Algorithm to pan audio

Question

I'm looking for a way to pan the PCM audio I have. At the moment the audio is in a stereo format and I would like to pan it to the desired side (or more/less to a side).

I've recently figured out how to do mixing here so I guess it would be something similar (adding stuff to each other and such). What I was thinking is to add the audio data from one side to the other side.
For example if I were to pan hard left, I'd get the data from the right channel and add it to the left channel. I would then set the right channel to a constant value so that it would be silent.

Am I thinking in the right way or am I missing something obvious?

Thanks in advance!

Answer 1

The basic technique to place a mono source in stereo is called constant power panning.

If you want to place a mono source at angle $\theta$ you can just use $A_\mathrm{amp}$ and $B_\mathrm{amp}$ as amplitudes for your channels:

$A_\mathrm{amp} = \frac{\sqrt{2}}{2} (\cos{\theta} + \sin{\theta})$

$B_\mathrm{amp} = \frac{\sqrt{2}}{2} (\cos{\theta} - \sin{\theta})$

Typically $\theta$ ranges from $-45^{\circ}$ to $45^{\circ}$ with $0^{\circ}$ being the center.

Hope, that helps.

Reference: Roads, Curtis (1996). The Computer Music Tutorial. Cambridge: The MIT Press, pp. 457–461.

In addition:

You can put it in code directly. E.g. if you use Python and you have mono audio in a numpy array, you can convert it into stereo by a given angle like this:

def panner(x, angle):
    """
    pan a mono audio source into stereo
    x is a numpy array, angle is the angle in radiants
    """
    left = np.sqrt(2)/2.0 * (np.cos(angle) - np.sin(angle)) * x
    right = np.sqrt(2)/2.0 * (np.cos(angle) + np.sin(angle)) * x
    return np.dstack((left,right))[0]

You can use it like panner(np.array([1,2,3]), np.radians(20)). (Of course [1,2,3] is a quite pointless audiobuffer.)

Answer 2

I just wanted to point out that if you're planning to use these formulas in your code, you can get the exact same results with fewer calculations by using an angle $\theta$ between 0 and 90 degrees and simply calculating $A_{amp} = \sin(\theta)$ and $B_{amp} = \cos(\theta)$.

You may have run across these before (they seem to be more commonly referenced in my searches for Equal or Constant Power Panning), and thought the formulas above would give you a different curve. They sure do look different, but the curves are the same.

Answer 3

For a stereo file, if pan is not centered you just need to keep one channel same while attenuating the other side linearly.