Then I must admit I didn’t understand what you were on about in the first place.
Actually, you're both right. If you stare at the FFT screen long enough, and if you have enough processing power in your brain, you may be able to have the big picture, including the harmonic content vs time, and their correlation with the envelope of the note with the attack, sustain, and decay. Or chop the note up in slices and FFT each one and then try to figure out some sort of synthesis. And do it again varying the force applied to the bow.
Or just listen and enjoy.
It is worth to remember that this way you're not doing an "ABX test" anymore but instead are just using a software named "ABX" to do another kind of listening test.
Or just listen and enjoy.
It should be understood that there is no contradiction between enjoying listening of music and doing measurements and analysis. Some of us do like to make both
What I do not understand is the fact that we, who are interested in measurements and technology are labeled as some with limited hearing abilities and no interest in listening of music or going to concerts. It should be understood that education, measurements and analysis help us to better understanding what we hear and why we hear it.
But how will you know it doesn't sound crapOr just listen and enjoy.
I know I have no right to comment because I'm just a guessing amateur audiophile according to Pavel
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BZZZZZT!
Fourier theorem (the foundation of the Fourier transform) does not assume or need strict signal/function continuity. Piecewise continuous functions/signals (meaning grossly that they have a finite number of discontinuities) are also good enough, provided that they have finite limits at the continuity intervals endpoints. Trivial example, a periodic ideal triangle signal is perfectly Fourier transformable.
A non periodic signal/function can either be extended to periodicity (as mentioned) or consider it's direct Fourier transform, but the coefficients will now be continuous integrals instead of discrete sums.
A Fourier series is NOT necessary the Fourier transform of a signal, otherwise said, not all Fourier series have an inverse Fourier transform in the time domain. More precise, not all Fourier series are originating in real world signals, some are a physical impossibility (that is, for example, violating causality).
Discrete Fourier Transform has nothing outstanding, is simple writing the standard Fourier transform with coefficients as convergent infinite series and conveniently truncate the result, at the price defined in the Nyquist theorem (frequencies over a certain value are lost).
Fourier Theorems | Mathematics of the DFT
Not easy to further explain these without rather complex math, you may want to check the next free reference.
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Of course, PMA.
More than this, I tried, years ago, to increase the Open loop bandwidth by compensating the hf losses at the VAS emitter* and had those kind of trouble with variations of the stability margin with temperature changes.
And this kind of problems can be tricky with a complex amplifier.
But I believe Dadod has explored this aspect in each and every detail: I think he is good enough.
* BTW: I gave-it up on this idea because the added open loop gain at HF did not made, on my listening experience, big changes in the quality of the reproduction, despite the measured measurements improvement of harmonic distortion between 10 & 20 KHz. So I keep with optimized simple 3 poles CFAs. I gave-it up too with cascoded VAS as well. But, may-be it is stupid ?
I know I have no right to comment because I'm just a guessing amateur audiophile according to Pavel
I think it is a nice misinterpretation of my post
Thank you, no need, I have my own resources. You said that the Fourier transform is applied to periodic signals only (or signals extended to periodic) which is an incorrect statement - here:
John Curl's Blowtorch preamplifier part III
And I am not going to play a QUOTE/PROOF misquote game with you.
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Then I'd really love to have his opinion, if any.
For me it's about the same dilemma as digital vs analog: on the "digital" side, I have a mass-produced Epiphone with perfect CNC cutting, machine assisted glueing and an almost indestructible epoxy finish. On the "analog" side, I have a Gibson and a Heritage, both hand made with all the little flaws, like a head nut that's off by a mm on the Gibson, or a fret board that's not quite level on the Heritage, and both have the extremely fragile nitro lacquer. But guess what: I prefer analog.
Or just listen and enjoy.
When we think of all the efforts that it requires of our brain to compute all this, including our integrated camera and all our other senses, we should not be surprised that we are dying so young.
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If you want to apply the Fourier transform to aperiodic signals and hence prefer to work with continuous integral Fourier coefficients (that usually you cannot calculate in a closed form) also lose any DFT benefits in the process, you are welcomed to do so. Sane engineers prefer to use the Laplace transform for aperiodic signals.
Just for the heck of it, the much beloved Spice simulator uses a signal periodic extension (it assumes the input/output signal is periodic from -oo to +oo on the time axis, even if the transient simulation starts at t=0) to calculate the distortions spectra.
Otherwise, do you have a point to make or you just feel like trolling?
Neither am I. Richard and Dadod just discovered (the expensive way, unfortunately) the root cause why there are no known power amplifiers on the market with an ULGF of 6MHz or higher. Add testing on a shoestring and you got a safe recipe for a potential commercial disaster.
But how will you know it doesn't sound crap
Oh man!.....who’s wallerin in self pity now?
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