The Fundamentals of Signal Processing - Part 1
By Paul Marossy
If you have been a musician for a while, you have probably heard a lot of buzzwords, like distortion, headroom, clipping, etc. The purpose of these pages is to help bring about a better understanding of what is meant by some of these terms. This is by no means intended to be an exhaustive primer, just a general overview.
To most electric guitarists, a little bit of distortion is a good thing - it gives an edge to the sound of a guitar. Or for some, it's that wall of sound that fits their style of music. Or maybe it's to get singing lead guitar tones. All of these use different shades and amounts of distortion. It would be a good exercise to learn just what distortion is, and what makes for a good sounding one and one that doesn't sound good. Distortion does just what its name implies - it distorts the signal. This is different than compression, but the two can coexist in a signal, such as the distortion some pedals can produce. To better understand what distortion looks like, lets see at what it actually looks like on an oscilloscope.
Here is what is referred to as a sine wave. Shown below is a 1kHz sine wave from an audio oscillator. The fundamental tone from an uneffected guitar signal would also look something like this:
Notice how the waveform is uniform and rounded. A pure sine wave has mostly the fundamental frequency with relatively few harmonics.
Distortion is commonly produced by really amplifying the signal and then "clipping" the tops of the sinewaves off. So you get something that looks like this:
This is what the output of one of my distortion pedals looks like with the same 1kHz signal, gain control at maximum. Now it looks a lot like a square wave, this is an example of really "hard clipping". Notice the rounded corners? That is important. A pure square wave sounds buzzy, but the waveform above sounds more like a really high gain distortion because some even order harmonics are present in the signal, but it is approaching sounding buzzy. Square Waves have a lot of odd order harmonics packed in them - only odd order, which accounts for the way they sound. Too many odd order harmonics can really sound horrible with a guitar signal, but acceptable with a synthesizer. Why is that? I think it's because once someone has heard an uneffected guitar and then hear it through something that turns it into a square wave, it just doesn't sound right, or at least to most people, very unpleasant. On the other hand, a synthesizer, well, it's supposed to sound like that - after all, the sounds are synthesized via a voltage controlled oscillator, commonly referred to as a VCO. (But, even a synthesizer doesn't really produce a true square wave, due to filtering) A smoother, lower gain distortion would have a more gentle slope on the rising parts of the waveform and a much more rounded top and the amplitude of the signal would be smaller in comparison to something that really amplifies the heck out of the signal before it is clipped. This is commonly referred to as "soft clipping". This is also what tube amps will produce when they are overdriven. Solid state equipment does not sound as good, but there are some circuits that use JFETs or MOSFETs that seem to sound just as good as tube distortion. Sometimes even a plain old NPN transistor can sound good.
So, when one refers to the signal clipping, that is what is occuring. In tube amps, the clipping sounds more pleasant because of the inherent nature of tubes. That is because in terms of harmonic distortion, tubes produce mostly 3rd order harmonics along with a very strong 2nd order harmonic and many other harmonics as well, mostly even ordered ones. This is one reason why tubes sound "warmer" than solid state. Solid state devices produce predominantly strong 3rd order harmonics and not a whole lot else compared to the 3rd order. That is why they can sound harsher and colder than tubes. But, these are only generalizations, and are not set in concrete. There are other contributing factors as well, and not everyone can even hear any differences between tube and solid state amps when participating in hearing tests.
According to an article apparently published by Fender around 1981, "Listening tests indicate two causes for differences in perceived sound in tube and transistor amplifiers. These are ripple intermodulation distortion and frequency response differences caused by the reactive speaker load interaction with the output impedance of the amplifier." Also quoting the article, "The change in frequency response caused by the high output impedance of the tube amp is by far the predominant cause for the differences." I think these few lines out of the conclusion of the article really sum it up. People can hear a difference between the two, but it's apparently not for the reasons usually cited: the relationship between odd and even order harmonics, especially the 2nd and 3rd orders. I do, however, feel that all these things probably work together in the overall sound that a subject hears and shapes the perception of what is being heard. The study of sound and its perception by the listener is called "psychoacoustics".
Now, when you want no distortion, but a more true representation of the original signal, you don't want the signal to be clipped, at all. If this happens, it may not sound good and of course, it will alter the original signal so that it doesn't sound like it did originally. This is where "headroom" comes into the picture. Headroom is simply referring to the ability of a circuit to handle the signal it receives before it will clip the signal. Headroom can be increased in many ways, but it is not in the scope of this article to go into depth on the subject since it really is getting into circuit design, which was not the objective of this article. There are other measurements that can be made, such as THD (total harmonic distortion), power in watts RMS, etc. But, for our discussion, we are mostly concerned with what is happening to the signal itself.
For some in depth discussions on distortion, see the "Distortion 101" article at www.geofex.com.
For more information on compression, harmonics and limiting in distortion pedals, see the Lab Notebook section at AMZ.
For a comparison of tubes and solid state devices and discussion on the harmonics related to them, visit this page.
The
next page in this series will talk about EQing, and how it affects the sound
of different instruments.