why does frequency modulation have a higher signal to noise ratio than amplitude modulation?

Question

A mathematically backed answer would be much appreciated! Please by all means use fourier to answer if you can.

Even an answer without mathematical backing would be appreciated.

Answer 1

In an AM signal the carrier wave is set at a static frequency and it is modulated by an audio signal that varies the amplitude to encode information into the waveform.

In an FM signal the carrier wave has a constant amplitude and is modulated by an audio signal that varies the frequency in order to encode information.

The measured signal in both AM and FM is a combination of the ideal signal (carrier + modulator) and the noise.

Normal noise in the radio spectrum is primarily amplitude varying. A lightning strike as measured within the relatively narrow frequency band of a carrier wave would be seen to have enormous amplitude variation and far less frequency variation.

With AM, the noise is additive in the same dimension as the signal (amplitude signal corrupted by amplitude noise) while in FM the noise is more orthogonal (frequency signal + narrow-band high variance amplitude noise)

The fourier analysis would basically show that the frequency spectrum of noise is minor and therefore has little effect on the SN of FM.

Answer 2

Shannon's information theorem shows that a signal can propagate through a lower S/N ratio if the bandwidth is higher. In an ideal situation, the propagation is exponential in the bandwidth, but nobody knows a good way to get a result that good. FM modulation gives a propagation which is the square of the deviation ratio; for a typical FM signal limited to 15 kHz, the deviation ratio is 5, so the bandwith of the first sideband is 75 kHz. Ths gives a S/N a factor 25 better than AM.

Answer 3

Hi AM is sensitive to external influences (lightning, electric fields, etc.) whereas FM is not. An external noise which does not result in a frequency change (as most do not) has no effect on the detector circuit.