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24/192 music downloads make no sense

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Re: 24/192 music downloads make no sense

#241

Post by thescriptkiddie »

hamiltonkibbe wrote: post #156
thescriptkiddie wrote: post #117

Earlier quoted context omitted.

Is there a difference? Audio is one-dimensional, frequency is just the derivative of amplitude. An arbitrarily high frequency sound wave becoming louder and softer 440 times per second is just as much an A as a 440 Hz sound wave at constant volume. A lot of cheap audio gear even uses a "1-bit DAC" that is just very high frequency PWM.

The signal you describe in your comment is very much NOT an A. look at the fourier transform of a 1kHz signal modulated by a 440Hz signal, and you won't see any frequency component at 440Hz, nor any integer multiple 440Hz! You can look at your "A440 at a constant volume" example as a 0Hz(DC) signal getting louder and softer 440 times a second, but this is the only case in which your example holds. Amplitude modulatio…

All of that makes sense if we consider the case of amplitude modulation, which is multiplication. But if we are talking about the interference patterns caused by two overlapping audio signals, that is addition, is it not?

Re: 24/192 music downloads make no sense

#242

Post by hamiltonkibbe »

thescriptkiddie wrote: post #241
hamiltonkibbe wrote: post #156

Earlier quoted context omitted.

The signal you describe in your comment is very much NOT an A. look at the fourier transform of a 1kHz signal modulated by a 440Hz signal, and you won't see any frequency component at 440Hz, nor any integer multiple 440Hz! You can look at your "A440 at a constant volume" example as a 0Hz(DC) signal getting louder and softer 440 times a second, but this is the only case in which your example holds. Amplitude modulatio…

All of that makes sense if we consider the case of amplitude modulation, which is multiplication. But if we are talking about the interference patterns caused by two overlapping audio signals, that is addition , is it not?

The two signals which are "interfering" are added together. The amplitude of the resultant signal varies sinusoidally, as the instantaneous phase difference between the two signals goes from 0->2pi. One way of describing the signal would be that it is a separate tone (sitting in the middle of the two frequencies) being amplitude modulated by a signal at the beat frequency... which is what you hear and why you "hear" the beat frequency) I went with this way of describing the signal because you were talking about "an arbitrarily high frequency signal getting louder and softer 440 times per second" which is the definition of amplitude modulation.

Counterintuitively, there is no frequency component generated at the beat frequency when you sum a 1kHz and 1.001kHz signal, its easy to test that out with matlab, octave, scipy/numpy/matplotlib, etc. Generate the two signals, add them together, and look at the Fourier transform, you'll see two components, one at 1kHz and one at 1.001kHz (assuming you take a long enough window to have that type of resolution) and no component at the beat frequency. A third sinewave doesn't just jump out of nowhere when you add two separate sinewaves together.

If you take the sum of those two signals and run them through an ideal brickwall highpass filter at 999Hz so there are no frequency components below 999Hz, you'll still "hear" the beat frequency because it isn't a separate spectral component, its just the two signals slowly going out of phase, cancelling eachother out, and then going back in phase and boosting the amplitude.

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