As I stated earlier, the trumpet is does not produce a symetric signal. Hugh Masakela looks almost like a rectified sine with points on top and a rounded neg swing. Again, this is music, not steady simple sinusoids.
Watch some music. you'll also notice how big the tranients are in compairison to the average (unless you listen to pop rock). Justifies 200W+ amps.
Watch some music. you'll also notice how big the tranients are in compairison to the average (unless you listen to pop rock). Justifies 200W+ amps.
lumanauw said:
As you mention, these waveforms are not symmetrical. They are usually made of a low frequency carrier with different harmonics on top of low and high halves of the carrier respectively. That usually leads to asymmetric peak values also. Inverting the polarity of such a signal is equivalent to inverting the polarity of all its components.
However, the only things that are well proven to be perceived by our ear are the amount of energy in each frequency band and the difference in time arrival between ears of energy level changes.
But, if some block in the sound chain is distorting and adding even harmonics to an asymmetric signal, the resulting signal will have different frequency content depending on polarity.
BTW: Multi-way speakers are playing different frequency ranges with different polarities. Paranoids should also care about that (I don't care because I've already given up trying to detect phase shifters by ear).
Let me give you my second Q of elementary school boy.
As far as I understand, the musical instruments are based on the ability of strings or air columns to excite various harmonics, that are mechanical vibrations over the frequency range from 20 to 20,000 Hz.
(Assuming that the music is after all the superposed mechanical vibrations) Is there any one asymmetric mechanical vibration . . . ?
Thanks.
As far as I understand, the musical instruments are based on the ability of strings or air columns to excite various harmonics, that are mechanical vibrations over the frequency range from 20 to 20,000 Hz.
(Assuming that the music is after all the superposed mechanical vibrations) Is there any one asymmetric mechanical vibration . . . ?
Thanks.
Workhorse said:
My voice is very bad to be an example . . .
Note that the square waves or sawtooth waves are, as an example, by a sum of sines of different frequency and amplitude (harmonic summation). Of course, they do not look like a simple sine, but look like square waves and sawtooth waves, or whatever . . .
What is the music wave type, then?
Sinusoids, rectangulars etc are not music they are periodic signals.
Each period looks EXACTLY like the one before and they can therefore be predicted until eternity. Such signals can be "dissected" via Fourier-ANALYSIS. They give a so called line spectrum consisting of discrete sinewaves.
From the information-theory point-of-view they don't carry any information since every subsequent state is known in advance. But information as such is something like "removed uncertainty" (maybe someone of English mothertongue knows a better expression). So their use as test signals for information transmission systems 8like HiFi) is of limited value.
Music is NOT periodic. Only in very few instances will you find two subsequent signal periods that are exactly the same. Such signals can be analysed by the use of the Fourier-TRANSFORM. Its result is not a line spectrum (consisting of discrete sinusoids) but a density spectrum.
Therefore it is incorrect to regard music just as a sum of sinusoids.
Regards
Charles
Each period looks EXACTLY like the one before and they can therefore be predicted until eternity. Such signals can be "dissected" via Fourier-ANALYSIS. They give a so called line spectrum consisting of discrete sinewaves.
From the information-theory point-of-view they don't carry any information since every subsequent state is known in advance. But information as such is something like "removed uncertainty" (maybe someone of English mothertongue knows a better expression). So their use as test signals for information transmission systems 8like HiFi) is of limited value.
Music is NOT periodic. Only in very few instances will you find two subsequent signal periods that are exactly the same. Such signals can be analysed by the use of the Fourier-TRANSFORM. Its result is not a line spectrum (consisting of discrete sinusoids) but a density spectrum.
Therefore it is incorrect to regard music just as a sum of sinusoids.
Regards
Charles
You should cure your misunderstanding with some texts on fourier transform, because you are obviously NOT phase accurate
Any arbitrary signal can be expressed both as set of sinewaves or as a set of instantaneous amplitude values. Both representations are equivalent and interchangeable.
I'm seeing little phase, frequency and amplitude accuracy in that thread.
p.s. Your DSL lines would no longer work if what I tell wasn't true.
Any arbitrary signal can be expressed both as set of sinewaves or as a set of instantaneous amplitude values. Both representations are equivalent and interchangeable.
I'm seeing little phase, frequency and amplitude accuracy in that thread.
p.s. Your DSL lines would no longer work if what I tell wasn't true.
Fourier theorem . . .
Thanks for the in-depth explanation, P_A.
If the restoring force for an oscillator is nonlinear, the oscillation is nonsinusoidal and has a spectrum of frequencies. Therefore, a nonlinear device (maybe music) can be used to generate oscillations at integral multiples of the fundamental frequencies.
Very intersting discussion . . .
Thanks for the in-depth explanation, P_A.
If the restoring force for an oscillator is nonlinear, the oscillation is nonsinusoidal and has a spectrum of frequencies. Therefore, a nonlinear device (maybe music) can be used to generate oscillations at integral multiples of the fundamental frequencies.
Very intersting discussion . . .
1. ) I keep to what I said.
2.) I don't see what these relationships have to do with the DSL working or not. It is not the rules themselves making a transmission system work but rather their thoughtful application. We never ever have ideal situations in any technical area. There are always physical and mathematical laws that are against us. So we have to make the best out of it.
