xiphmont’s ‘There is no point to distributing music in 24 bit/192 kHz’
Reply #105 – 2012-10-14 02:34:02
No disagreements there, I was just wondering how it can perfectly reproduce the wave when the sample points have to be approximated, the ideal position for them lies at the end of an infinite series of decimals so naturally those get truncated at one point or another and what I'm wondering is if this truncation implies any errors in the reproduction concerning amplitude or the resulting frequency itself. The displayed sample points only appear to be chaotic. They are actually accurately positioned to the limits of the numeric resolution. There is one sine curve that exactly (to the limits of the resolution) passes through all of the sampling points. Any inaccuracy introduced by "truncation of an infinite series" appears as noise in the output from the D to A conversion. This noise will be equal to or less than that represented by the least significant bit of the digital signal. When you digitise a signal to 16 bits, each sample has to be represented by one of 65535 different numbers. If it falls part way between two possible values, it is set to the nearest. This means the digitised value can be up to half a "bit's worth" different than the original input. When you reconvert it back to analog, the output can be up to half a bit plus or miinus different than the original. This is noise, because it is different than the original signal. For a 16 bit signal, this noise is insignificant. Try it for yourself. Use Reaper or Audacity to generate a 1 KHz signal using all 16 bits (0dBfs). Do it again using only the least significant bit (-96 dBfs). Play the 16 bit signal at the loudest level you can stand. Without changing the volume setting, play the 1 bit signal. Can you hear it? (I doubt it). Once you understand this, we'll move on to dither. Edit: mjb2006's picture would have saved me a thousand words if I'd seen it in time...