrum of a stationary signal.
You can calculate the envelope of the signal using a Hilbert Transform and that would demodulate the AM signal and give a constant for the FM signal.
The human auditory system might do an envelope detection which makes the signals stand out as very different for the same reason - not my area of expertise, just speculation
Outdoing yourself,which is an achievement in its own right, after dissing Science you are now attacking the English Language itself.
Sinking lower and lower by the minute.
Is it that you speak only of difference apparent on spectrum analyzer?
Real sound files, provided for listening, have completely different properties.
No one can say that amplitude modulated signal differs from constant amplitude phase modulated signal only in phase.
Yes, that is my opinion. It is envelope of modulation we hear so easy or sound volume going up and down 43 times per second. I suppose, resulting sound is called warble.
Unless defined what "better" is in this context (sound reproduction), there's nothing to debate about. Your experience is only useful to you and you alone.
Around where I am, also the country where Markw4 is in, there is a legal principle that goes, "Innocent until proven guilty." The word proven is universal whether it's in court case or support for audio electronics parts audibility claim. If listening isn't done, how would you know the audibility claim is legit or just a marketing ploy?
One must be very thick skinned to shill for boutique audio business these days.
"Jam, my high end audio designer friend came over one day and pulled out some XLR cables."
...
"Wow! Everything sounded better, less distorted, and the difference was easy to hear! I was basically stunned, never expected it."
...
"Next year one of Jam's audio businesses will start selling cables designed by him."
...
"EDIT: By the way, I did not write the above for any commercial purpose."
You should know that the above quotes are posted by one person on one post. Yes, both "Next year one of Jam's audio businesses will start selling cables designed by him." and "EDIT: By the way, I did not write the above for any commercial purpose." by one person.
https://www.diyaudio.com/community/threads/es9038q2m-board.314935/page-263#post-6012247
by applying the Fourier Transform and comparing magnitude and phase
pls elaborate
well, that statement is contradicted by the shown example signals that are pure AM and pure FM, respectively and only differ in the phase of the spectra. That is mathematics - hard to argue against
See post #240.
Are you sure it cannot be proven, even by listening comparison test?
Nope. There are no measurements where vinyl is superior to redbook digital. Whether the experience is more pleasurable is a whole different ball game.
I'm not prepared at this time to present those results. But yes, it's been done.
I have never claimed otherwise.
They are NOT produced by simple phase rotation around the carrier!!!!!! Or you would NOT get that resulting spectrum.
Phase "rotation"(a term we don't really use, but probably means phase shift vs frequency) has been shown to be audible, if of sufficient magnitude and in the right frequency band. It's also inaudible in other conditions. This is not some binary quantity. You can't just say it's audible or not, you MUST state the conditions.
So, if I put a tape measure on a 10' 2x4, all I'm really doing is providing a statistical concept?
If I put a volt meter on an unknown voltage and it measures 1.5V, and my meter calibration is verified, all I'm doing is providing a statistical concept?
As I said, I'm not discussing this further until you generate the signal I asked for.
Of course all measurements are statistical. Do you really think your voltmeter is perfectly repeatable? Its mfr doesn't, even newly calibrated.
No physical quantity will measure exactly the same each time, with the best equipment, even basic quantities like charge, mass, time, and length.
Anyone who has done scientific work knows this. Remember graphs of measurements with error bars? Freshmen in college do that.
There is no Platonic ideal number, which is then messed up by measurement. It's statistical all the way down.
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A mathematician and an engineer agreed to take part in an experiment. They were both placed in a room and at the other end was a beautiful woman. The experimenter said every 30 seconds they would be allowed to travel half the distance between themselves and the woman. The mathematician said "this is pointless" and stormed off. The engineer agreed to go ahead with the experiment anyway. The mathematician exclaimed on his way out "don't you see, you'll never actually reach her?". To which the engineer replied, "so what? Pretty soon I'll be close enough for all practical purposes!"
Oh...and I'm the engineeer.
Some people here hate engineers. But every device they use and enjoy wouldn't exist without the help of more than one engineer.
Isn't it? I measured AAA battery with a cheap voltmeter today and it shows 1.596 VDC each 3 different times.
So what are the "normal audibility levels" of distortion?
A quarter century ago I read online that audiophiles were complaining about the sound quality of those newfangled mp3 files. I downloaded a file and Winamp, and offhand it sounded fine to me. I kept reading complaints, so I got an mp3 encoder to make files from a ripped CD. At lower bitrates of 64 and 96kbps the wishy-washy sound was pretty obvious, and it gave me hints for what to listen for in the "standard" 128kbps mp3 files, and having the original to compare with helped too. Apparently (and despite discovering Audio Amateur magazine two decades earlier) I hadn't been quite the hifi enthusiast I thought I was.
Around that time I saw this mentioned on the rec.audio.pro newsgroup - from what you said, you most certainly do NOT want this:
http://www.moultonlabs.com/full/product01
I didn't buy it but I considered it. What made me hesitate to go into music production was the thought of making less money than I was making doing such mundane things as a DSP based modem for a remote water meter.
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No such thing. It's very complex, and audibility depends on many factors. The single figure THD specs are pretty pointless, however, have been for years. That doesn't mean we can't hear distortion, and with familiarity (I sorta hate "trainging") you can detect lower levels. But there's no single figure anyone can quote that has any real meaning.
I wouldn't say it that way. There are many ways to be an enthusiast.
I first heard MPEG lossy codecs professionally in the early 1990s, and the bit rate was really low, so the artifact was easy to hear. Unfortunately that experience resulted in familiarity, and to this day, I can detect low rate codec artifact very easily. Even before that, because of working in broadcasting, I learned what dynamics processing of many kinds sounded like. 50+ years later I have no problem picking it out. But none of that is enjoyable, nor am I enthusiastic about it. I have enjoyed .mp3 files just fine, and use compression and limiting on a daily basis without huge objection. Enjoyment comes from experiences other than picking out the flaws.
You don't go into the music biz to make money, that mostly doesn't work. The rare successes are just a tease.
Yeah, my voltmeter reads the same voltages the same way every time. Completely repeatable. I guess some theoreticians don't own volt meters, that's why they think the results are not repeatable. In practice, repeatable measurements of reasonable accuracy is the goal, and easily achieved, by necessity and design. As is the case with all practical measurement devices.