What is Distortion?

In the audio sense, a distortion occurs whenever there is a difference between the input and output signals into and out of a device. In terms of signal processing, distortion could roughly be defined as ‘the signal changing in form, or introduction of a signal that was not in the original input’.
If you look at the frames below as an aid, you will see that there is distortion in the picture depending on how the screens are oriented relative to the projector – to compensate for this, most projectors have a feature called ‘Keystone correction’.





A normal image (in the middle) along with images distorted due to angle between the projector and the screen

In order to see the ideal, distortionless picture, the Keystone correction must be employed to compensate (there are other distortions that must be taken into consideration, such as the spherical aberration or distortion on CRTs due to the curved screen – optics and video processing also has a lot to do with distortion and its elimination).
To switch gears a bit to return to the original topic, there are also many types of distortion in audio:



1. Frequency Response Distortion
The Frequency Response Distortion is basically a way of looking at the Frequency Response graph. The underlying idea is that if the input signal is flat, then the output must also be flat; otherwise, the difference is attributed to distortion.


Unlike the original input (in white), the frequency response of the output (in green) is not flat. The low-pass filter has been poorly engineered in this product (in terms of frequency), and the same characteristic could also be expressed in terms of signal over time, as follows:

Original Signal


Signal through a high pass filter


Signal through a low pass filter

2. Amplitude Distortion
Amplitude Distortion refers to when the linear relationship between the amplitude of the input and output signals are broken.
For instance, if there is an amp that is supposed to amplify the signal by a factor of two, then a 1V signal through the input should result in a 2V output; we would then expect to see a 0.5V input produce a 1V output, but the output measures differently (0.9V, 1.1V, ….), the amplifier is said to exhibit amplitude distortion. Perhaps the most common example of amplitude distortion is the dynamic compression used in mastering modern records.


Original signal


Output through a non-linear
(e.g. Dynamic compressor used in recordings)

image reference : http://en.wikipedia.org/wiki/Distortion

3. Harmonic Distortion
The Harmonic Distortion is one of the most commonly used measures of distortion regarding audio products, and also happens to be the main subject of this article (more on that later).
When a pure tone (1kHz) signal is fed as input, the ideal output should only have the corresponding peak at that frequency. What actually happens though, is that signals are detected at 2kHz, 3kHz and so forth in addition to the original signal – these signals are called harmonics.


Harmonic signals from a 1kHz Sine Wave input

Since the harmonics were not a part of the original signal, they are considered to be distortion; the corresponding empirical measurements are the THD (Total Harmonic Distortion) and the IMD (Intermodulation Distortion).

4. Miscellaneous Distortion
There are many other types of distortions in addition to the ones mentioned, such as the phase distortion caused by capacitance and inductance (which plays an important role in designing speakers), or the group delay, which is caused by signal delays of each frequency, but we will not go further into these in this article.

To summarize,
Distortion refers to the difference between the input and output signals through a particular system, be that difference a newly created peak, change in relative intensity of frequencies, etc.. And such distortion is detrimental to high-fi audio, where the intent is to be as faithful as possible to the original.


What do distortion measurements sound like?

Each type of distortion has its own testing methodology, today we will be looking at results from RMAA (used at GE for reviews).

1. Frequency Response – Frequency Response Distortion


The original signal (white) compared to the output of a product with an uneven frequency response

(green – the low pass filter has been poorly designed)

The horizontal axis on the frequency response graph represents the frequency, or the pitch, and the vertical axis represents the sound pressure or sound intensity in dB.


If you pay close attention, you’ll notice that the horizontal axis is plotted on a log scale (where each movement to the right represents an equal increase by proportion). The reason why the frequency axis of a FR graph is drawn this way is because this is how we perceive sound pitch. That is, it helps make the graph more relevant to perception.
The vertical axis, in decibels, does not need to be plotted on a log scale because decibels are already calculated logarithmically.
Due to both axes being adequate representations of human hearing, the frequency response graph is already in terms of what we feel and hear, without requiring further explanation.

2. Dynamic Range, Noise Level – Amplitude Distortion
Though the dynamic range itself is not directly related to amplitude distortion, we will consider dynamic range in relation to the noise level and the amplitude distortion since compressors (again, the staple example of amplitude distortion) tend to reduce the dynamic range.



Dynamic range and noise level, both having to do with the maximum contrast in intensity, are plotted on a log scale on the horizontal axis (frequency) with a linear scale vertical axis in dB representing intensity.

As the unit dB was devised with the human perception in mind, the numbers closely reflect what people hear. Thus, an equipment with a smaller dynamic range will have little contrast in intensity between loud and small sounds (relative to each other) and a product with a higher noise level will have a sound muddled by more noise relative to the music itself. And there is a very good correlation between the perceived sound and the empirical data.

3. THD(Total Harmonic Distortion), IMD(Intermodulation Distortion) – Harmonic Distortion
The distortion data that we’ve seen thus far have mirrored the perceived sound rather closely, owing to the fact that the data were expressed in terms of what we hear. Unfortunately, the same cannot be said of the THD and IMD measurements, which are used to measure harmonic distortion.


Just as in previous examples, THD and IMD are both drawn on the Hz – dB plane, but there is another factor that we have to consider before we translate them to perception: the Masking Effect.




Harmonics and the Masking Effect

There is a couple that I should mention on this subject: Mr.Earl Geddes and Ms.Lidia Lee, who have conducted research on the topic. If you are interested, please take a look at: Sound Quality Perception


The below diagram represents the envelopes inside which the harmonics are rendered inaudible due to the masking effect of the signal itself. You’ll see that lower order harmonics are relatively inaudible as they are inside this envelope, whilst the higher order harmonics relatively stand out as they occur outside the masking zone.
The diagram beneath shows similarly the masking envelopes, but for low level signals; the masked area shrinks dramatically with the reduction in signal, thus exposing the harmonics.


For this reason, THD and IMD (which fail to reflect masking) are not the best indicators of how much distortion is actually heard – this necessitates a new metric that has been weighed (so as to make more audible portions have more weight) to better reflect human hearing.

If you want to read more on this topic, try the following:
AES presentations on Distortion Perception I  and  Distortion Perception II
In these papers, the following formula is suggested as the new metric for harmonic distortion, intended to add weighting to the commonly used THD and IMD measurements:


This might appear random due to the math, but when the harmonics data were translated using the formula, the Gm value was found to have a close correlation with the perceived sound, where below 1 was inaudible and 3 represented barely audible.
The GedLee Principals concluded that
* THD and IMD have no correlation to the subjectively perceived distortion in a nonlinear system.
* This study offers strong support for the contention that distortion metrics must include some form of masking model.
* A new metric, Gm , is proposed which has been shown to have a very high level of correlation to the subjective perception of distortion in a nonlinear system.


Currently, Orfeo SoundWorks provides the THD and IMD values using the RMAA – we wanted a software that supported Gm  because of the problems above, but we encountered several problems.
1. The Gm  metric is yet to be considered mainstream (it was a ‘proposal’).
2. There wasn’t any software that supports Gm .
In conclusion, while the current measurements used at GE and elsewhere for harmonics distortion is not optimal with regards to the subjective perception, it is difficult for us to present an alternative that better reflects the perceived sound.