Dissident Sound on Nostr: i think i figured it out, from your link: "A mathematically ideal way to interpolate ...
i think i figured it out, from your link:
"A mathematically ideal way to interpolate the sequence involves the use of sinc functions. Each sample in the sequence is replaced by a sinc function, centered on the time axis at the original location of the sample with the amplitude of the sinc function scaled to the sample value, Subsequently, the sinc functions are summed into a continuous function.
A mathematically equivalent method uses the Dirac comb and proceeds by convolving one sinc function with a series of Dirac delta pulses, weighted by the sample values.
Neither method is numerically practical. Instead, some type of approximation of the sinc functions, finite in length, is used. The imperfections attributable to the approximation are known as interpolation error.
Practical digital-to-analog converters produce neither scaled and delayed sinc functions, nor ideal Dirac pulses. Instead they produce a piecewise-constant sequence of scaled and delayed rectangular pulses (the zero-order hold), usually followed by a lowpass filter (called an "anti-imaging filter") to remove spurious high-frequency replicas (images) of the original baseband signal."
in other words if the STRICT condition of less than 1/2 frequency is met the signal can be THEORETICALLY recovered, but is not actually recovered by any practical real world digital to analog converters because the amount of math required is untenable.
so actually us and them are both right. it works in theory but doesn't work in practice. i never actually understood this until now. this been bothering me for 25 years but back then Wikipedia was a lot more basic than it is now and of no help.
also i think hzrd149 (npub1ye5…knpr) may be muting me, so somebody let him know that the first link in your post is totally botched by NoStrudel ( stable ). i had to use Gossip to see what it links to.
"A mathematically ideal way to interpolate the sequence involves the use of sinc functions. Each sample in the sequence is replaced by a sinc function, centered on the time axis at the original location of the sample with the amplitude of the sinc function scaled to the sample value, Subsequently, the sinc functions are summed into a continuous function.
A mathematically equivalent method uses the Dirac comb and proceeds by convolving one sinc function with a series of Dirac delta pulses, weighted by the sample values.
Neither method is numerically practical. Instead, some type of approximation of the sinc functions, finite in length, is used. The imperfections attributable to the approximation are known as interpolation error.
Practical digital-to-analog converters produce neither scaled and delayed sinc functions, nor ideal Dirac pulses. Instead they produce a piecewise-constant sequence of scaled and delayed rectangular pulses (the zero-order hold), usually followed by a lowpass filter (called an "anti-imaging filter") to remove spurious high-frequency replicas (images) of the original baseband signal."
in other words if the STRICT condition of less than 1/2 frequency is met the signal can be THEORETICALLY recovered, but is not actually recovered by any practical real world digital to analog converters because the amount of math required is untenable.
so actually us and them are both right. it works in theory but doesn't work in practice. i never actually understood this until now. this been bothering me for 25 years but back then Wikipedia was a lot more basic than it is now and of no help.
also i think hzrd149 (npub1ye5…knpr) may be muting me, so somebody let him know that the first link in your post is totally botched by NoStrudel ( stable ). i had to use Gossip to see what it links to.