8/10/14 - THD - Part 2

As I mentioned in the previous blog post, THD measurement allows us to see the response of a nonlinear system to a spectrally pure sine wave.

This means we can quantify, in the frequency domain how linear a system is in one dimension. This is also the flaw of THD. As we will see in later distortion analysis, the effect of distortion on a complex signal is far more variable and complex than that of a sine wave.

Below is an fft graph of a 1kHz sine wave, being clipped at a ratio of 1:2 i.e. the output of the system at the sine to (if the system was linear in response) would be a single tone at 1kHz of 0.5.

As we can see, there is harmonic content distributed at multiples of the fundamental frequency. The magnitude of the fundamental is reduced, but is still greater than the 0.5 intended limit. This is due to the fact that this is a graphical representation of the magnitude of frequency components, of a signal which has been analysed using a Fourier transform. Such is the companies between frequency domain analysis of changes that are made in the time domain. If we did a correlation between the distorted and non-distorted vector, we would be presented with a coefficient of 0.9739, which means that the change in values within the vector for a signal of roughly 23% THD, presents a 0.9739 similarity to the non-distorted signal.  

If you have ever heard something with 23% THD present, you will know that it doesn’t sound 97% similar to the non-distorted version, anecdotally. So where does this leave us? We cannot use THD to analyse complex signals, because there is inherent interaction between the frequency content a complex signal and the components caused by the nonlinear behaviour. Another angle which is not looked at In this view is the effect of phase on the signal. We need a way of looking at the effect of a nonlinear device on more than one frequency component.

We can also see that the first harmonic is dominant in this signal, and far out-weighs the energy of the following components of the signal. However, this relationship may change depending on the nonlinearity. An example of this is taking the square of the signal. This pitch-shifts the output signal, as can be seen below. Not that no other frequency components occur, and the amplitude is limited to 0.5.

It is possible to modify a nonlinear behaviour to give a pattern which is far less predictable that those shown previously, as can be seen below. This came from using the nonlinear expression (2.5*atan(0.9*x)+2.5*sqrt(1-(0.9*x).^2)-2.5) - x;

Performed on the sinewave vector x.

This is the result:

As it happens, this behaviour sounds more like a bitcrusher, where some of the other behaviours sounded rough and distorted in a more regular or recognisable pattern.

I WILL LATER ADD SOME REFERENCES TO LOOK AT

I have found a number of papers discussing methods of looking at THD in the time domain, but nothing that is either well written or seems to work.

There is another method for analysing the effect of a nonlinear device on a signal. This is Intermodulation, which I will discuss in the next post.

In the next week I am to look at ways of comparing distorted and clean signals.