Bandlimited PWM

Question

Trying to figure out how to synthesize a Bandlimited PWM in my audio code in C.

I have already figured out a bandlimited pulse wave but I can't really figure out how to translate that to PWM. I have used the Polynomial Bandlimited Step (PolyBLEP) approach to get a nice bandlimited pulse wave.

Here's my code:

float generateSample() {
    float sample = 0;
    sample = sinf(phase);
    if (sample >= dutyCycle) sample = 1;
    else if (sample < 0) sample = -1;

    float t = phase/(2*M_PI);
    sample += poly_blep(t, phase_incr);
    sample -= poly_blep(fmod(t + 0.5, 1.0), phase_incr);

    phase += phase_incr;
    phase = wrapPhase(phase);

    return sample;
}

// Phase Wrapper
float wrapPhase(float phs) {
    if (phs >= (2*M_PI)) phs -= (2*M_PI);
    return phs;
};

double poly_blep(double t, double phs) {
    double dt = phs / (2*M_PI);
    // 0 <= t < 1
    if (t < dt) {
        t /= dt;
        return t+t - t*t - 1.0;
    }
    // -1 < t < 0
    else if (t > 1.0 - dt) {
        t = (t - 1.0) / dt;
        return t*t + t+t + 1.0;
    }
    // 0 otherwise
    else return 0.0;
}

I'm guessing here that I have to adjust my t variable in generateSample() to fit the PWM's duty cycle (ranges from 0.5->1) but I'm not totally sure how to do that... any help is appreciated!

Thanks! :)

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EDIT: Guess I wasn't clear, but I'm producing audible tones with a pulse wave. The PWM controls the pulse width of the pulse wave. I was encountering aliasing issues before I implemented a bandlimited waveform. With a duty cycle of 50%, there are no aliasing issues. However when I try to increase the duty cycle, I encounter aliasing issues again and it sounds audibly not what I want it to sound like

Answer 1

Hey guys I figured it out through reading this: enter link description here and this: Pulse wave Wikipedia

Basically, I was reading that a bandlimited pulse wave could be synthesized with two bandlimited sawtooth waves. One of the saw waveforms will be out of phase with the other to create a rectangular waveform (50% duty cycle is sqr wave). To do PWM, just shift the phase of the out of phase saw waveform. I implemented this and it totally worked!

The wiki explanation:

A pulse wave can be created by subtracting a sawtooth wave from a phase-shifted version of itself. If the sawtooth waves are bandlimited, the resulting pulse wave is bandlimited, too.

Great learning experience and I'm sure there's a more efficient way to do it and will still be looking out for that. Hopefully this helps another person who is having the same problem one day!