6 ms·

Nothing reproduces the original signal, it's distorted by the inertia and impedance of the microphone and amplifier that recorded it. As you know it's then pas

Nothing reproduces the original signal, it's distorted by the inertia and impedance of the microphone and amplifier that recorded it. As you know it's then passed through an ADC and stored as a sine wave, cause no one is mastering inaudible square waves on a reel for kitsch value.

ChrisLomont 4y ago
Agreed - and after quantization nothing reproduces the signal before quantization. So claiming Nyquist-Shannon proves the OP wrong is incorrect. >It's then passed through an ADC and stored as a sine wave. After an ADC it is not stored as a sine wave. It's stored as quantized values, thus the 'D' in Analog-to-Digital-Converter. >cause no one is mastering inaudible square waves on a reel for kitsch value Pretty much all audio processing is now done digitally, which is the same as square waves - each jump in discrete digital value is a step function. When you push it through properly engineered output devices the squareness is smoothed somewhat, but still has frequency ringing because it is square edged. Take a good speaker, take something that can grab audio spectrum far beyond audible, and look at the output. There is stuff far outside human hearing coming from the speaker because of these square waves. Naively, this is because the Fourier transform of the square waves have high frequency ringing, and this is because the playback has sharp edges. (See this [1] for some related info for example). Also Nyquist-Shannon is about frequencies, not about amplitudes, which are also quantized. Physical devices making sound have a (up to quantum level) continuum of possible amplitudes. Quantization necessarily loses this forever. For example, take A0, the lowest standard piano note, freq ~27.5. Sample a pure sine wave at 60 hz, in 8 bit audio. Now record this tone going from no sound up to very loud, very smoothly, over some time. The 8-bit audio will necessarily have less smoothness to it, since it is 8 bit audio. It perfectly matched your Nyquist-Shannon claim, yet it fails to reproduce what you hear. Take 16 bit audio - better. Take 32-bit or floating point audio, better again. And so on. I agree that really well engineered systems can push the errors outside human hearing, but to claim they reproduce the same signals is incorrect. The gist of this is: to get the most accurate reproduction of the original, merely sampling at 2x the top human freq is no where near state of the art. An counter-intuitive example: to get the best quality and most accurate output, one needs to add noise to the input. The reason is that due to quantization, if some input signal is between possible quantized output values, adding noise (usually Gaussian, of std dev ~sqrt(step size)) makes that signal trigger both high and low quantized values in proportion to the intermediate value, making the output playback the step square waves as close to approximating the original as possible. The entire field is full of stuff like this. For reference, I've worked on stuff like this on and off for decades, having written libraries used by others, designed high end audio simulation software (think raytracer for audio in physical settings to help design stadiums), written articles, and produced hardware in a company I own. I am quite familiar with all sorts of audio processing. [1] https://electronics.stackexchange.com/questions/156197/can-computer-speakers-emit-ultrasound/156203#156203 https://electronics.stackexchange.com/questions/156197/can-c...
- gwbas1c 4y ago
  > which is the same as square waves ... There is stuff far outside human hearing coming from the speaker because of these square waves. Maybe back in the 1980s on some of the early consumer digital equipment; but those problems were solved in the early 1990s by oversampling in the DAC, and then using some basic analog filtering far above the human hearing range. IE, a consumer DAC will oversample a 44.1khz signal to (example) 705.6khz in the digital domain; and then use a very gentle analog lowpass filter to deal with the ultrasonic distortion. At that point the difference between the original analog signal and the one coming from the DAC is approximately as accurate as if there was no DAC in the first place. (Granted, some people can hear up to 27khz, which is why some people like 96khz sampling rates.)
  - ChrisLomont 4y ago
    >but those problems were solved in the early 1990s by oversampling in the DAC, and then using some basic analog filtering far above the human hearing range. You're writing about the sampling end. I said the physical speaker creates high frequencies on playback based on material properties of the device - and I gave a decent reference where you can read the discussion on it. No amount of filtering at the sampling end will remove physically created noise due to the physical playback membrane that moves air to create sound waves. I am fully aware of using bandpass filters during sampling. I use them all the time to remove things I don't need before doing things like wavelet transforms to pull music information out of the result. And I often design things up front based on the physical playback mechanism if I know it ahead of time. Or if the hardware (such as embedded devices) will only sample at certain rates, or certain bit depths. Knowing as much about the entire audio path up front helps design each and every piece of the complete signal path. Here's a simple example: basic speakers are an electromagnet coil - apply voltage V and the membrane jumps to a position. Different values for V make different positions. Quantized playback, going through an DAC, will create distinct voltage levels. 8 bits will give 256 such levels. 16 bits, 65536 levels. When that hits a speaker, the speaker membrane jumps to that level. There is some noise with inertia and momentum and point to point, but the end effect is the same - the speaker trying to make a square wave edge. There is no uniformly smooth movement from position to position - only jumps. This can be seen by putting a mirror on the speaker, and bouncing a laser off it to a large wall, and record the wall in high speed - you see jumpy movement. Fiddle sometime with a pure tone sent at various bit depths to a speaker and watch the laser. Now, these movements create frequencies in output not in the original analog signal, not in the digital signal, but purely as a physical artifact. And they depend on the playback device - all sorts of work and research is spent on speaker tech, materials, reproducible construction, and on and on, to make the output physical waveform as uniform and smooth as possible over all the possible input voltage jumps and frequencies desired. But all are imperfect, similarly to how all physical lenses (well, except 1-1 and flips) must distort images. It is all about the tradeoffs.

