Weighted THD

It has been understood since the 1930s that total harmonic distortion (THD) correlates very poorly with our perception of the nonlinear distortion generated by audio equipment.

In 1937 the Radio Manufacturers’ Association in the US suggested a method of making an overall distortion figure more relevant, by weighting the amplitude of individual harmonics by N/2 prior to summing, where N is the harmonic number [1]. So the amplitude of the second harmonic remains unaffected, the amplitude of the third harmonic is multiplied by 1.5 (+3.5dB), the amplitude of the fourth harmonic is doubled (+6.0dB), and so on. It was understood that higher-order harmonic distortion is more audibly objectionable than lower-order distortion, and the RMA's weighting scheme was an attempt to reflect this.  

Following WW2, the BBC’s D E L Shorter suggested that the RMA hadn’t been severe enough. In 1950 he described experiments which showed a better correlation of summed harmonic distortion measurements and sound quality if a more severe N2/4 weighting was applied instead [2]. Again this leaves the amplitude of the second harmonic unaffected, but that of the third harmonic is now multiplied by 2.25 (+7.0dB), that of the fourth harmonic by 4 (+12.0dB), etc. Around a decade later, another BBC employee, E R Wigan, revisited the subject of harmonic weighting, and confirmed the improved subjective/objective correlation of an N-squared weighting scheme, [3]. The underlying reasons for this are explored in reference [4].

At the time these weightings were proposed, spectral analysis was not readily available, and a weighted THD figure was thus impossible for many to calculate. So unweighted THD established an undeserved hegemony that – despite today's ready availability of spectrum analysis – it continues to enjoy.

[1] Radio Manufacturers' Association, "Specification for Testing and Expressing Overall Performance of Radio Broadcast Receivers – Part 2 – Acoustics Tests", 1937
[2] D E L Shorter, "The Influence of High-Order Distortion Products in Non-Linear Distortion", Electronic Engineering, April 1950
[3] E R Wigan, "New Distortion Criterion", Electronic Technology, April and May 1961
[4] K Howard, "The Weighting Game", Hi-Fi News, December 2001