[music-dsp] Re: Waveshaping

[Nigel Redmon]

Linear interpolation is only a good choice if you're fairly  
oversampled to start with (that is, you don't have a lot of high  
frequency components. When upsampling by a factor of 4 or more, it's  
usually better to do it in multiple steps--you can use some tricks to  
gain a large advantage in efficiency. (You could even upsample with a  
high quality interpolator, then go to linear interpolation to go  
higher if you want and it meets your criteria.)

As for the bandpass--it's more efficient to filter what you can at  
lower rates, so it would be best to block the DC first, then  
upsample, and put the effort into low-pass filters.

As for "if you're working at 96 kHz or higher I'd say forget about  
aliasing"--you need to oversample by more than that for distortion  
algorithms (192 kHz is not enough either)--even if you source signal  
is heavily bandlimited (say, a guitar, even with the highs reduced).


On Oct 5, 2007, at 12:44 AM, Aaron Oxford wrote:

> Hi all,
>
> I am by no means an expert on oversampling, but FWIW I recently  
> needed to upsample some stuff to between 4x and 16x from 'normal',  
> and I found that a simple linear interpol upsample followed by a  
> couple of passes through a bandpass (I wanted to remove DC also)  
> worked well (and more importantly in my case was easy to write from  
> first principles in C#).
>
> I didn't need to downsample but I'd imagine the same would work  
> well in reverse - as someone else already suggested you can do the  
> bandpass first and then just throw away samples, using the linear  
> interpolation if you aren't doing a nice easy 'just throw away  
> n-1of every n samples'-type downsample.
>
> I'm aware that there are far more advanced and accurate techniques,  
> but again this worked well from first principles without very much  
> effort.
>
> As for the technique you suggested yourself, I'm not sure if you're  
> applying that equation to create intermediate samples or simply  
> using that function to effectively create a smoothed waveform as  
> your input (you're just applying the shaping function in the same  
> step, right?). Either way, you'll probably find it works, but I've  
> found that that particular 'filter' function is too severe for  
> working with sound high in treble (e.g. a hihat sample) at 'normal'  
> sample rates.
>
> Which brings me to my next point. This all depends on the sample  
> rate you're working with to start with too - if you're working at  
> 96 kHz or higher I'd say forget about aliasing - since only a  
> discontinuous or 'extreme' shaping function would introduce  
> aliasing to your already fairly highly 'oversampled' data (which we  
> will blatantly assume is nicely bandlimited), and aliasing on the  
> output can be dealt with by the output stages of whatever it is  
> you're doing. Again, if you're working at 48 kHz or lower, I think  
> that your filtering will be a bit too severe for certain sounds, so  
> I'd suggest something a little less forceful, such as o[x] = f(0.9*i 
> [x] + 0.1*o[x-1]).
>
> One of the smart people on this list might tell you what the low- 
> pass cutoff and steepness of that transfer function is. :-D
>
> Anything more complex than that and you may as well be working out  
> the coefficients for a 'proper' filter. Having said that I simply  
> ripped off some 2p filter psuedo-code from this list's archive. :-)
>
> Hope this is helpful,
>
> Aaron.
> ---------------------------------------------------------------------- 
> -----------
> Aaron Oxford   -   aaron+hardwarehookups .com .au
> Director, Innovative Computer Solutions (Aust) Pty. Ltd.
> 49 Maitland Rd, Mayfield, NSW 2304 Australia
> http://www.ic-solutions.com.au
> Developer, SourceForge project VioLet Composer
> http://sourceforge.net/projects/buzz-like