ChrisLomont 4y ago

Agreed - and after quantization nothing reproduces the signal before quantization. So claiming Nyquist-Shannon proves the OP wrong is incorrect. >It's then passed through an ADC and stored as a sine wave. After an ADC it is not stored as a sine wave. It's stored as quantized values, thus the 'D' in Analog-to-Digital-Converter. >cause no one is mastering inaudible square waves on a reel for kitsch value Pretty much all audio processing is now done digitally, which is the same as square waves - each jump in discrete digital value is a step function. When you push it through properly engineered output devices the squareness is smoothed somewhat, but still has frequency ringing because it is square edged. Take a good speaker, take something that can grab audio spectrum far beyond audible, and look at the output. There is stuff far outside human hearing coming from the speaker because of these square waves. Naively, this is because the Fourier transform of the square waves have high frequency ringing, and this is because the playback has sharp edges. (See this [1] for some related info for example). Also Nyquist-Shannon is about frequencies, not about amplitudes, which are also quantized. Physical devices making sound have a (up to quantum level) continuum of possible amplitudes. Quantization necessarily loses this forever. For example, take A0, the lowest standard piano note, freq ~27.5. Sample a pure sine wave at 60 hz, in 8 bit audio. Now record this tone going from no sound up to very loud, very smoothly, over some time. The 8-bit audio will necessarily have less smoothness to it, since it is 8 bit audio. It perfectly matched your Nyquist-Shannon claim, yet it fails to reproduce what you hear. Take 16 bit audio - better. Take 32-bit or floating point audio, better again. And so on. I agree that really well engineered systems can push the errors outside human hearing, but to claim they reproduce the same signals is incorrect. The gist of this is: to get the most accurate reproduction of the original, merely sampling at 2x the top human freq is no where near state of the art. An counter-intuitive example: to get the best quality and most accurate output, one needs to add noise to the input. The reason is that due to quantization, if some input signal is between possible quantized output values, adding noise (usually Gaussian, of std dev ~sqrt(step size)) makes that signal trigger both high and low quantized values in proportion to the intermediate value, making the output playback the step square waves as close to approximating the original as possible. The entire field is full of stuff like this. For reference, I've worked on stuff like this on and off for decades, having written libraries used by others, designed high end audio simulation software (think raytracer for audio in physical settings to help design stadiums), written articles, and produced hardware in a company I own. I am quite familiar with all sorts of audio processing. [1] https://electronics.stackexchange.com/questions/156197/can-computer-speakers-emit-ultrasound/156203#156203 https://electronics.stackexchange.com/questions/156197/can-c...

gwbas1c 4y ago
> which is the same as square waves ... There is stuff far outside human hearing coming from the speaker because of these square waves. Maybe back in the 1980s on some of the early consumer digital equipment; but those problems were solved in the early 1990s by oversampling in the DAC, and then using some basic analog filtering far above the human hearing range. IE, a consumer DAC will oversample a 44.1khz signal to (example) 705.6khz in the digital domain; and then use a very gentle analog lowpass filter to deal with the ultrasonic distortion. At that point the difference between the original analog signal and the one coming from the DAC is approximately as accurate as if there was no DAC in the first place. (Granted, some people can hear up to 27khz, which is why some people like 96khz sampling rates.)
- ChrisLomont 4y ago
  >but those problems were solved in the early 1990s by oversampling in the DAC, and then using some basic analog filtering far above the human hearing range. You're writing about the sampling end. I said the physical speaker creates high frequencies on playback based on material properties of the device - and I gave a decent reference where you can read the discussion on it. No amount of filtering at the sampling end will remove physically created noise due to the physical playback membrane that moves air to create sound waves. I am fully aware of using bandpass filters during sampling. I use them all the time to remove things I don't need before doing things like wavelet transforms to pull music information out of the result. And I often design things up front based on the physical playback mechanism if I know it ahead of time. Or if the hardware (such as embedded devices) will only sample at certain rates, or certain bit depths. Knowing as much about the entire audio path up front helps design each and every piece of the complete signal path. Here's a simple example: basic speakers are an electromagnet coil - apply voltage V and the membrane jumps to a position. Different values for V make different positions. Quantized playback, going through an DAC, will create distinct voltage levels. 8 bits will give 256 such levels. 16 bits, 65536 levels. When that hits a speaker, the speaker membrane jumps to that level. There is some noise with inertia and momentum and point to point, but the end effect is the same - the speaker trying to make a square wave edge. There is no uniformly smooth movement from position to position - only jumps. This can be seen by putting a mirror on the speaker, and bouncing a laser off it to a large wall, and record the wall in high speed - you see jumpy movement. Fiddle sometime with a pure tone sent at various bit depths to a speaker and watch the laser. Now, these movements create frequencies in output not in the original analog signal, not in the digital signal, but purely as a physical artifact. And they depend on the playback device - all sorts of work and research is spent on speaker tech, materials, reproducible construction, and on and on, to make the output physical waveform as uniform and smooth as possible over all the possible input voltage jumps and frequencies desired. But all are imperfect, similarly to how all physical lenses (well, except 1-1 and flips) must distort images. It is all about the tradeoffs.