# How exactly does AM/FM carry both pitch and loudness of voice?

Almost every tutorial on AM/FM modulation shows the modulating signal as something like a simple tone or continuous sine wave. Now that's easy, and for AM you just superimpose the modulating signal over the carrier wave as an envelope, and voila, and for FM you continuously and consistently vary the frequency. but no one seems to point out the obvious problem... Voice has both pitch, i.e. frequency, and loudness, which are two separate analog data streams. No tutorial nor explanation I have seen then takes the next, glaringly necessary step, to explain how both aspects are transmitted over radio schemes that apparently can only take one degree of variation, i.e. amplitude for AM or frequency for FM.

TL;DR:

1. How does AM or FM modulation, each of which only have one modulatable variable, carry both the pitch and loudness of voice, which are at least two distinct analog streams of data?

2. Why does absolutely nobody seems to address this glaring question in any tutorials/video/write-up on radio modulation?

• You understand how a signal is modulated, right? So it has the frequency, which is a pitch (roughly speaking), and amplitude - which is the "loudness". These are not different streams. These are parts of the same "wave", which is the "envelope" of ,say AM-modulated signal.. Sep 20, 2018 at 21:47
• Both modulation schemes modulate the carrier amplitude or frequency with all aspects of the audio signal, though stations do use compression of the audio to avoid over modulation which leads to severe distortion and side-band noise.
– user105652
Sep 20, 2018 at 21:53
• frequency, and loudness, which are two separate analog data streams ... that is incorrect .... it is only one analog data stream Sep 21, 2018 at 2:38

Voice has both pitch, i.e. frequency, and loudness, which are two separate analog data streams.

No. Voice is transmitted initially as one analog 'stream' of sound pressure waves in which the air pressure variation amplitude corresponds to the volume (at that instant) and the rate of change gives the pitch.

No tutorial ... explain[s] how both aspects are transmitted over radio schemes that apparently can only take one degree of variation, ...

The AM and FM modulation schemes are analog and are called analog because the modulation is analagous (adjective, comparable in certain respects, typically in a way which makes clearer the nature of the things compared) to the original signal - voice or music.

But I am also curious as to why this next obvious question that never seems to arise to the people making these tutorials and explanations, nor is the answer easily found out there, as I've been fruitlessly searching.

Maybe there's an opportunity for you there when you figure it out.

The tutorials demonstrate the results with sinusoidal signals because otherwise it would be impossible to see the modulation of a complex signal on a reasonable scale on a diagram.

Figure 1. The Simplified analysis of standard AM from Wikipedia goes a little bit of the way to describe what you are asking.

Notice in the illustration that the waveform is not sinusoidal but is an arbitrary waveform. Notice also that the amplitude modulation just follows the signal waveform. There's not much more to it. The microphone will convert the voice into an analog electrical signal and the modulator will modulate the carrier analogously too.

• Aaaah. I got it now. I feel kinda dumb...although, certainly, no tutorial I have seen addresses the second part, showing how it works with complex waves, but I totally missed the part about the instantaneous amplitude of versus the rate of change of the amplitude being the actual frequency change. Darn it. And all these years I didn't get it. Sep 20, 2018 at 21:57
• @Sparky256: AM radio was around much earlier than the 1950s - Wiki says widespread broadcasting started in the 1920s. FM was invented in 1933 with experimental broadcasts in 1934. Sep 20, 2018 at 22:35
• This is a good answer! @aAaaaAaa; one thing that helped me understand this was when I realized how stunningly fast the carrier wave is compared to the audio which is being transmitted. Sep 20, 2018 at 22:55
• @bits: One of the things that surprised me as I aged was the realisation that some of the AM frequencies weren't all that high. The European LW (longwave) band starts at 148.5 kHz which is roughly only ten times the highest audio frequencies it will transmit. (Maybe you can't even transmit 10 kHz audio on LW radio?) Sep 20, 2018 at 23:04
• @Transistor nyquist would tell you that you only need a carrier 2x higher than the highest frequency for AM. Sep 21, 2018 at 8:48

Forget about radio — how do you think voice is transmitted over a wire, which only has "voltage" — again, a single variable?

The point is, "pitch" and "amplitude" are abstract parameters of a single-valued function of time. In fact, you can superimpose many different signals at different frequencies on a single wire. Each component of such a complex waveform has its own frequency, phase and amplitude, yet we can still tell them apart.

It is possible to convert voltage to amplitude in an AM transmitter, and convert it to frequency in an FM transmitter. In both cases, the signal can be converted by the receiver back into a replica of the same voltage waveform that created the modulation in the first place.

