Smoothing Filter
Most audio filters are linear, which means that the maths behind them is pretty well understood (not by me, but by smart people), and their behaviour can be predicted, and duplicated easily. There are even devices you can buy that will let you plug an expensive filter into it, give it a moment, and then it will have a perfect duplicate of that effect (see convolution reverbs (and a reverb is just a type of filter)).
But, not all filters are linear, and in my opinion, the interesting ones aren't (like the sorting filter). Mainly because you get a bit more surprised when you hear them applied to different sounds.
So todays filter is a smoothing filter. We start out with a sound wave, and we try to approximate the wave by just picking a few key points on it, and fitting a curve through those points. I've chosen to do it the super inefficient way:
- Approximate the whole sound wave with 2 points, one at the start and one at the end.
- Find the place where the approximated wave is the most different to the actual wave.
- Refine the approximation by adding a new point at this spot with the most error.
- Go to 2, until we are close enough to the original wave.
So, for this to work, we need to have the entire sound available (you can't do this on a live sound - though you could do it on short windows of sound), and a fair bit of computer time (depending on how long the sound is). The actual effect it produces is probably best explained by a picture:
(top is original, middle is quite filtered, bottom is very much filtered)
And of course, the actual clips (as FLAC):
Original Filtered Aggressively Filtered
I interpolate using a cosin-ish thing, based on the two points either side of the point we are interpolating. Just because it is simple, and it isn't linear.
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