The Phantom's Mask by Joe Gerhardstein

During NI Week 2005, I attended a session by Dan Foley of Listen, Inc. This presentation centered around measurements made by students at the University of Hartford of defective loudspeakers. The students were looking for an empirical method of detecting buzzing failures found in the speakers (assembly faults, rubbing voice coils, bent frames, loose spider). Typically during the manufacturing process, buzzing failures are detected using a human listener. The students were hoping to find a way to replace the subjective testing with a more objective and automated measurement.

A sine sweep from 20 Hz to 1 kHz (these were mid-bass� automotive speakers) was fed to the speakers and the output of the speakers measured from 20 Hz to 100 kHz. The recorded time data were analyzed via Fourier Transform and power at the fundamental (drive frequency) and harmonics were determined. For these experiments, the first 100 harmonics were calculated. Previous attempts to replace human listeners with objective testing had focused on the calculation of THD (Total Harmonic Distortion) to determine whether a speaker was defective. THD is calculated using the following formula:



where Hn is the power of the n-th harmonic (n=1 being the fundamental). In this formula, all harmonics are equally weighted regardless of their level or frequency.

The students found during their measurements that THD did not correlate well with audible distortion. The reason for this is a feature of our hearing broadly called psychoacoustic masking, in which the sensitivity of the human ear depends on the frequency and level of the components in the sounds as well as in their frequency spacing and level difference. In other words, the human ear applies a weighting function� which depends on frequency and level, and resolves individual frequencies based upon their spacing. Hence different harmonics are not perceived to contribute equally to audible distortion, contrary to the THD formulation.

Let's illustrate this with three sounds. The first is a simple sine wave (tone) at 85 Hz with a level of 70 dB. The second sound includes the 85 Hz (fundamental) and its 2nd harmonic, a tone at 190 Hz. The 3rd sound has the same fundamental and its 20th harmonic, a tone at 1900 Hz at 50 dB. In the speaker testing example, the first sound represents the perfect case where the measured signal is the same as the input signal (e.g. a pure tone). The second and third sounds represent cases with audible distortion in the speaker. All three sounds have the same total power.







The second and third sounds have the same THD, but to a human observer they are perceived as exhibiting different degrees of distortion. In the study, most buzzing failures in the speakers created higher-order harmonics (10th harmonic or higher). The study therefore recommended the use of a weighted distortion metric that takes into account psychoacoustic masking, and not the simpler THD calculation that weighs all harmonics equally. Complicating this, however, is the fact that this weighting metric is a function not only of the power and frequency of the fundamental tone, but also of the human observer! Well, no one ever said that replacing a human observer with a machine would be easy.