On Tue, May 4, 2021 at 11:25 AM Dan Wilcox danomatika@gmail.com wrote:
Sure but there tends to be a point to where it makes sense. The discussion seems to indicate this. Also, I suppose would have separate objects for sound file types, [wavfile], [aifffile], etc but a unified object clearly made sense in that context. As I mentioned before, it seems like there is a set of "tried & true" algorithms for interpolation...
I'm still looking for a single best review on the subject, but it seems like most methods are either:
- piecewise polynomials
- windowed sinc functions
You'd think polynomials would be a totally solved implementation---but a few searches turn up relevant, current research [1-3]. Singla and Singh compared window functions with a simple construction that performs better at separating the signals from the noise [1]. I'd really like to read the springer article by Zaitsev and Khzmalyan which has the abstract opening line: "The problem of synthesis of low-order polynomial window functions with an arbitrarily specified decay rate of spectral lobes (optimal with respect to minimization of the maximum side lobe on a specified segment of the frequency axis) is solved." [3] It's from June 2021.
For the window choice, there's Bartlett, Hanning, Hamming, Lanczos, Blackman-Harris, ..., ... If you multiply a C-N function by sinc truncated at an integer, you get a C-(N+1) function. The maximum rate of attenuation increases as you go to higher degrees of smoothness. So, there's a very clear reason why you find variations in performance based on window choice. The windowed sinc function is C0: rectangular window C1: Lanczos, Bartlett C2: Hann C3: Blackman C4: Blackman-Harris (and others.... so many others)
The other parameter you can control is the length of the window. All I can offer is a rule of thumb, use minimum length (2*N+2) for interpolator functions that have N-degrees of smoothness. I'm still working on this area
And check out Sample Rate Converter comparisons at infinitewave [4], to get a look at how much variation there is in performance from one software's implementation to another.
I have yet a third approach that I'm studying: truncated sinc plus polynomial correctors. I think I can make a family of functions that converges to the ideal performance faster than windowed sinc functions as the length and degree become large. There would be a 4-point, 6-point, 8-point, etc...
All of these are functions that are too expensive to calculate at runtime for a fundamental, highly used object like delread~ or tabread4~. So, a table based approach is warranted but has trade-offs. You could choose to calculate the tables at compilation time, start-up, or as needed at runtime.
Max and Clemens have made the first implementation and found a relevant test case. Waveguide synthesis is one where the errors get compounded as the signal gets resampled again and again passing through the delay. I'd bet there are a series of ever more badly behaved waveguide problems that could be tamed by using successively higher-degree-and-length methods
[1] http://code.eng.buffalo.edu/jrnl/Window [2] https://pdfs.semanticscholar.org/2196/5128dd419fd8d0117c97cb23b62724d7c56b.p... [3] https://link.springer.com/article/10.1134/S1064226921050107 [4] https://src.infinitewave.ca/