As has now been reaffirmed....
The addition of two sines creates a modulated signal with an envelope and a carrier, that carrier at the average frequency, exactly equivalent to sin(a)cos(b).
Start with the sincos waveform, when the upper freq is removed, the unmodulated lower freq remains.
When an incorrect modulation is used, the raised sine, a carrier that does not flip every lobe is generated. Filter the upper freq, and what remains is the lower AND the carrier. Two sines.
As has been proven, the addition of two sines has an instantaneous frequency, and it is NOT the lower, not the higher. The instantaneous frequency will depend on the amplitude ratio of the two signals that made it through. If they are equal in amplitude, the inst freq is the exact average.
The incorrect modulation in this specific case, produced a 16 kHz lower, a 24 kHz upper, and a 20 kHz carrier. Passed through the brick, what came out was the 20 kHz and the 16 kHz. That sum has an instantaneous frequency of 18 kHz and a beat frequency half what was put into the filter.
That was what I have been pointing out all along. It was visually obvious in the time domain.
Using only an FFT to try and argue this stuff really doesn't exist is counterproductive, and leads to incorrect interpretations.
Jn
Agreed. This is not a rise time discussion per se. It is about a physical process that goes from zero amplitude to full scale amplitude instantly. A string is full acceleration at release. As Benb points out, the pickup filters that violating leading edge out by lumped (inductance) and interstitial (capacitance).
But the discussion of a physical process that will violate Fs by transient behavior is extremely valuable, the string being the simplest example I could think of.
Percussion instruments by their very nature, are far more likely to violate Fs at the start, however are a tad more complex in description.
Transient cluster?? Love it.
Jn
As with most of the things you raise on here as some demented enrichment play this does not parse as written.
You assume I meant zero to full scale as in gating a cosine at zero degrees.
No, I am speaking about a gated sine at zero degrees.
Demented... Well, the jury is still out on that one..😉
Jn
The only "learning" I would try to emphasize is, to always question assumptions.
Jn
A LOT!!! And YES, it matters!!!
Because that's not the whole story. The way an electric guitar pickup works has been described a few pages back: it's a crude device invented way before I was born and totally unable to capture the upper harmonics, with a resulting dull sound.
Alright for the jazz guys such as Charlie Christian who would turn the tone control all the way down given a chance. Then came the "modern" era when the players tried to regain the lost harmonics, like Link Wray who poked a screw drive through the cone of the speaker, or Eric Clapton who turned the Marshall stack all the way up.
Also in the time domain (why are people so focused on the frequency domain?): if you run your amp at (or usually above) its nominal power, and you hit a note, you'll have the peak power for a bit, then the power supply will sag and reduce the power delivery, so you're getting back the attack lost in the pickup, and more. Same goes with a compressor: it needs a few cycles before reaching its set level, so you could actually get more attack. Sorry Monsieur Fourier, music is no math.
The moral of the story is: you need the BW even if your transducer APPEARS to be severely limited.
Maybe you mean that the initiation of a sinus signal contains much higher frequencies than the sinus itself and if there where no filter to suppress those high frequencies, Nyquist would be violated.
Yes, but don't bend the message.
//
No it isn't because if it would you have invented a PM. To the patent office again 😉
//
(You know this... why did you choose to use the word "exactly"?)
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That's actually what I said.
I'm reminded of the nun scene in "airplane".
PM? Really, you felt the need to go there? Especially since a test waveform I find useful is a damped oscillator?
One of my hobbies entails the use of a pendulum in a vacuum, where an initial impulse will last for days. The fact that it will be a few nanometers lower every period is not pertinent to the discussion. So please, try not to divert.
Jn
No I am just thinking interms of simple harmonic motion, ignoring the damping and the travelling waves along the string of the reality situation. Just as when I put the munchkins on the swing in the garden when velocity is zero acceleration is maximum.
