software filter: non fixed sampling rate filter

[KammutierSpule]

Most (all?) of the software filters implementation are based on a fixed (pre calculated parameters) sample rate.

I was looking some source code, some filters pre calculate the 1/FS to it will be used to calc other parameters.

Now, I am looking / wondering if I don't have a fixed sample rate but a variable (eg: adaptive) rate.
So all I know is the next step advance.

How can I develop a filter with this variable step? Any other considerations?

[blue hell]

Not sure what you want to make ... so maybe this is trivial to you ...

When you change the sample rate the filter cutoff frequency would scale 1:1 with that.

I think that your lowest sample rate still would have to be high enough to treat the highest frequencies ok to avoid distortion.

[KammutierSpule]

If I have a regular filter / processing, this will look similar to this:

[blue hell]

Ah, ok. You could just move the code from InitFilter into the loop then ... but there is a price for that of course in calculation cycles needed.

The separate initialization function basically is an optimization strategy.

What I did in my synth is that I made a SampleRateChanged( NewRate) function which will then call all the InitXXX functions that have a sample rate dependency.

In an object oriented structure that's not too hard to code, for a non object oriented thing you could maybe make a linked list of function pointers to iterate over when the sample rate changes.

This would depend a bit on the actual platform used.

[KammutierSpule]

true but.. My questions was not related with the general code implementation but with the filter design and concerns?

As the filters work as an incremental processing (i.e: the result depends on the previous results and input values) it expects that the input be added at some cadence (frequency sample)
even changing every step should it work? or any other concerns should taken in account?

[blue hell]

That would be hard to answer in general ... some filters don't like it much when there parameters are updated too fast .. while others do not have such issues.

Recalculating for a new sample rate would amount to the same thing I'd say.

[JovianPyx]

Can you tell us why you want to do this? What could you do with such a filter that you believe you cannot do with a fixed sample rate filter?

Filters such as the state variable are very easy to tune (set Fc to desired value) as well as Q setting by changing just one number.

To what Blue Hell said, I'll add that changing FS can be more trouble than it's worth since the relationship between the highest harmonic frequency to FS may be difficult to determine and can easily result in alias artifacts (which are something most DSP designers try to avoid).

A single fixed sample rate also allows you to run more than one filter in the same program and have Fc set differently for each one. That will be significantly more troublesome with a variable FS.

Consider also that you will need to use interpolation to get a smooth range of FS values. Interpolation comes in many varieties and performance as well as computational load all of which vary with the chosen method.

Have you seen the free information at www.dspguide.com ? It's a wonderful down-to-earth site that explains the principles of DSP in plain English.

HTH.

[KammutierSpule]

[JovianPyx]

Dealing with "middle of the sample" is usually done with interpolation. I use this technique to tune wavetable samples to precise pitches, but I do it with a fixed sample rate.

Is fractional sample interpolation what you mean when you refer to "variable sample rate"? When I think of sample rate, I think of the rate at which the DAC is updated which is normally fixed.

There should be numerous good articles on fractional samples and interpolation on the web.

[KammutierSpule]

I dont much about processing so I dont know how this is called.

I will explain again. consider you have the triangle wave:

at t time, the tri wave, it will be at one voltage level (some intensity value)
at t+1 you will output a sample to be played.

but.. lets say that at t+0.12 there was the time when the triangle wave get the peak (max value).
So I am wondering if the filter result will be different if I consider (catch) that max peak of the wave..

I can do oversampling.. but.. it will also not solve "my idea of adaptive" (sample at the precise moment that the change happen)

[KammutierSpule]

[JovianPyx]

Ah - OK - That means interpolation. www.dspguide.com should have info about the various ways to do that.

[blue hell]

It makes no sense to adapt the rate to the peaks of the waveform .. what counts are the frequencies in it - there is not even such a peak in the digital representation.

[KammutierSpule]

Sorry but if that is the same interpolation I know, it is not interpolation I am looking for..
What I know of interpolation mean is: calculate an estimation of some value between two (or more) know values.
There are different kinds of interpolation I know: nearest, linear, cubic,..
But I am not interpolating the tri wave because I know exactly the value at every moment (it will be math defined)

Please note on my example when I say I want to process the value of the filter at t+0.12 (the sample rate will be at t+1) I know exactly the value of my VCO at t+0.12 .. so it is not interpolated.. and I want to pass the value to the filter at that time... because it is the moment when the wave changes the direction..

[JovianPyx]

I'm failing to understand too much about what it is you're trying to accomplish. I understand the idea of knowing the value of a calculated waveform point between two integer DAC samples, but I'm not understanding what that has to do with using a filter with a "variable sample rate".

One thing to keep in mind is that a triangle wave or any periodic wave other than a pure sine has an infinite number of harmonics. No matter how you calculate it, if it's a "naive" waveform, there will always be alias artifacts regardless of the sample rate or upsampling, so the simulation will not be a perfect one. To eliminate the alias artifacts, you must band limit the triangle waveform - and then it will sound like a triangle, but will no longer look like a triangle.

Again, I think there's something about this project I don't understand, so please pardon me

[KammutierSpule]

I am also not sure about my ideas, they may don't make sense but thats why I am discuss it here with someone more expert on the subject!

I may will abandon this idea, but I'm just happy to discuss it.

I understand also the concept of "band limited waveforms" but that will not easily work for me, as I will be mathematic simulating the triangle waveform (and I dont have a way to pre-calculated as it will be modified realtime)

I was thinking that if I compute the filter at the exactly instant when the wave change (eg: a tri wave or a sqr) that it will make a slight different result as only sample it at moment (rate) of the output. It may be.. but will be very small.

So in another topic, is there any way that you can think of how can I compute a band limited wave based from the original math representation? (without pre-calc bufering)

[blue hell]

I've used polyBlep to bandlimit waves - it can be done on the fly as it's reasonably efficient - not perfect though, but pretty good.

[blue hell]

Here is some example code (Pascal) :

[JovianPyx]

There are only two ways I know of to calculate a periodic waveform as bandlimited:

1) add up all of the required sines at harmonic frequencies below the Nyquist limit. This is not easy to do realtime because there can be many sines to add.

2) a "brute force" brick wall filter that has Fc somewhat below Nyquist. You can take the simply calculated naive waveform and run it througbh the "brick wall" filter and out comes a band limited version of that waveform. This is done at an upsampled sample rate and then downsampled after the filter to maintain the correct pitch. This also has problems in terms of high computational load and has amplitute artifacts at the high end if the range (near Nyquist). This is normally done with several FIR filters. The "kernels" of these filters need to be prepared using something like Matlab or Octave, but I'm afraid I don't know enough about those to spell that out here. I tried doing it as an experiment years ago and while it worked, it was too computationally expensive to be practical. That experiment made it clear to me that a pre-computed wavetable was a computationally more practical method to get non sine periodic waveforms to work. And there are issues with that method too given that you probably need to be able to change the pitch and one wave table is not going to cut it.

This is what I would call a "classic" DSP problem - the simulation or computation of classical waveforms that we import from the analog world into the digital world. Stuff that's easy in the analog domain is just messy in the digital domain.

[JovianPyx]

Yes - as Blue Hell posts, there is "BLEP" and other similar methods that begin with BL such as BLIT (band limited impulse train). I've personally no experience with these, but they are widely used in the digital synthesizer realm.

[gdavis]

[KammutierSpule]

[gdavis]