I'm going to run it by you (and others) anyway 🙂 Any waveform can be constructed by summing sine waves, agreed? 😉 Consider how a multiway speaker acoustically sums the drivers....now.....extrapolate...I told you it was simple 🙂
Yes, that much is obvious. Then why are you attempting to use physics as we know it to justify your own pataphysic universe views?
hahahaha. nice spin for your debating position.
Fact is many of the best performing and most popular headphones are planar type. Fact is they are low Z. Fact is, driving them with typical opamp directly will produce high distortion.
Regardless, Devices, circuits etc ought to be measured how they are used.... not only to an arb standard. Test at the level and Z being listened to is a good starting point.
-RNM
Who could use some Nuvistors?
Nuvistor's were used in some FM tuners back-in-the-day.
and Tek scope plug-ins.
-RNM
I'm not sure what you are reading, there is no position to debate?
We were all talking about the Apple dongle used as line output until some confused it by bringing in headphone performance. Line out is a perfectly valid and normal use case for something with a 3.5 mm jack, like the millions of cars that have 3.5 mm stereo aux inputs.
No one said that this device would provide good performance driving planar magnetic headphones.
If the ESS headphone IC doesn't work for your planar magnetic headphones, complain to them. I didn't specify or design it. Fact is, they are not that popular and if they represented 0.001% of worldwide headphone sales I would be surprised.
I understand the difference, but I suspect you do not which is why you keep calling Fourier decomposition a "model" when it is not a model but reality. When you look at reality from a different angle (e.g. by moving your head) does this turn that reality into a mere model of reality? No, of course not; it is merely a different viewpoint of the same reality. That is how Fourier works: you can have a time-based signal or you can have a frequency-based signal or you can have some combination; all are views of the same reality and contain exactly the same information.mmerrill99 said:
Fourier is not the map; it is a different way of viewing the terrain.
Now there are several positions you could adopt:
1. accept this as true, and use it to understand audio
2. be baffled by it and refuse to believe it
3. accept it as true 'in a mathematical sense' but then deny its truth by saying that music is exempt from this
Steady-state measurements may not reflect the whole of the reality of reproducing music, but they do reflect a considerable proportion of the whole. There are those who genuinely believe that steady-state measurements tell us almost nothing useful; in some cases (although not all) they believe that music does not consist of sine waves (i.e. they deny Fourier theory). I assume they believe that there is maths and physics still to be discovered which explains their directional cables, magic goo, secret military technology etc.Jakob2 said:
I suspect that most, if not all, aspects of amplifier behaviour can be investigated by using one, two or three sine waves. In some cases two of the sine waves should be quite close in frequency, so that the envelope varies at a low rate.
Fourier does not need defending; it is simply true. It is not a model, or a photograph - using poor analogies just exposes your lack of understanding of mathematics. Steady-state test signals are a subset of useful test signals; people who believe they tell us everything are mistaken; people who believe that they tell us nothing are seriously mistaken.mmerrill99 said:
That is almost a 'how long is a piece of string' question. However, on the assumption that you are talking about what happens in an ideal world when a single frequency sine wave has its amplitude changed, then the answer is that your question contains a contradiction. A waveform cannot both be single frequency and have its amplitude changed. So then let us assume that you are asking about the spectrum of a sine wave with varying amplitude. The answer is that you will get sidebands and you can use Fourier theory to calculate them.Max Headroom said:
As I said, there are more than one viewpoint. A time-based signal and its Fourier transform are both as real as each other; both contain exactly the same information and neither of them is a model. We use whichever is the most appropriate for our purpose. People get into a mess if they try to pretend that one is more or less real than the other.Markw4 said:
To help us help you understand Fourier, could you tell us how far your mathematical education went? If you understand linear vector spaces, inner products and orthonormal basis sets then we have an easy task; if calculus has passed you by then our task may be difficult. It would help us to know whether Fourier is something you don't understand or something you can't understand.mmerrill99 said:
FFT cannot show "bandwidth" (frequency spread) and "duration" (temporal spread) at arbitrarily small levels simultaneously & yet we know that is reality. So FFT is not reality - it is a very useful function that approximates reality.
