There are others allowing spectral leakage of images to get "pretty" waveforms you don't need splines to do the wrong thing. Funny all this worry over playback of impossible digitally generated signals. These days it is safe to say all your music has already gone through a lot of those 8-legs and some horrifying "ringing" digital filters and awful text book generated sample rate conversion.
Yep, and strangely when I design gear using the math from my DSP books and use digital filters from the standard references it usually works more then well enough to sell to studios and broadcasters, when I ignore the correct maths it seldom works at all.....
I do wish the whole stupid 1KHz (Or worse 10KHz) 'square wave' (which is never band limited, so is not at all what it appears) 'test' would just die already, all it tells you is that the writer is 'hard of thinking'.
Regards, Dan.
Seems to me that the place for a spline would be at the output end, since nominally the goal is to create a smooth function free of nasty things like "overshoot" and "ringing"
Using the spline generator to create what would be effectively interpolative oversampling is an interesting idea, but probably ends up being of limited value since the output side is still going through the same bandwidth limiting reconstruction filters. To get this effect of finding a point (or points) inbetween 2 data points i suspect there are simpler and faster means than dealing with all the issues that splines create. (you'd likely end up with some sort of adaptive spline generating algorithm, I'm guessing)
No matter what the spline is not going to be 100% faithful to the original waveform, but then again the typical digital methods are not either.
The question is how will the ear receive a spline vs. a LP filtered reconstruction.
_-_-
Using the spline generator to create what would be effectively interpolative oversampling is an interesting idea, but probably ends up being of limited value since the output side is still going through the same bandwidth limiting reconstruction filters. To get this effect of finding a point (or points) inbetween 2 data points i suspect there are simpler and faster means than dealing with all the issues that splines create. (you'd likely end up with some sort of adaptive spline generating algorithm, I'm guessing)
No matter what the spline is not going to be 100% faithful to the original waveform, but then again the typical digital methods are not either.
The question is how will the ear receive a spline vs. a LP filtered reconstruction.
_-_-
Yes, psycho-acoustics play a large role. What's technically "wrong" may sound better for reasons of ear and brain. No idea if that's the case for splines, tho.
I would be very, very surprised.
Consider: .... 0.707,0.707,-0.707,-0.707,0.707,0.707,-0.707,-0.707.... (repeating) and
...1,0,-1,0,1,0,-1,0...(repeating) are BOTH discreet time sample series representing a sine wave of unit peak amplitude @ Fs/4 differing only in phase relative to the sample clock.
Now reconstruction with a lowpass reconstruction filter will give the correct sine wave in both cases, curve fitting will make one look like a square wave!
If you want images, non linearity and all kinds of distortion there are easier ways to get there, this is the sort of thing that might be fun in a synthesiser, but probably not in anything claiming to be hi fidelity.
73 Dan.
Consider: .... 0.707,0.707,-0.707,-0.707,0.707,0.707,-0.707,-0.707.... (repeating) and
...1,0,-1,0,1,0,-1,0...(repeating) are BOTH discreet time sample series representing a sine wave of unit peak amplitude @ Fs/4 differing only in phase relative to the sample clock.
Now reconstruction with a lowpass reconstruction filter will give the correct sine wave in both cases, curve fitting will make one look like a square wave!
If you want images, non linearity and all kinds of distortion there are easier ways to get there, this is the sort of thing that might be fun in a synthesiser, but probably not in anything claiming to be hi fidelity.
73 Dan.
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