So i may be being dense to failing to see where the violating transient is. The rise time of the signal is effectively acceleration to the centre point but there are many other things that will delay the actual acoustic output, like the bridge.
Of course you're right, I should have said "adds noise" to the signal which is seen as a raised noise floor in a spectral analysis.
It was a rather good Cabernet. As you could have figured from the fact that I was talking about the first derivative, it should have been velocity. Of course. But otherwise I think my argument stands as a house.
If at time zero, a sine is instantly started, there is a discontinuity in the velocity and acceleration. That requires bandwidth to describe mathematically.
Jn
Edit:vacuphile, it is this discontinuity in velocity and accel I speak of. In my motion control work, some users want motion started abruptly at a specific velocity, they do not understand that I only have vel, accel, and jerk to play with, the system can never have BW to support instant velocity or instant velocity change.
A fine cab, yet you are online???
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Install a four pole lowpass filter between the switched sine generator and the recording device. This removes velocity, acceleration, jerk, and snap.
Folks who simulate distributed parameter transmission lines using lumped parameter approximate equivalent circuits, will recognize the problem and its workaround.
Folks who simulate distributed parameter transmission lines using lumped parameter approximate equivalent circuits, will recognize the problem and its workaround.
Mr. Neutron, it was dissing the cab, no doubt, and received punishment. When the concept has landed, many times words are a mere afterthought.
My point is that if a string is released, there is no sharp discontinuity in velocity. There is no difference between the string vibrating steady state and the string being released as its point of maximum stretch, both from the point of velocity and acceleration. No additional sinodal components are required to replicate this, but the innate fundamental plus harmonics of the string.
This is very different from starting to measure a signal from a random point. Infinite velocity is required to jump from 0 to the signal level, and this impulse requires a full zoo of sinoids into infinity to be reconstructed.
My point is that if a string is released, there is no sharp discontinuity in velocity. There is no difference between the string vibrating steady state and the string being released as its point of maximum stretch, both from the point of velocity and acceleration. No additional sinodal components are required to replicate this, but the innate fundamental plus harmonics of the string.
This is very different from starting to measure a signal from a random point. Infinite velocity is required to jump from 0 to the signal level, and this impulse requires a full zoo of sinoids into infinity to be reconstructed.
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😀
Actually, I do mean discontinuity in accel, the rate of change in velocity has the discontinuity. You are correct.
Every period will look exactly the same (assuming lossless of course), we certainly agree. It is the windowing at the start that differs.
I have never seen a sine summation that duplicates a sine that starts at zero time.
We certainly agree on that.
Always a pleasure..
Jn
Much appreciated electroj, interesting stuff.....although my question is how to find what the recording pedigree of a specific session/event was, not how the recording process works.
Bill, Thx for the links, Do specialty hi-res resellers like that website offer info on the recording itself (other than bit/sample rate?) I’m thinking I really need to step up my digital game so I can see for myself, right now I’m equipment limited to 24/48 playback but with a little more processing power to feed it my dac is capable of 32/384......looks like at a minimum I’d need about $2k in upgrades but would also allow more dsp capabilities and a few other things I’ve been wanting to try.
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Nevertheless it is a bit strange to criticize someone for sharing his own experience (because it was 40 years ago and already posted sometime before) while posting as argument second hand anecdotal evidence from people still loving their xy-microphone (since 40 years ago?),isn't it?
I don't know if it's true, but it seems plausible that due to the bandwidth restrictions of the CD format people were less thinking about any extended bandwidth mircrophones. AfAIR Sennheiser came up with their extended bandwidth microphones when it started to distribute music in less restricted formats.
Is it really a suprise that the music industry and (presumably) the majority of consumers are not _that_ interested in the best possible sound quality?
I've mentioned the loudness war the last time for a reason.
As fair I've read John Curl was talking about Crystal Clear records (and mentioned "hundreds") and as usual it its better to have mutual understanding about the meaning of terms before starting to debate .... 🙂
The number of different records published overall will be (I suppose) in the millions.