Why does FM sound better than AM?

I don’t buy this explanation. The FM modulation uses a much higher bandwidth than AM. The distance between channels on FM radio is 200 kHz compared to only 9 kHz on AM. That’s more than 20x more bandwidth for FM. On AM, no matter how deeply you modulate the carrier, the bandwidth will not exceed twice the bandwidth of the input signal. On FM, the deeper you modulate it, the wider the output spectrum will be, and it can easily exceed the bandwidth of the input signal.

In addition to that, the whole FM band is much higher frequency, while I guess quite a lot of noise, especially burst noise caused by eg thunderstorms is relatively low frequency. So it’s not picked up because it’s out of band.

Any noise that falls inside the channel does get picked up by the receiver regardless of modulation. However because the available bandwidth is so much higher than the real bandwidth of the useful signal, there is actually way more information redundancy in FM encoding, so this allows to remove random noise as it will likely cancel out.

If I encoded the same signal onto 20 separate AM channels and then averaged the output from all of them (or better - use median filter) that would cancel most of random noise just as well.

Also another thing with modulation might be that if there is any narrow-band non-white noise happening to fall inside the channel (eg a distant sender on colliding frequency), on AM it will be translated as-is to the audible band and you’ll hear it as a single tone. On FM demodulation it will be spread across the whole output signal spectrum, so it will be perceived quieter and nicer by human ear, even if its total energy is the same. That’s why AM does those funny sounds when tuning, but FM does not.

The wider channels is the source of the available audio fidelity, but wider channels make you more exposed to noise, not less. A wider channel means listening to more noise sources, and having transmitter power stretched thinner for a much lower SNR.

In other words, the noise rejection of FM is what enabled the use of wider channels and therefore better audio quality. An analog answer before digital error correction.

In FM, the rejection is so strong that if you have two overlapping transmissions, you will only hear the stronger one assuming it is notably stronger. This in turn is why air traffic still use AM where you can hear both overlapping transmissions at once (possibly garbled if carrier wave was off), and react accordingly rather than being unaware that it happened.

Technology moved on from both plain AM and plain FM a long time ago, and modern “digital” modulation schemes have different approach to interference rejection.

Shannon theorem disagrees with you. The wider the channel, the MORE noise you can tolerate when transmitting signal at a given data rate.

In audio, the amount of information you need to transmit is naturally limited by the audio bandwidth (for FM truncated at about 15 kHz), so the useful signal bandwidth is fixed. Hence, if you transmit the same audio band over a broader channel of frequencies, you can tolerate more noise; or, for the same density of noise in the channel, you can get better SNR at the output. This is exactly what FM does. It uses the information multiplied in the most of that 200 kHz channel and projects it on 0-15 kHz band.

While you are right that a wider channel captures more noise in total, noise does not add up the same way as useful signal, because it’s random. Doubling the channel width only increases the amplitude of noise by sqrt(2).

There is no “magic noise rejection” coming from different ways of modulating the signal if all other things are the same. You can’t remove noise; you can’t magically increase SNR. If anything, FM makes the noise more pleasant to listen to and perceivably quieter by spreading non random, irregular noise over the whole band so it sounds more like white noise.

But it also allows to use wider channels, and increase the fidelity of the signal, including increasing SNR. But that’s thanks to using significantly wider channels than audio.

Also, it’s not like FM can use wider channels because of better SNR. FM can use wider channels because of how this modulation works - the spectrum of FM signal can be arbitrarily wide, depending on the depth of modulation. AM cannot do that. It only shifts the audio band up (and mirrors on both sides of the carrier). It can’t “spread it”.

Btw: this is a very similar phenomenon as when you average multiple shots of the same thing in photography, eg when photographing at night. By adding more frames (or using very long exposures) you obviously capture more total noise, but the amount of useful signal grows much faster because signal is correlated in time, but noise is not.

You are applying Shannon theorem incorrectly. Both AM and FM modulations are nowhere even remotely close to using their bandwidth with 100% efficiency, due to technology costs, and the difference in modulation is crucial. The article is correct and the mathematical models of AM and FM are well understood since decades.

Where did I say AM and FM are close to 100% efficiency?

I was only replying to an obviously incorrect statement that by using more bandwidth you decrease SNR. If it were the case, Shannon theorem would not work.

It doesn’t matter how close to the limit your encoding is, whether it is 20% or 99% the relationship between the bandwidth, noise floor and how much data you can send stays the same - by increasing bandwidth you can usually send considerably more information even if your encoding is poor. Which in translates to either a wider useful bandwidth or lower noise floor or any combination of both.

A trivial thought experiment to illustrate this: For any analog encoding, if I double the transmission bandwidth by encoding the same signal over 2 channels instead of one, I can average the output signal coming out the receivers and get better SNR than using one channel and one receiver. That works regardless of AM, FM or whatever fancy encoding you could use.

> A trivial thought experiment..

That's not how this works. That's not how any of this works. Averaging a high SNR channel with a low SNR channel is likely to produce something less good than the high SNR channel. Could you get an improvement over the high SNR channel? Yes, and the limit of the improvement is related to the SNR of each and averaging the signals won't get you anywhere near that.

Averaging two noisy signals increases SNR. That’s not even a thought experiment, that’s a reality. This is a technique used by probably all modern smartphone cameras to do night photos, as well as a common technique used by astrophotographers. Instead of taking one picture, you take a series of pictures and then align them and average. This improves SNR dramatically. A very long time ago we used this technique to get razor sharp, low noise pictures of the Moon at 3k x 3k resolution using… a cheap VGA internet camera: https://astronet.pl/wydarzenia/n2309/ Note that cameras at those times were barely capable of doing videoconferencing in artificial evening light - what you saw was mostly noise. Those sensors were really, really terrible.

What you seem to be missing is the fact we’re talking here about transferring the same fixed bandwidth signal over a wider channel, not transferring a wider bandwidth signal over a wider channel.

// edit: just noticed someone else gave another nice application of this phenomenon: GPS

Let's take it to the limit:

Signal0: infinite SNR. Signal1: anything less.

I just don't see how the output of averaging these would improve over Signal0. I don't think it can.

They're thinking about when you sample from the same noise distribution, averaging gives an unbiased estimator of the mean. But when you know one SNR is higher than the other, maybe this doesn't hold? But maybe if you transform the distributions to look the same, thus taking a weighted average? I'm not sure.