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Originally Posted by chesebert /img/forum/go_quote.gif
So since everyone uses some type of filter, I presume no one has figuered out how to actually use the damn formula.
Here is the formula for your amusement: Xa(t) = Summation [Xa * (n/(2B)) ( (sine2piB (t-n/2B))/ (2piB (t-n/2B))], from negative infinity to infinity.
You presume wrong. The filter is there to implement the very formula.
Actually, the perfect implementation is what is called a brickwall filter, or Sinc filter. The sinc function is defined by sinc(t) = sin(t) / t). But these are not used in audio because they lead to unwanted artifacts. They introduce ringing at the Nyquist frequency. That's the normal behaviour of perfect sampling. First you lowpass your original, which introduce a lot of ringing, then you sample, then you reconstruct your original lowpassed signal with all its ringing.
Using a lowpass filter with an cosinus attenuation profile, as viewed in the frequency domain, is much cleaner. If you can generate lowpass filters by yourself, compare a given sample lowpassed at 10 kHz with a perfect sinc filter, then with a cosine filter starting at 9500 Hz and ending at 10500 Hz.
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Originally Posted by
chesebert
On to quantization errors:
Theoretically, quantization of analog sigansl always results in a loss of information.
Right. It introduce noise at -96 dB if you quantize with 16 bits, at -144 dB if you quantize at 24 bits etc.
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My question is whether or not rates above 44.1 khz will provide greater detail within the spectrum we can hear even though we cannot hear the ‘new’ frequenzies that they can reproduce.
Yes, by using the additional bandwidth to add noise shaped dither, you can increase the resolution in you working bandwidth. It is the same thing as increasing the number of bits.
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Isak said:
sample rate of 8 hz, right? If that is the case wouldn’t you only be able to reproduce 4 tones (1, 2, 3 and 4 hz) on such a recording?
Not at all. You can reproduce any frequency below 4 Hz with a sampling rate of 8 Hz. 3.255664 Hz is perfectly possible, for example.
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Originally Posted by chesebert /img/forum/go_quote.gif
The most basic one is the zero-order-hold D/A, which results in the stepped response many magazines like to print. Then stepped signal is "smoothed" out by a LPF (yeah..like that's a really accurate representation of the analog signal). I believe we have moved beyond that, but still making crap up by not using the formula.
No ! The signal is oversampled first, which allow to apply the Nyquist formula with good accuracy.
Only very high end DACs directly lowpass the zero-order hold. That indeed leads to crappy results (-2 dB of treble in the audible range). That's a coloration that they either believe is "more musical", either deliberately introduce to distinguish them from their competitors.
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Originally Posted by
chesebert
oh if you can believe this, at 96khz sampling frequency, D/A has less crap to make up in between samples.
There is more crap between the samples ! All the ultrasonic noise, parasites from computer displays etc is recorded and fed into the amplifier during playback.
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The higher the sampling freq. the less deleterious effects of brick wall filters on the passband, including aliasing, etc.
There is no deleterious effects of brick wall filters in the audible range at 44.1 kHz.
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- Upper harmonics of fundamentals do lend "air" and aliveness to a recording
No, they don't. They're inaudible.
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- Because upper harmonics are generally greatly diminished in amplitude from the fundamental, low level resolution and detail is also critical for the preservation of an accurate recording so not only is sampling frequency important, but bit depth as well so that low levels can be faithfully maintained and not lost in the dither.
16 bits are enough in all practical situations for this purpose.