Regards
Charles
2.) I don't see what these relationships have to do with the DSL working or not. It is not the rules themselves making a transmission system work but rather their thoughtful application. We never ever have ideal situations in any technical area. There are always physical and mathematical laws that are against us. So we have to make the best out of it.
Regards
Charles
Theoretically all signals can be expressed as summation of signwaves if the infinite series can be calculated, but since nothing infinite can be calculated, therefore in reality you can only get close to the original signal but not exact.
Additionally, if you are able to look into 0.1 ms resolution of a piece of audio signal, you will find that music signals are not symmetric, thus if the phase in inverted during playback, you will notice the difference on a good audio system.
Additionally, if you are able to look into 0.1 ms resolution of a piece of audio signal, you will find that music signals are not symmetric, thus if the phase in inverted during playback, you will notice the difference on a good audio system.
Real world signals do have a noise floor and are bandwidth limited, so the required series are no longer infinite.
Indeed most people here is listening to CD quantized audio. Such a digital datastream has finite components and can be perfectly converted to the frequency domain and back to the time domain with no data loss.
phase accurate:
I would rather your DSL and all your electronics equipment followed your frequency rules (most appliances would no longer work!).
p.s. The number of frequency components in a CD track is equal to the number of samples.
Indeed most people here is listening to CD quantized audio. Such a digital datastream has finite components and can be perfectly converted to the frequency domain and back to the time domain with no data loss.
phase accurate:
I would rather your DSL and all your electronics equipment followed your frequency rules
(most appliances would no longer work!).p.s. The number of frequency components in a CD track is equal to the number of samples.
Ah...Fourrier analysis. Like any mathematical model it has its uses and its limitations.
A couple things to be wary of:
1) Fourrier is a mathematical means to convert between a time domain REPRESENTATION of something to a frequency domain REPRESENTATION. I highlight the word to emphasize that this is a model and isn't REAL in and of itself.
2) When you do a transform on a time domain signal between time A and time B, the spectral representation you get is not of that signal. Rather it is of that signal repeated infinitely over time, both before A and after B. So Fourrier is only exact if you have an inifinitely repetitive signal. Which you don't.
The frequency domain representation is a mathematically exact transform of a signal which does not exist. Just suppose we ignore this and accept some error, then the next mistake is to assume that because the model decomposes the signal into discrete sinusoids that each sinusiod can be treated independently in our thinking about amplifier design. No. The model of creating a signal by summing sinusoids assumes a perfect LINEAR system. In analogue electronics the system is NOT linear. One plus one does not equal two.
So don't make the mistake of assuming if an amp reproduces each component sinusoid perfectly on its own that it will reproduce all of them together perfectly. And also don't make the mistake of thinking you can accurately predict time domain response from frequency domain response in a non-linear system.
Be very careful before thinking of a music signal as a sum of discrete sinewaves. It may lead you to design an amp that sounds mathematically perfect
A couple things to be wary of:
1) Fourrier is a mathematical means to convert between a time domain REPRESENTATION of something to a frequency domain REPRESENTATION. I highlight the word to emphasize that this is a model and isn't REAL in and of itself.
2) When you do a transform on a time domain signal between time A and time B, the spectral representation you get is not of that signal. Rather it is of that signal repeated infinitely over time, both before A and after B. So Fourrier is only exact if you have an inifinitely repetitive signal. Which you don't.
The frequency domain representation is a mathematically exact transform of a signal which does not exist. Just suppose we ignore this and accept some error, then the next mistake is to assume that because the model decomposes the signal into discrete sinusoids that each sinusiod can be treated independently in our thinking about amplifier design. No. The model of creating a signal by summing sinusoids assumes a perfect LINEAR system. In analogue electronics the system is NOT linear. One plus one does not equal two.
So don't make the mistake of assuming if an amp reproduces each component sinusoid perfectly on its own that it will reproduce all of them together perfectly. And also don't make the mistake of thinking you can accurately predict time domain response from frequency domain response in a non-linear system.
Be very careful before thinking of a music signal as a sum of discrete sinewaves. It may lead you to design an amp that sounds mathematically perfect
Agreed but here we already have a very special case of a Fourier transform i.e. a DISCRETE Fourier transform. The original signal didn't have a discrete spectrum even if bandwidth limited !
A digital storage system is LOSSY (as every other one also) if you look at it from first analog input to the last analog output. The only thing that works without loss is the storage and retrieval of the DIGITAL data.
Regards
Charles
Per fourier analysis a square wave is equivalent to an infinite seiries of sines that are odd ordered harminics of the fundamental period of the square wave. Don't ask me to do the math, it's over my head. However, for a more intuitive understanding consider that a rough test for flat frequency response is ti feed a piece of equipment a square wave and look at the output square wave. If the the top is sloped it indicates either rising or falling frequency response. This is consistenr with the idea that the squasre wave is a sum of sines, even if it wasn't generated by literally summing sines.
It is true that any signal can be expressed as sum of sinewaves (even non-periodical signal), but so what? You only need to sum two sinewaves to get asymmetrical signal, that will look completely different when polarity is changed. If ears have different response to rising and falling pressure it might also sound different with reversed polarity. And it's only two completely symmetrical sinewaves. Not thousands that we are talking about with music signals. So fourier transform does not lead to any theoretical evidence against audibility of the absolute polarity.
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