Since the 1930's, measurement of Total Harmonic Distortion (THD) has been recognised as a poor arbiter of sound quality. The Gedlee Metric, Gm, attempts to overcome the shortcomings of traditional THD measurements, and to quantify non-linearity in a way that corresponds much more closely to the psycho-acoustical perception of distortion. It is derived from the Transfer Function T(x) of the DUT. Since, in principal, any signal can be used as an input to determine the Transfer Function, Gm can be said to be a characteristic of the DUT rather than a characteristic of the output signal. Characteristics of the human hearing system such as masking have also been allowed for in the formula for Gm. Experimental results indicate that for low to intermediate levels of non-linear distortion, the Gedlee Metric has a much improved correlation to the subjective perception of distortion, and is a significant predictor of subjective sound quality, when compared to traditional metrics such as THD and IMD.

The original AES papers describing the Gedlee Metric are available on Earl Geddes's website:

Lee and Geddes: Auditory Perception of Nonlinear Distortion, AES October 2003. Part I: http://www.gedlee.com/Papers/Distortion_AES_I.pdf

Part II: http://www.gedlee.com/Papers/Distortion_AES_II.pdf

An undoubted obstacle to the adoption of Gm is that the mathematics involved in calculating Gm are complicated compared to the simplicity of THD calculations. It is also likely that many manufacturers are comfortable with consumers' misguided belief that low THD is a meaningful predictor of sound quality, and design and market their products accordingly.

The calculation of Gm involves two steps: 1) the derivation of a function T(x) which represents the normalised transfer function of an audio black box and which is amenable to differentiation; b) plugging T(x) into the equation for the Gedlee Metric Gm proposed by Geddes and Lee in their AES papers.

Published suggested methods for deriving T(x) have to date utilised either the theory of non-linear systems or trigonometric identities to derive a polynomial expression of T(x). I found both approaches very complicated, so I developed a hassle-free method of calculating Gm, and have created a spreadsheet to facilitate this. The spreadsheet derives the coefficients of a trigonometric expression of T(x). This set of coefficients can then be plugged into a short worksheet for Sage Math Online which then calculates Gm virtually instantly. The spreadsheet contains directions on how to use it, together with a breakdown of the mathematics I have used.

The rapid calculation of Gm is therefore possible, given a sinewave input to the DUT and the amplitude and phase information of the harmonics present in the output.

The spreadsheet file can be downloaded from Google Drive using the link below (the file is too large to post directly on diyaudio).

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Gm_Sine_Mixer_and_Coefficient_Calculator_Shared.xslx

Download from: Gm_Sine_Mixer_and_Coefficient_Calculator_Shared.xlsx - Google Drive

This version has been developed in Excel 2016, and is best viewed with Auto-hide Ribbon selected. It should also work without problems in Excel 2010 and Excel 2013. It does not load correctly into LibreOffice Calc, but a version for Calc also exists which I may post in due course if there is any demand for it.

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Questions/comments on the use of this solution are invited, though I am reluctant to get embroiled in discussions such as subjective/objective assessments of audio gear, the "best" objective assessments, etc. I am simply posting here a tool that simplifies a particular calculation. The Gedlee Metric does, however, have the potential to explain and quantify, for example, the difference between alternative circuit architectures, even when THD measurements are the same (see first two examples in the spreadsheet).

Forum contributors who quote THD and other distortions in their postings of their designs are, however, encouraged to use this tool to quote Gm too.

Thanks go to Earl Geddes for his support in this study.

Stephen

The original AES papers describing the Gedlee Metric are available on Earl Geddes's website:

Lee and Geddes: Auditory Perception of Nonlinear Distortion, AES October 2003. Part I: http://www.gedlee.com/Papers/Distortion_AES_I.pdf

Part II: http://www.gedlee.com/Papers/Distortion_AES_II.pdf

An undoubted obstacle to the adoption of Gm is that the mathematics involved in calculating Gm are complicated compared to the simplicity of THD calculations. It is also likely that many manufacturers are comfortable with consumers' misguided belief that low THD is a meaningful predictor of sound quality, and design and market their products accordingly.

The calculation of Gm involves two steps: 1) the derivation of a function T(x) which represents the normalised transfer function of an audio black box and which is amenable to differentiation; b) plugging T(x) into the equation for the Gedlee Metric Gm proposed by Geddes and Lee in their AES papers.

Published suggested methods for deriving T(x) have to date utilised either the theory of non-linear systems or trigonometric identities to derive a polynomial expression of T(x). I found both approaches very complicated, so I developed a hassle-free method of calculating Gm, and have created a spreadsheet to facilitate this. The spreadsheet derives the coefficients of a trigonometric expression of T(x). This set of coefficients can then be plugged into a short worksheet for Sage Math Online which then calculates Gm virtually instantly. The spreadsheet contains directions on how to use it, together with a breakdown of the mathematics I have used.

The rapid calculation of Gm is therefore possible, given a sinewave input to the DUT and the amplitude and phase information of the harmonics present in the output.

The spreadsheet file can be downloaded from Google Drive using the link below (the file is too large to post directly on diyaudio).

********************

Gm_Sine_Mixer_and_Coefficient_Calculator_Shared.xslx

Download from: Gm_Sine_Mixer_and_Coefficient_Calculator_Shared.xlsx - Google Drive

This version has been developed in Excel 2016, and is best viewed with Auto-hide Ribbon selected. It should also work without problems in Excel 2010 and Excel 2013. It does not load correctly into LibreOffice Calc, but a version for Calc also exists which I may post in due course if there is any demand for it.

********************

Questions/comments on the use of this solution are invited, though I am reluctant to get embroiled in discussions such as subjective/objective assessments of audio gear, the "best" objective assessments, etc. I am simply posting here a tool that simplifies a particular calculation. The Gedlee Metric does, however, have the potential to explain and quantify, for example, the difference between alternative circuit architectures, even when THD measurements are the same (see first two examples in the spreadsheet).

Forum contributors who quote THD and other distortions in their postings of their designs are, however, encouraged to use this tool to quote Gm too.

Thanks go to Earl Geddes for his support in this study.

Stephen

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