Auditory Perception of Nonlinear Distortion
In this blog post I bring attention to an interesting convention paper published by Dr. Earl Geddes back in 2003. I regularly read white papers and this one stood out to me for the following reasons.
- It develops a new measurement metric for nonlinear distortion called Gedlee distortion (Gm)
- It provides statistical evidence based on a pool of 32 participants listening to 21 different types of nonlinear distortion.
- Direct comparison is made between Harmonic and intermodulation distortion.
- Test subjects are exposed to various distortion types based on various nonlinear functions commonly encountered in various devices (.ie crossover distortion in audio amplifiers, or loudspeaker motor strength weakening at cone travel extremes(non-flat BL(x) curve)
- The study is designed to isolate the variables in question. MathCAD was used to generate .wav files for a 15 second piece of music, each file contained the unique nonlinear distortion embedded into the soundtrack which was created in MathCAD prior to writing the file. Listeners then subjectively qualified the perceived sound quality of each .wav file, 21 in total. This to me, is an excellent way to isolate the variable in question as apposed to evaluating two physical devices where other variables could be introduced contaminating the results. For example, one could compare two preamps having different levels of nonlinear distortion, however nothing conclusive could be drawn from this.
Before discussing the subjective portion of the convention paper, I want to focus on how the study develops their own nonlinear functions in MathCAD software. This is a very novel approach and I can only wish that I had the ability myself to create custom wave files of this nature. Three of the twenty one nonlinear functions are graphically shown in the study as examples (see above).
It would have been nice to see all twenty one nonlinear function graphs out of academic interest. Perhaps this could have been included in an addendum from the main study paper. This would shed some light in what specific nonlinearity is so offensive to the ear. Gedlee does describe in general what nonlinearities are more offensive than others which I believe are based on the subjective evaluation data.
The non-linear functions are presented in the paper as though the reader should already have a cursory knowledge of the nonlinear function graph. This is typical of nearly all AES papers, which make no effort to educate the reader on the underlying subject. I feel that this paper provides unique insight into nonlinear distortion as a subject, but I think additional information is needed for the audio enthusiast trying to connect the pieces of the puzzle.
We are used to seeing harmonic distortion sweeps overlaid on a frequency response graph. However what is not generally understood is that these distortion response curves are driven by nonlinear transfer functions from the specific device (as we see above), be it an amplifier, amplifier sub-systems, loudspeaker subsystems such as a driver’s motor, horn or waveguide, enclosure, or the room. Loudspeakers for example can have completely different nonlinearity types than those commonly found in class A/B amplifiers, as an example. Nonlinearity function types are multiplied together to form the overall nonlinear character of a device or complete system. By nature these nonlinearities are level or gain dependent. For example some nonlinear functions types do not exhibit its behavior until a certain gain is reached through the transfer. Others, such as crossover distortion, inversely intensifies. This means that the distortion increases as the signal gain into the device is lowered.
Generally, the fact that 21 nonlinear functions can even exist as a function in MathCAD highlights the complexity of the subject. For example some people try to categorize K2 and K3 harmonic as being either audibly harmful, benign, or preferable. However what is the phase relationship of K2 and K3 to the fundamental tone? The standard measurement for harmonic distortion is blind to this aspect, and there's virtually no research as the audibility and offensiveness on "in-phase" or "reverse-phase" K2 and K3 products. This is touched on in a follow-up paper by Keith Howard titled 'Weighing In" (see below). The Vertins Measurement software manual references Keith's work found here: Virtins Software manual on page 288. This is another rabbit hole for those interested in the topic!
Harmonic Distortion a Good Thing?
Geddes' study shows that harmonic distortion has an inverse correlation to auditory preference, meaning that participants preferred some harmonic distortion rather than none! This does not come as a surprise to me as I find that some of the best sounding loudspeaker drivers have around -45dB to -55dB of K2 and K3. This provides a little bit of “richness” to the sound character. All of this assumes that the intermodulation distortion is kept below -65dB. If IMD was any higher it would negate the smoothness generated from K2 and K3. These are just my own empirical observations after measuring and listening to hundreds of drivers and loudspeakers. Not all loudspeakers that have just the right amount of K2 and K3 sound good either, leading me to suspect that a certain “type” of K2 and K3 are preferable. What is good and what is bad K2 and K3? That’s a very good question!
Gedlee takes the research results from the pool of 32 participants and creates a preferential weighting system to the various nonlinear functions to derive a new metric for distortion. This new distortion metric is called the Gedlee Metric (Gm) which applies more weight to distortion types that are more offensive to the ear. This is a valiant effort and exceeds any effort I’ve seen to date. On a personal level I am a bit jealous that he had opportunity and support through the University of Michigan along with financial support from the U.S. Government. It’s a shame that the metric did not become standardized, or at least not yet, almost twenty years later. I can only speculate that individual manufacturers did not want a metric that revealed the true performance of their products. However third party testers like myself should jump at the opportunity to have a weighted distortion metric that is backed by subjective/objective correlation research.
The Gedlee metric goes a lot further than any other effort on the topic but I think the work stopped short on a number of levels. First, I don’t know how much effort was placed on marketing the new metric to bodies such as AES and IEC, measurement software companies, or manufacturers. I could only find one measurement software program that included Gm as a feature. I even attempted to use the software (Vertix) and found the program itself incredibly complicated to use. It’s my hope that I will be able to include this metric along side the usual harmonic and IMD tests that I regularly conduct.
The other area that stops short is described in the concluding remarks of the paper: "Future research will focus on efficient ways to measure Gm as well as ways to deal with values of Gm that have a frequency-dependence. In loudspeakers, for example, the Gm values, like THD and IMD, will virtually always be frequency dependent and dealing with this frequency dependence presents some interesting issues regarding masking, etc. The main point to be made, however, is that now that we have a metric with a high degree of stability and predictability we can begin to do a whole array of subjective studies of distortion mechanisms that were heretofore impossible to quantify for lack of a value yardstick with which to measure the results. "*
Geddes is posturing this paper as a starting point towards further research. If the metric can be furthered to include frequency-dependence (time-domain) we can then start to measure, for example, loudspeaker motor flux modulation. It's also conceivable that a perceptual weighting could be added to include the ear's sensitivity at certain frequencies.
Generally I think the Gm metric deserves more attention. It has really fallen under the radar and if it works as advertised, can have huge potential towards furthering our ability to discern sound quality performance based on objective methods. Perhaps if ARTA or REW measurement software would consider including it as a feature it might gain popularity, at least among manufactures and DIY enthusiasts.
* EA. R.. Geddes, and LI. W.. Lee, "Auditory Perception of Nonlinear Distortion," Paper 5891, (2003 October.). doi: