The elegance of FM stereo

FM radio is going to die. Slowly, inevitably, it is going to be overtaken by digital radio that squeezes many more stations into the same frequencies. Which is a shame, as FM exhibits what is, for me, an elegant engineering solution to a problem.

Originally FM was mono-only. That is, the stations broadcast just one signal that was fed to all speakers on the radio. In the 1950s it was realised you could broadcast stereo signals easily on FM. However this required sending two signals; one for the left-hand speaker and one for the right. An obvious approach would be for the left-hand signal to be broadcast on the mono frequency, and the right-hand on a frequency broadcast a short distance away.

However by this stage there were many mono FM radios in homes, and this approach would have made these useless as they would only get the left-hand signal (try listening to only one speaker of a stereo system to hear the problem).

To solve this, they came up with a simply cunning solution.

They broadcast a sum signal (left + right) on the main (mono) frequency and, a short frequency hop away, a difference (left - right). From these, both the left-hand and right-hand signals can be retrieved using simple analogue circuitry, and the mono signal maintains the qualities of the combined stereo channels.

Say at any one period the left-hand signal is at 5, and the right-hand at 7 (they are really sine waves, but the maths works well enough for discrete digital values).
This means 12 (5+7) is broadcast on the sum frequency, and -2 (5-7) on the difference.

To obtain the original left and right stereo values, you simply:
1) To get the left-hand signal, you add the difference and sum values, i.e. 10, then divide by 2 to get 5
2) To get the right-hand signal, you subtract the difference from the sum, i.e. 14, then divide by 2 to get 7

Of course there are other complexities, but the basic approach is simple: what is even better, it was easy to perform in 1950s-era electronics.

It is an utterly elegant solution. It also explains why, if you have poor signal quality, the radio degrades to mono, which is broadcast on the main frequency.

Digital radio has many interesting engineering and mathematical tricks, (for instance the magnificent Fast Fourier Transforms), but nothing beat the simple elegance of the FM stereo solution.

As usual Wikipedia has much more information and this page goes into more detail than almost anyone will want...