Aliasing Square Wave

Question

I'm having a really weird issue with generating waveforms from frequencies C1 to C8.

When I generate sine waves, everything sounds good; no problems whatsoever. However, when I generate a square wave... BAM weird aliasing issues on the higher frequencies (around C6 to C8). I have no idea what I'm doing wrong at this point.

I'm going to take a wild guess here but I'm thinking it might be because square waves have a lot of harmonics so it's not producing the higher harmonics correctly when I reach a higher frequency... thus the really high harmonics are getting aliased. Would like someone to confirm with me/guide me to a solution to this. Is it possible to try to implement a filter or is there a better solution ?

Thanks!

I'm setting my sample rate to 44.1 kHz and here are my functions for waveform generation:

float generateSin {
    sample = sinf(_phs);

    _phs += _phs_incr;
    _phs = wrapPhase(_phs);
}

float generateSqr {
    sample = sinf(_phs);
    if (sample > 0) sample = 1;
    else if (sample < 0) sample = -1;

    _phs += _phs_incr;
    _phs = wrapPhase(_phs);
}

Answer 1

My guess is there's a problem with your wrapPhase function.

If I use the R implementation of it below (C8 shown), then I get all sorts of funny results. That's the second image. Removing it from the iteration (but including it in the calculation), makes for much cleaner signals (the first image).

---

R Code Below

#30582

wrapPhase <- function(phi)
{
  return(phi %% 2*pi)
}

# https://en.wikipedia.org/wiki/Piano_key_frequencies
cs <- c(32.7032, 65.4064, 130.813, 261.626, 523.251, 1046.50, 2093.00, 4186.01)
c1 <- cs[1]
c8 <- cs[8]

fs <- 44100

phs <- rep(0,T + 1)
phs_incr <- c8 / fs * 2 * pi

T <- 1000

sample <- rep(0,T)
sqr_wave <- rep(0,T)

for (t in seq(1,T))
{  
  sample[t] <- sin(wrapPhase(phs[t]))

  if (sample[t] > 0)
  {
    sqr_wave[t] <- 1
  }
  else 
  {
      sqr_wave[t] = -1;
  }

  print(sample[t])

  phs[t+1] <- phs[t] +  phs_incr
  #phs[t+1] <- wrapPhase(phs[t+1]);
}

phi <- seq(-pi, pi, 0.001*pi)
phi_wrap <- rep(0, length(phi))

for (k in 1:length(phi))
{
  phi_wrap[k] <- wrapPhase(phi[k])
}

plot(sample[1:50], col="blue", type="l")
lines(sqr_wave[1:50], col="green")

Answer 2

After brainstorming/researching for a little longer, I've realized that there are things called Bandlimited Waveforms; these waveforms basically get rid of the aliasing issues that exist within waveforms with harmonics (triangle, square, sawtooth for example).

The cause of my issue was that even though I had the right sampling rate for my base tones, they did not support the harmonics that my square waves had, thus creating aliasing. I found out this is a common problem for many others and my implementation of my square wave would be perfect for LFOs/lower frequencies.

Anyways, I implemented a Bandlimited Square Wave and BAM! problem solved!!! no more aliasing! NOW there's a problem with trying to implement a bandlimited PWM but that's another problem for later ;0