audiosignal-processingsynthesizer

Bandlimited waveform generation

I am writing a software synthesizer and need to generate bandlimited, alias free waveforms in real time at 44.1 kHz samplerate. Sawtooth waveform would do for now, since I can generate a pulse wave by mixing two sawtooths together, one inverted and phase shifted.

So far I've tried the following approaches:

  1. Precomputing one-cycle perfectly bandlimited waveform samples at different bandlimit frequencies at startup, then playing back the two closest ones mixed together. Works okay I guess, but does not feel very elegant. A lot of samples are needed or the "gaps" between them will be heard. Interpolating and mixing is also quite CPU intensive.

  2. Integrating a train of DC compensated sinc pulses to get a sawtooth wave. Sounds great except that the wave drifts away from zero if you don't get the DC compensation exactly right (which I found to be really tricky). The DC problem can be reduced by adding a bit of leakage to the integrator, but then you lose the low frequencies.

So, my question is: What is the usual way this is done? Any suggested solution must be efficient in terms of CPU, since it must be done in real time, for many voices at once.

Solution

  • There are a lot of ways to approach the bandlimited waveform generation. You will end up trading computational cost against quality as usual.

    I suggest that you take a look at this site here:

    http://www.musicdsp.org/

    Check out the archive! It's full of good material. I just did a search on the keyword "bandlimited". The material that pops up should you keep busy for at least a week.

    Btw - Don't know if that's what you looking for, but I did alias reduced (e.g. not really band limited) waveform generation a couple of years ago. I just calculated the integral between the last and current sample-position. For traditional synth-waveforms you can do that rather easy if you split your integration interval at the singularities (e.g. when the sawtooth get's his reset). The CPU load was low and the quality acceptable for my needs.

    I had the same drift-problems, but applying a high-pass with a very low cutoff-frequency on the integral got rid of that effect. Real analog-synth don't go down into the subhertz region anyway, so you won't miss much.