We present a mathematical definition of Total Harmonic Distortion + Noise suitable for testing high-resolution digital audio systems. This formal definition of the "distortion analyzer" mentioned in AES17 defines THD+N as the RMS error of fitting a sinusoid to a noisy and distorted sequence of measurements. We present the key theoretical result that under realistic conditions a modern THD+N analyzer is well-described by a Normal probability distribution with a simple relationship between relative error and analysis dwell time. These findings are illustrated by comparing the output of a commercial distortion analyzer to our proposed method using Monte Carlo simulations of noisy signal channels. We will demonstrate that the bias of a well-designed distortion analyzer is negligible.
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