Hey guys I just came up with a mathematical theory on why speakers and components sound different, and the good part is that it takes one chart to illustrate it.
It's a square wave at 40khz.
A square wave contains infinite harmonics up to it's frequency point. A square wave also gets a record of its impulse (instantaneous speed and Q (damping))
Okay, so why 40khz? It's a fancy mathematical principle, but all information is contained in a frequency range, when twice that frequency is sampled. That's why CD's, MP3's, are recorded @ 44.1khz (the resolution limit was set a bit higher than human capacity at 22,000hz.
Only 40khz is needed....if you have perfect hearing... less in reality for most people.
Sample rates
Be careful, don't go blowing up your speakers with square waves lol. This theory should work for electronics /crossovers too.
It's a square wave at 40khz.
A square wave contains infinite harmonics up to it's frequency point. A square wave also gets a record of its impulse (instantaneous speed and Q (damping))
Okay, so why 40khz? It's a fancy mathematical principle, but all information is contained in a frequency range, when twice that frequency is sampled. That's why CD's, MP3's, are recorded @ 44.1khz (the resolution limit was set a bit higher than human capacity at 22,000hz.
Only 40khz is needed....if you have perfect hearing... less in reality for most people.
Sample rates
Be careful, don't go blowing up your speakers with square waves lol. This theory should work for electronics /crossovers too.
I do not understand your point. Could you please explain the link between the Nyquist theorem and the sound of speakers? What chart are you referring to?
Basically a square wave up to 40khz gives us data on: impulse response, frequency reaponse range, Q (damping), phase characteristics, and harmonic data up to the set frequency limit.
Let's imagine a speaker or electronic component can play a perfect square wave at 40khz, then it would have the "ultimate resolution". Amplifiers and dacs can do this, but I dont think any crossover or speaker can.
You could also imagine as ringing or overshoot as "sharp". Hell maybe we even think a perfect square is "sharp" and like something with rolled-off edges.
Let's imagine a speaker or electronic component can play a perfect square wave at 40khz, then it would have the "ultimate resolution". Amplifiers and dacs can do this, but I dont think any crossover or speaker can.
You could also imagine as ringing or overshoot as "sharp". Hell maybe we even think a perfect square is "sharp" and like something with rolled-off edges.
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If you want to measure the behaviour of a speaker with one single maesurement then you will have to measure its impulse response and not its response to a rectangular signal. Periodic signals have a line spectrum while signals like a pulse have a density spectrum which is much more accurate. Thre frequency response can then be calculated by the means of a fourier transform. In practice the impulse response is not measured by the use of pulses directly because of its not so ideal crest faCTOR.
But you are then still missing harmonic dirstortion, lobing …..
Regards
Charles
But you are then still missing harmonic dirstortion, lobing …..
Regards
Charles
No amps or DACs will ever be able to do this as no electronic devices have infinite frequency response.
Not many amplifiers or DACs can reproduce a perfect 40khz square wave. And why 40khz? It contains no frequencies in the audio range?
Are you talking about a sweep now?
A fixed 40kHz square wave will tell you nothing about frequencies below 40kHz and would therefore be completely useless for audio purposes.
Ummm... no... it contains all harmonics above it's fundamental frequency. The first harmonic above 40khz is 80khz.
Nice idea though.
Bill Waslo’s IMP audio analyzer—about 20 years ago. The IMP was a sophisticated speaker testing system that could test loudspeaker frequency response and complex impedance using impulse response (later upgraded to MLS).
... Except, as others have pointed out, a square wave contains harmonics above the fundamental frequency. ie, 40kHz, 120kHz, 200kHz, 280kHz, etc. Nothing in the audio band.
If you did want to put out a 40kHz square wave, then you'll need specialist ultrasonic stuff. There'll be no content there for a typical HiFi speaker.
Assuming you've just made an error in your reasoning and actually you think a 40Hz square wave is a good idea, my initial thought is that, okay, you might find a system that can produce a 40Hz square wave.
If the square wave is imperfect (most, I suspect, would be) then how do we interpret those results?
Would it be possible to spot a peak/dip combo at 10-12kHz and reliably identify those features?
There's also limited data in that 40Hz square wave. What happens in the 50-100Hz octave? We have no idea.
It's great that you're thinking outside the box, but I'm afraid this one's not particularly useful.
Chris
A square wave is made up of ODD harmonics only. So in the case of a 40Khz square you would have 40, 120, 280 and so on. In addition the harmonics are added at ever decreasing levels. If the OP wants a system to reproduce a square wave of 40KHz then said system will need one heck of a bandwith - at least 280Khz to make a reasonable job. Plenty of amplifiers will struggle with that never mind speakers.
Utterly useless for what the OP is supposedly trying to do. Is there a translation error here? - because the more you look at it the original post makes no sense.
Utterly useless for what the OP is supposedly trying to do. Is there a translation error here? - because the more you look at it the original post makes no sense.