So if you believe that voice (and music, for that matter) can be transmitted over a wire, it's a simple extension to transmit it as a radio signal.

• Actually, you can even forget about voltage over a wire. How does the sound of a voice get from the mouth of one person to the ear of another person in the same room? Again, it's a single value, instantaneous air pressure, that varies with time.
– user197845
Sep 21, 2018 at 14:49
• @besmirched: Fair point, but this is an EE site, so I needed to keep my answer on-topic :-) Sep 21, 2018 at 15:06
• Maybe the tiny charges created by the stereocilia in response to changes in pressure count?
– user65586
Sep 21, 2018 at 15:17

Sound is just a single-dimensional time-varying signal. Microphones essentially continuously track variations in air pressure. At any point in time, this is a single value. This value is what gets 'modulated' onto the carrier.

This single-dimensional time-varying signal carries both the loudness and pitch information. It can actually contain the loudness and pitch information for many different voices at the same time, or many musical instruments at the same time, etc. in this single time-varying value.

Voice has both pitch, i.e. frequency, and loudness, which are two separate analog data streams.

There's more than two, depending entirely on how you perceive/analyze it, and what else is going on, on the track. There could be hundreds in a My Bloody Valentine song, the streams have streams and they go to 11.

What if we forced them all to fit onto one data stream?

Because that is exactly what happens when those things all enter the medium of air, which is the innate medium for all sounds. It can only handle one data stream, so the compression is forced.

When we stick a microphone in that air and get a waveform, we are getting the one data stream. Separating Bilinda Butcher's breathy trill in the chorus from what her MP-41 Phase Compressor (particularly) did to her guitar amongst the 16 other effects pedals in the stack... It's impossible. Because so much uniqueness has been lost in the compression into that single stream.

And yet, that's what music is, and we love it.

This one microphonable stream is the thing that gets encoded on AM or FM. That's what you have been missing.

I'm ignoring stereo, that's a deal of its own.

In a simple AM system, the transmitted signal is something like

$$x(t) = A\left(1+m(t)\right) \sin\omega_c t$$

and $$\m(t)\$$ is called the message signal.

In an AM radio, the message signal basically just says how hard to push the speaker cone at each instant in time. If the audio signal is a single tone, $$\m(t)\$$ will itself be a sinusoid.

If you want a louder tone, you increase the amplitude of $$\m(t)\$$. If you want a higher frequency tone, you increase the frequency of $$\m(t)\$$.

And if you want a musical audio signal, you sum together multiple tones with different frequencies and amplitudes, and vary them in a melodic way.

Voice has both pitch, i.e. frequency, and loudness, which are two separate analog data streams.

"Pitch"/"frequency", "loudness"/"amplitude". Those words belong to a model that we construct to understand sound/voice/music and human hearing. But many phenomena can be modeled and understood on different levels--sometimes, on many levels.

Another way to describe sound is with a single quantity, sound pressure, that varies with time. (See Dave Tweed's answer). Sound pressure is a concept that belongs to a lower level/more primitive model. It also is the quantity that AM or FM radio modulation conveys.

Why does absolutely nobody seems to address this glaring question...?

IMO, it is very common for authors and educators to focus on teaching one particular model of some phenomenon, and they lose track of the fact that there are other models and other levels of understanding. Someone who's main interest is understanding how human brains process speech or music can have a completely different understanding of what sound "actually is" as compared to somebody who is interested in designing radios. And, if both of them are sufficiently closed minded, they can have a hot argument about which one of them is "right."

Neither of them is right. Sound isn't actually what either one of them says it is. Sound is just what it is, and they have different ways of understanding it.

Not yet mentioned is how FM does this. The amount of frequency deviation from the carrier frequency corresponds to amplitude. Higher frequency is positive amplitude, lower frequency is negative amplitude. The rate of change of the FM signal corresponds to the frequency.

Wiki article includes a moving image for both AM and FM.

