Use AVAudioRecorder metering to make triangular wave

Question

I am trying to make triangular waves for audio recorder through metering. I am using AVAudioRecorder this means that Fast Fourier Transformation will not work in this case (Secondly i don't have enough knowledge how to implement it). I found this project on github. In this project author is using the following equation to make smooth sine wave:

CGFloat y = scaling * self.maxAmplitude * normedAmplitude * sinf(2 * M_PI *(x / self.waveWidth) * self.frequency + self.phase) + (self.waveHeight * 0.5);

If you consider this sinf(2 * M_PI *(x / self.waveWidth) * self.frequency + self.phase) part of equation you will find that it is the equation of sine wave (wikipedia). If i replace this part with the equation of triangular equation (wikipedia) it still make sine wave with little difference. I want to transform this equation in such a way that it make triangular wave instead of sine wave.

My triangle wave equation looks like this:

CGFloat t = x / self.waveWidth;
CGFloat numerator = sinf( (2.0 * M_PI * (2.0 * self.amplitude + 1.0) * self.frequency * t) );
CGFloat denominator = (2.0 * self.amplitude + 1.0) * (2.0 * self.amplitude + 1.0);
CGFloat multiplyer = (8.0 / pow(M_PI, 2.0));
CGFloat result = multiplyer * (numerator / denominator);

Then finally y position is calculated by:

y =  (result * scaling * self.maxAmplitude * normedAmplitude) + (self.waveHeight * 0.5);

Animation is also look unnatural. Output of this equation is:

Thanks

Answer 1

Well by looking at the equation you're using (which is the fourier transform), you're implementing it a bit wrong (k samples should be increasing but you've left it constant with 2.0 * self.amplitude + 1.0. You're also leaving out (-1)^k which adds in the odd harmonics.

Wikipedia wrote this:

It is possible to approximate a triangle wave with additive synthesis by adding odd harmonics of the fundamental, multiplying every (4n−1)th harmonic by −1 (or changing its phase by π), and rolling off the harmonics by the inverse square of their relative frequency to the fundamental.

I'm guessing (as I'm not a DSP expert) that because you're leaving the k value as a constant it is just giving you a sine wave output.

Look at this algorithm block for the triangle wave (try it, then change it for your code):

phaseIncr = (2.0 * M_PI / sample_rate) * self.frequency;
for (int i = 0; i < numSamples; i++) {
    triVal = (phase * 2.0/M_PI);
    if (phase < 0) triVal = 1.0 + triVal;
    else triVal = 1.0 - triVal;
    sample = amplitude * triVal;
    if ((phase += phaseIncr) >= M_PI) phase -= (2.0 * M_PI); 
}

I also see that the original project wrapped the phase in setLevel method so check that out. Hope this helps out and let me know if this doesn't work, I'll try to help as much as I can.