Signal to Noise Ratios

I was thinking about signal to noise ratios.  I don't know why reading The Hobbit would cause me to think about signal to noise ratios, but it does.  Sometimes I have trouble communicating topics like balanced signals and CMRR to people, so I decided to make some graphics to help out.

I made some noise (recorded a quiet room with my laptop's built-in microphone) and then generated a sinusoid in a second track.  The two wave forms are in the first picture (sinusoid on bottom).  The sinusoid has an amplitude that is much greater than the 'noise' signal.  I call it the good signal to noise version.



Then I cut the amplitude of the sinusoid to make what I call the bad signal to noise version (sinusoid on top). Note that in both the good and bad versions the noise level is the same, only the sinusoid level changes.


Then I summed each grouping of two waveforms to create a resultant waveform for both the good and bad signal to noise ratios.  The sum from the 'good' version is on top and the 'bad' is on bottom.  Notice that in the top (good) version you can easily tell what the original sinusoid is.  In the bottom (bad signal to noise ration) version, it is extremely difficult to tell what the original sinusoid signal was.



Now for why it's important.  The noise added to any signal is the same no matter what the level (volume) of the signal is.  Pretend that the sinusoid is what you want to hear (perhaps it is part of a guitar solo).  Most electric guitars have a volume control, as do effects pedals and amplifiers.  Cutting the amplitude of the sinusoid in step 2 is like turning the volume down on your guitar or amplifier.  As you can see in the third picture, when you have a bad signal to noise ratio, you can't really tell what the original signal is, but when you have a good signal to noise ratio that guitar solo comes through really well.

So the next time you're trying to set your volume levels between a source and a sink, try this method.  Play something that is the loudest possible volume you'd ever want, then set the source volume as high as you can without getting unwanted distortion (or damaging any of the equipment), but then back off just a bit.  Backing off just a bit allows for those times when you want to play something just a little bit louder than you did during the loudest part of soundcheck.