https://en.wikipedia.org/wiki/Frequency_modulation

• Sure, but that does not in any way address the question, or the fundamental misconception driving it. Answers need to either answer the question, or explain why it is mistaken, not make tangential commentary. Sep 22, 2018 at 5:42
• @ChrisStratton - the OP asked how frequency and loudness information is transmitted. My answer was specific to FM, since there are already other answers for AM. I assumed that noting amplitude is related to frequency would explain how loudness information is transmitted, and that that the rate of change in that amplitude the amplitude information would explain how frequency information is transmitted. The animated image in the wiki article shows this fairly well. Sep 22, 2018 at 5:46
• I believe rcgldr is correct, that while both loudness and pitch were well-explained above for AM, the pitch for FM was not explained well. And in my experience, it's typically because most don't understand it. Pitch in FM is represented by the rate at which the signal deviates from the carrier frequency. FM can be represented mathematically as y(t) = Acos[2πgt + (Mp/f)sin(2πft)] in which A = carrier amplitude g = carrier frequency M = voice (modulating) amplitude p = peak deviation f = voice (modulating) frequency.
– Noji
Mar 2, 2020 at 10:45
• From this equation, you can see that a) the louder the voice M, the greater the swing (deviation) away from the carrier frequency and b) the higher pitch the voice f, the quicker the swing between the two deviation maxima. This allows for a high pitch in a soft voice (a quick but not far swing), low pitch in a soft voice (a slow and not far swing), high pitch in a loud voice (a quick and far swing), and low pitch in a loud voice (a slow and far swing).
– Noji
Mar 2, 2020 at 10:45

It's been pointed out that the instantaneous signal level is just a one-dimensional time-varying variable. So why bother with sine signals? Because both AM and FM are used for transmitting a band-limited signal through a higher-frequency carrier signal, and the simplest band-limited signal is a sine signal as it has only a single frequency. AM is pretty straightforward regarding its frequency spread (and you can double the capacity by using sideband modulation) whereas FM is quite more fuzzy and involves Rice distributions, with the frequency spread partly depending on modulation depth.

Either way, the simplest signal for analysing the combination of a carrier frequency and a band-limited signal remains a sine signal.

• I think they meant to ask why more arbitrary waveforms aren't used more often as the signal to be sent in examples. I don't think they were asking why the carrier wave is a sine wave. Sep 21, 2018 at 15:43

In addition to the existing answers which point out the fundamental misconception about signals in general, let me point out something. You write:

Almost every tutorial on AM/FM modulation shows the modulating signal as something like a simple tone or continuous sine wave

Yes, and that's perfectly fine without loss of generalization thanks to Fourier's theorem, according to which most signals we care about can be expressed as a sum of sines.

The (quasi) linearity of our devices then makes it admissible to reason about simple sines guaranteeing that things will work out even in the presence of more complex signals - linearity essentially means that feeding a sum of sines to a device is the same as summing the results of feeding n sines to n devices.

• I had considered adding some comment on Fourier in my answer but decided that it only covered periodic signals and general music and voice would not fit into that category. Sep 23, 2018 at 9:20
• This is not really my field and I don't think that going too much in depth will help OP, so I think some handwaving is okay, but as I understand it a non-periodic signal such as speech is simply taken to be piecewise periodic in order to leverage Fourier's theorem. And lo, we can still get MP3s of Milli Vanilli. Sep 23, 2018 at 9:30

I agree with you that there are two separate information components of sound waves, pitch (frequency) and volume (amplitude).

As shown in fig 1 of Transistor's answer, not only does the sound wave varies in amplitude, it also varies in frequency. The amplitude of the sound, modulates the amplitude of the carrier, while its frequency modulates the frequency of the carrier. So the carrier also has both information components of the sound wave. After the carrier is demodulated, both information components of the original sound wave are recovered.
Hopefully this clarifies your misunderstanding of the capabilities of the carrier, and makes it clear that it has two (not one) degrees of variability.

• Have another look at my Figure 1. You can see that the AM frequency is constant. There is only one degree of variability - the amplitude. You are missing something in your understanding of modulation. Sep 28, 2018 at 5:40
• You're making the same mistake as the poster - amplitude is not really separable from frequency, you only have the strengths (and phases) of frequency components, or to put it another way, a frequency is present only if it has a non-zero magnitude. To really understand the original mistake, consider how timbre is conveyed, ie how we hear a trumpet as distinct from a clarinet. Is that a third degree of freedom? No. It's just a different mix of frequency component strengths (even overtones are missing on a clarinet). The same goes for multiple instruments or multiple people talking at once. Sep 28, 2018 at 6:19
• But then Transistor is also wrong - the frequency of an AM signal is neither constant nor singular, if it were there would be no information content. The information content is all in sidebands displaced in frequency from the central or carrier frequency component. All the carrier does is serve as a reference permitting simpler detectors, vs needing to manually or algorithmically tune the local oscillator feeding the product detector that would be needed if the waste power in the constant frequency carrier component were removed (as long routine outside of legacy settings) Sep 28, 2018 at 6:25
• @Transistor: The frequency I am referring to is the sound. You can clearly see that the left side of the wave has a higher frequency than the right half. Sound does not have a constant frequency (or amplitude). Sep 28, 2018 at 7:00
• @Guill: But that's not quite what you said. "The amplitude of the sound, modulates the amplitude of the carrier, while its frequency modulates the frequency of the carrier." Sep 28, 2018 at 11:11