I must admit I never read Kotelnikov's version (I don't understand Russian), nor Whittaker's version (while I do understand English) of the sampling theorem.
In any case, you are right that causal perfect filters are somewhat impractical because of their infinite delay, but you can approximate them very well by filters with a finite delay. The Parks-McClellan program (based on the Remez exchange algorithm) can readily produce filters with a passband ripple of a few millionth of a dB, 140 dB of stopband suppression and a transition band of 5 % of the sample rate while needing only a couple of milliseconds of delay, so I don't see why the remaining bandwidth limitation, passband ripple and aliasing would be a problem from a practical point of view.
In any case, you are right that causal perfect filters are somewhat impractical because of their infinite delay, but you can approximate them very well by filters with a finite delay. The Parks-McClellan program (based on the Remez exchange algorithm) can readily produce filters with a passband ripple of a few millionth of a dB, 140 dB of stopband suppression and a transition band of 5 % of the sample rate while needing only a couple of milliseconds of delay, so I don't see why the remaining bandwidth limitation, passband ripple and aliasing would be a problem from a practical point of view.
I'm not knowledgeable enough to know whether this makes any sense or not. But let us assume this is correct, how do you then make the step to health hazard?
Music is full of 'dynamically shifting spectra', and I still like music!
Jan
It doesn't cause me any stress. In fact, it relieves the stress of trying to keep vinyl noise free with the super-duper brush and anti-static gun, and ensuring CDs are scratch free.
I only wish thread titles didn't cause me stress, such as this one which should read 'digitised' or, if from that country, 'digitized'.
I only wish thread titles didn't cause me stress, such as this one which should read 'digitised' or, if from that country, 'digitized'.
Nope. After shift it is no longer music, because the spectra also squeezed. Means the harmonics are no longer 1:2:3:4:5:6... This is the most painful for audiophiles, who immideately react to that.
P.S. Today I will leave this forum for two days of Eastern Church Easter (Pascha), so will not respond.
Cheers.
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But what you describe is also happening in music with almost all instruments. So how come music doesn't make us sick?
Has this ever been tested in a controlled way? Or is this one of those cases 'Everybody knows that...'?
Happy Pascha!
Jan
So, it is being claimed that converting an analogue signal into digital forms adds artifacts that affect the signal's harmonic frequencies.
How did you arrive at this conclusion? Have you had your papers peer reviewed by others? If yes, did they arrive at the same conclusion?
Readers would be in a better position to discuss this if they know the precise mathematical tools, theorems and methodologies, that were used in your analysis.
How did you arrive at this conclusion? Have you had your papers peer reviewed by others? If yes, did they arrive at the same conclusion?
Readers would be in a better position to discuss this if they know the precise mathematical tools, theorems and methodologies, that were used in your analysis.
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Squeezed how much exactly?
It may be recalled that modern music is typically played in a tempered scale, so the tones are already out of perfect harmonic ratios. Also, harmonics of instruments are often out of tune with fundamentals. Moreover, vocal harmonies are often sung a little out of key to produce more pleasing vocal textures. In other words, there are already many imperfections from theoretically perfect harmonic ratios in real music that humans enjoy.
To make a case that some signal processing effect is objectionable to humans (or to some subset of humans), or to show exposure to same stresses humans in some way, there would be a lot of work to do. Probably a lot of expense involved, as well.
No instrument can give harmonics out of tune with fundamentals.The laws of physics forbid it. The fundamentals may be out of tune.The harmonics level varies with their own phase which is again governed by the laws of physics, but we can only measure that once we translate sounds in electrons movement and from that point on we deal with the electronics laws .There's no harmonics out of tune with the fundamental anywhere in nature...
Actually this is incorrect. Violins for instance produce harmonics that are NOT exact multiples of the fundamental. Other instruments, wind instruments, do the same.
The 'exact multiple' only applies to ideal situations like a vibrating string with zero thickness and attached at a zero dimensional point. In reality, the frequency of vibration also modifies the effective length and effective attachment points and thus the frequency. And this is all a dynamic phenomenon.
Jan
HOW is this possible?Don't tell me about the air density related to instrument walls mechanical impedance!...
Even if the chords thickness are a problem, the chords thickness is standardized today in all instruments .If they produce some out of tune resonances they must have a recognizable pattern which is known and taken in consideration by the instrument manufacturers in the final product tuning system so that they sing harmonically...Otherwise nobody would buy them.
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