- From: robert bristow-johnson <rbj@audioimagination.com>
- Date: Sat, 06 Apr 2013 18:12:40 -0400
- To: "public-audio@w3.org" <public-audio@w3.org>

On 4/6/13 12:09 AM, Chris Rogers wrote: > > > > On Thu, Apr 4, 2013 at 6:57 PM, robert bristow-johnson > <rbj@audioimagination.com <mailto:rbj@audioimagination.com>> wrote: > > On 4/4/13 7:06 PM, Chris Rogers wrote: > > Another aspect of the WaveShaperNode is anti-aliasing. In > certain cases it would be great to be able to up-sample the > signal before applying the shaping, then down-sampling. This > is to avoid the extremely harsh aliasing that can occur in > applications such as guitar amp simulations. Once again we > could have an attribute .upsample ("none", "2x", "4x") or > something like that. Then the default value for that would be > "none" I think. > > > just lurking, and i haven't looked at the code at all, but thought > i might mention a couple of things that might be applicable. > > if you can get away from table lookup and implement the waveshaper > by use of a pure polynomial if finite order, you can get a solid > handle on aliasing. a finite-order polynomial is not as general > and a general lookup table, but for the purposes of distortion (or > "warmth" or whatever) in audio, it might be closer to what you > want anyway. you can fit polynomials to tube curves and the sort > pretty well. > > the images generated is no higher in frequency than the order of > the polynomial (let's call that M) times the highest frequency. > if that highest frequency is potentially Nyquist, then upsampling > by a factor of N means that the highest frequency is the *new* > Nyquist/N. that makes the highest frequency image (M/N)*Nyquist. > you can allow aliases as long as they don't get back into your > original baseband which is below the new Nyquist/N. that means > > 2*Nyquist - (M/N)*Nyquist > Nyquist/N > > or > > 2*N - M > 1 > > or > > M < 2*N - 1 > > if you upsample by 2x, you can have a 3rd-order polynomial. if > you upsample by 4x, you can have a 7th-order polynomial. > > then a decent brick-wall LPF with cutoff at Nyquist/N to kill the > images and aliases. then downsample by factor of N and you have > output. you will get the distortion components you were meant to > get (harmonics) and no non-harmonic components which are the > tell-tales of aliasing and cheezy distortion. > > you can do this with table lookup if you make sure the table ain't > defined to wildly (like if it's implementing a Mth-order > polynomial), have enough points in the table (memory is cheap), > and at least linearly interpolate between points. how many points > you need (based on what interpolation is done between points) in > the table is something that i had done some analysis about long > ago, but i might be able to find notes. if computational burden > is no problem, i might suggest implementing this as a polynomial > and use Horner's rule. > > just an idea. > > > Thanks Robert, this is really valuable information. I'd still like to > support general shaping curves and bit-crushing applications. But I'd > really like to get the highest quality sound and best general purpose > approach that is possible, especially for these "warming" applications. > probably, for generality and for efficiency regarding speed, you might want to implement the non-linear function simply with table lookup and linear interpolation. that is less computation than computing a 7th-order polynomial directly using the Horner method. but i might suggest that what goes *into* that table are the points of a polynomial of limited order. neglecting the error from linear interpolation (which can be very, very small if there are a decent number of points in the table), then they are mathematically equivalent, and since it's usually the case that memory is cheap, you may as well do this with a table. but if you define points in the table that would be the same as evaluating the limited-order polynomial, then you still enjoy the benefits of limited frequency to the images, and with enough upsampling (and downsampling on the other end), you can totally lose the non-harmonic aliasing (from foldover around Nyquist) that makes some digital distortion algs sound cheesy. again, you can do a 7th-order polynomial with no aliasing if you upsample 4x and, at the output, LPF well and downsample 4x. and you can make a 7th-order polynomial fit practically any tube curve to a very good fit. whether that 7th-order polynomial is implemented directly or is implemented with a decently large lookup table and linear interpolation, that shouldn't matter. but if your table implements some wild-and-crazy function with discontinuities or with amazing slopes and corners, that might generate harmonics that fold over and cause aliases that you can't get rid of. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."

Received on Saturday, 6 April 2013 22:13:10 UTC