# How Much Distortion Can You Tolerate?

I wanted to know how much audio distortion I could tolerate in speech or music. To find out, I wrote a Windows program that adds a calibrated amount to any .WAV file.

The program generates THD.WAV with audible pips that mark audio pairs. The first sound is undistorted. The second sound is distorted for aware comparison. For blind comparison, sometimes it is undistorted. The program writes a text file that identifies the pairs. Take notes while listening and check the file when you're done.

The program uses a polynomial to generate distorted sample y from input sample x:

```y = x + a2x2			second-harmonic distortion
y = x + a3x3			third-harmonic distortion
y = x + a4x4 + b4x2		fourth-harmonic distortion
```
The polynomial coefficients are
```a2 = 2d∕p
a3 = 4d∕(1−3d)∕p2
a4 = −8d∕p3        b4 = 8d∕p```
where d is distortion as a ratio (percent ∕ 100) and p is peak input amplitude. Referring distortion to the signal peak instead of full scale makes it independent of recorded level.

I've long wondered how much stereo channel separation was really necessary. These days the question arises for FM tuners because some methods that reduce HD Radio self-noise may degrade separation. To find out for yourself how much is enough, try this program. Your judgment may differ for speakers and headphones.

To change the font size for either program, click on the title bar icon and select Properties. Under Font, select a font and size.

September 24, 202188–108 MHz