Jakob(x) is a good teacher, congratulation, you are now an expert in generating word salads, an incongruent words juxtaposing. Are you expecting a debate starting from these phrases as premise? Please don't hold your breath.
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This seems to make no sense. Also, why would you conflate FFT, an implementation of the DFT, with the generalized Fourier Transform.
You guys could have pointed to some online links like you did from my last post. Perhaps I should feel honored that at least you think I'm educable.
I figured he's been keeping up on the thread and would have seen the links. In reality, there are probably hundreds of good sources for this info because it's covered in every decent undergraduate EE program in a Signals and Systems course. If you Google anything even close you get dozens of good results to pick from. That doesn't mean it's easy to digest without the proper background, though. I appreciate that it's not light reading material, but one should probably understand it before attempting to become a denier. I won't claim to remember all this offhand, but I know where to go back for reference and a refresher.
Ok, a 0db 1kHz sine wave is faded to -60dB in one second, what are the side tones and their levels please ?.
Also, does anybody have multitone signal suitable for 44k or 48k and no windowing please ?.
Dan.
Legitimate question and the answer can be calculated (perhaps it already was and is available somewhere in a table of Fourier transforms), I know I’m not going to spend a night calculating integrals to satisfy your curiosity. The signal you are talking about is a logarithmically amplitude modulated signal and indeed has two main side bands separated from the 1KHz sine carrier by 1Hz, so these main sidebands will be at 999Hz and 1001Hz. There are spectral components to all multiples of 1KHz+/-n*1Hz, n=1,2,3,... with quickly decreasing amplitudes the larger n is. That’s all I can tell on top of my head, for their exact amplitude levels, do your homework and google it, or pull a stack of paper and a pen and DIY it.
If the fade is periodic (every 1 seconds) then the spectrum as above will be stable. If it is a one time event, the spectrum above will last for 1 second, in which the spectral components will all wobble in amplitude around a decreasing (in time) to zero average, after 1 second the spectrum will vanish and you end up with a 1KHz signal attenuated by 60dB.
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A proposal-
First a multitone signal is a decent test and can show response, and nonlinear distortion but the challenge is keeping both harmonics and IM products from landing on tones. There was a paper published years ago at the AES with proposed collections of tones. I believe I shared a spreadsheet of those some time ago here. I'll try to find and share it again. One problem with lots of tones is crest factor. It starts to approach that of random noise limiting the useful measurement range with lots of tones.
Second- a classic test signal is a tone burst. It carries most of the qualities of a musical note with attack, sustain and decay, with the attack and decay instantaneous and sustain perfectly flat so any dynamic modulation should be pretty obvious.
Later this week I'll make some test tone bursts combining these. Analysis will not be real easy but there may be some trick around matching windows to samples etc. I'm not up to figuring out. However maybe someone here is. Given the claims about thermal modulations etc. it should be possible to tease those out with tone bursts.
First a multitone signal is a decent test and can show response, and nonlinear distortion but the challenge is keeping both harmonics and IM products from landing on tones. There was a paper published years ago at the AES with proposed collections of tones. I believe I shared a spreadsheet of those some time ago here. I'll try to find and share it again. One problem with lots of tones is crest factor. It starts to approach that of random noise limiting the useful measurement range with lots of tones.
Second- a classic test signal is a tone burst. It carries most of the qualities of a musical note with attack, sustain and decay, with the attack and decay instantaneous and sustain perfectly flat so any dynamic modulation should be pretty obvious.
Later this week I'll make some test tone bursts combining these. Analysis will not be real easy but there may be some trick around matching windows to samples etc. I'm not up to figuring out. However maybe someone here is. Given the claims about thermal modulations etc. it should be possible to tease those out with tone bursts.
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