Fix distortion using internal noise as test signal

Estimating the dynamic gain
The key is in the estimation of the derivative f´(x(t)), the gain of the system. To estimate this, one must determine the local standard deviation around a small interval of time. However, this poses a dilemma: a small averaging time will produce a relatively noisy estimate, but a large averaging time will have greater bias due to the presence of signal (recall that we assumed above that x(t) varied little over the duration over which the variances were computed!). Highpass filtering can remove much of this unwanted signal, but not all. The authors found, empirically, that the best results are achieved in most cases with between 50 and 100 samples. This parameter can be increased as the sample rate rises and so reduces the averaging time.

A simple single-device setup
What is interesting and appealing about the paper is that the authors use one of the most basic amplifier setups you could imagine – a simple common emitter stage without feedback. Labview and an NI USB-6341 16bit data acquisition unit were used to generate a 10Hz sinusoidal voltage, which was applied to this amplifier. The amplified signal was then digitized and processed in real-time to derive the compensation factor.

The results of their experiments appear in the figure. There is a substantial improvement in the distortion level – from about 10%, it drops by an order of magnitude to about 1%.

Conclusion
The authors say that the method described by them finds its greatest use when you are dealing with a system that cannot easily be taken offline for calibration of its transfer function. In real terms as I see it, it is most effective for systems which you have calibrated before installation, and then you want to monitor for any drifts in transfer function and the attendant distortion due to component ageing or environmental factors, or even signs of abrupt changes that indicate some component failure that allows the system to continue functioning but causes an increase in distortion. An intelligent adaptive distortion-correcting amplifier? Certainly something that would add marketing zing to any audiophile product! Before we do that however, it is important to test the effectiveness of the method with a wider range of input signals. Note that the authors used a subsonic signal of 10Hz. Will this method work well when the input signal has a spectrum up to 20kHz? That would be a worthwhile avenue for further research.

About the author
Ramkumar Ramaswamy earned his M.Sc in Physics from Delhi University in 1990 and his PhD in Operations Research from the Indian Institute of Management Calcutta in 1994. He built his first audio amp at the age of 12 using the popular TBA810 which, much to his delight then, instantly became a local MW receiver too. While as a pragmatist he believes that digital technologies have replaced analogue largely for the better, he rues the fact that some of the best principles of analogue design, such as the principle of minimalism which it implicitly embodies, are slowly dying away.

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