# Is FM effectively spread spectrum?

My understanding is that FM achieves better audio quality (under the right circumstances) than AM by spreading the narrow audio signal's information into a wider RF signal. Does this mean FM is technically a form of spread spectrum?

• to answer your title very distinctively: no. FM is not a spread spectrum method. The data is actually in the bandwidth used. Oct 31, 2022 at 13:16

This is the sort of question that often comes down to “what definition of the word is useful” — not necessary any objective truth. However, I would be inclined to say that no, wider FM should not be considered a form of “spread-spectrum”, even though it is a kind of “spreading” across the spectrum.

This is because modulation techniques that are considered spread-spectrum combine the increased bandwidth with some particular strategy for extracting the intended communication from that entire signal bandwidth (often by a pseudorandom sequence that the transmitter and receiver agree on). We can see this strategy as being a substitute for the simpler selection strategy of “use a narrow filter”. Thus, spread spectrum systems have resistance to interference of all kinds.

On the other hand, wide-band FM is not so general-purpose; it can result in reduced resistance to interference (assuming total power of the wanted signal and the interfering signal are kept constant), in at least one scenario: imagine an interfering single unmodulated carrier. If this falls within the bandwidth of the FM receiver, and is of equal or greater power, then the FM capture effect will greatly weaken reception of the wanted signal. Thus, all else being equal, increasing bandwidth increases the likelihood of interference. FM's “strategy” is “pick the strongest signal in this bandwidth”.

So, I would say that wide-band FM is not spread-spectrum because:

• Spread-spectrum increases signal bandwidth to improve signal-to-noise ratio against arbitrary interference (as long as it is uncorrelated with the chosen pseudorandom sequence).
• Wider FM increases signal bandwidth to decrease noise if the noise is not concentrated in a narrow band that could overwhelm the FM carrier.

Disclaimer: I'm not very well acquainted with the mathematical perspective on radio and signal-processing theory. There may be some considerations that I have missed.

In a spread spectrum system, you use a method of transporting data in some bandwidth, and then apply some way of spreading it over a larger bandwidth, whilst maintaining the original method of data modulation. "Spread" implies that the signal was narrow before and is made wide.

Common examples¹ of this include

• frequency hopping spread spectrum (FHSS), where you take some narrowband modulation method, but change the carrier frequency rapidly, so to spread the signal over more space where there's potentially narrowband interferers,
• direct-sequence spread spectrum (DSSS), where you take your data-carrying symbols (or bits), and multiply each of them with a sequence, thereby making many symbols (or bits) out of one, thereby increasing the symbol rate (or the bitrate), which leads to increased bandwidth requirement.

Now, FM is not such a technique: it doesn't take another method of transporting information and spread it. It just actually modulates the information in frequency.

¹ There's few others that you find in practice. Lora uses what they call Chirp spread spectrum, but that's really just using the delay of a cyclically shifted reference waveform (a chirp) in combination with DSSS. There's time-hopping, which is rarely used, for it doesn't have the narrowband-interferer robustness of FHSS, but all the average-power downsides.
If you need to make your low-datarate stream of data more robust and have bandwidth to spare, nowadays, you'd often rather go with something that can deal with a multipath channel, which you get through occupying much bandwidth, and has better gain than just repeating the same symbol – e.g., you'd do OFDM with N subcarriers and use a 1/N-rate code with heavy interleaving.

Classic spread spectrum takes a signal of a particular bandwidth and spreads it over a much larger bandwidth, typically in a discontiguous way. It uses a fraction of the bandwidth over which the signal is spread, potentially even blending into the noise floor when looking at the whole range.

On contrast, FM uses a contiguous portion of the spectrum in the bandwidth of its signal. The signal is not spread in a discontiguous way, as a true spread spectrum signal is.

A wider bandwidth FM signal tends to also have a wider audio bandwidth, so it uses the additional bandwidth to carry more information, where spread spectrum doesn't.

Well, one of the main reasons of saying FM may perform better than AM in terms of signal fidelity is hidden in the information transmission methodology.

It is known that an AM signal $$a(t)$$, if we consider $$m(t)$$ as the information or message that is going to be exchanged and $$c(t) = A_{C}sin({2{\pi}f_{C}t + \phi)}$$ as the carrier of the transmitter, can be written as;

$$a(t) = m(t)c(t) = A_{C}m(t)sin({2{\pi}f_{C}t + \phi)}$$

$$A_{C}$$ is the maximum amplitude of the carrier wave and $$f_{C}$$ is the frequency of that wave. I've also added that phase difference $$\phi$$ so as to show the more general formula of an AM signal. So, it is apparent that the message (which, theoretically, can be any kind of information but most of the time, because of the limitations on the bandwidth in the allocated frequency spectrum which makes things, e.g. streaming a video recording, impractical to be transmitted at required, sufficiently high information rates) is encoded into the amplitude of the carrier. The receiver, in this case, finds that information signal by applying specific processes on the amplitude of the modulated signal. However, this way of communication is prone to interferences and maybe, after implementing strong filtering mechanisms, the hardest to cope with appears to be the noise.

As a result of the superposition theorem, that noise directly affects the amplitude envelope of the modulated wave which means distorting the message from the first hand. Thus, on the receiver side, the SINAD (signal-to-noise and distortion ratio) is aggravated.

On the other hand, FM signal $$b(t)$$ (by using the same message and carrier waves) can be illustrated as follows:

$$b(t) = A_{C}sin[{2{\pi}f_{C}[m(t)] + \phi]}$$

Now, the information is altering the carrier frequency, i.e., the carrier frequency is the function of the message signal $$m(t)$$. Therefore, considering the same noise characteristics, the message is independent of amplitude-related issues.

As it can be seen from the drawing, although the noise slightly changes the amplitude of the FM signal, the frequency change of that wave is the same. So, the SINAD on the receiver could be much higher than that in the AM transmission scenario which increases the quality of the overall communications environment.

However, the FM transmitter should be equipped with very precise local oscillator waves. Otherwise, for example the phase noise on that FM local oscillator signal would act as an adverse factor as the AWGN (additive white Gaussian noise) in the AM scheme.

And, as to your question which is about possibility of assigning a spread spectrum feature to the FM technique: No, FM is not a form of spread spectrum but it can be considered as a frequency hopping mechanism.

The above figure shows the ideal (theoretical), one-sided magnitude spectrum of the FM signal $$b(t)$$. By changing the carrier frequency, the Dirac delta moves on both directions. This may be useful in avoiding a specific jamming signal component in the spectrum. But, the spread spectrum technique is a different topic which utilises rectangular pulse signals (here, digital systems come into play) and coding. Very briefly, by resorting to the relationship between temporal-spectral information when expanding-compressing signals in the time domain, the spread spectrum can be achieved.

• Hi, while this is an explanation of FM, it does not address the question asked in the question, at all! Oct 31, 2022 at 13:17
• I wonder how we can make the most of this answer! It's a high-effort answer, and I like that. Could you maybe explain what you think about the question, based on your explanations in the answer? Maybe there's just one final small paragraph missing that says "So, yes, FM can be considered a spread-spectrum method because…", or "So, no, FM can not be considered a spread-spectrum method because…"? Oct 31, 2022 at 13:20
• (by the way, no, spread spectrum techniques don't necessarily use rectangular pulse shaping.) Oct 31, 2022 at 14:07
• The word "hopping" implies discrete hops. This is really not the case here. And, again, the frequency is the data-carrying quantity, not a way to spread it :) But I do like the analogy you're making here: The signal has more bandwidth than the message has. Oct 31, 2022 at 14:48
• a hop cannot be "continuous". That's really an oxymoron. It's really not a spread spectrum technique if the frequency swept is actually the message content ;) Oct 31, 2022 at 15:21

My understanding is that FM achieves better audio quality (under the right circumstances) than AM by spreading the narrow audio signal's information into a wider RF signal. Does this mean FM is technically a form of spread spectrum?

To answer your implied question: Why does FM sound better than AM?
The first thing to understand is what AM is; AM is generated by an audio signal modulating the power output of a transmitter, at the same rate (frequency) as the audio signal. The "A" in AM refers to the amplitude, or power output, relative to the unmodulated carrier. It is the power difference between the unmodulated and modulated carrier that the receiving radio actually uses to recreate the audio signal. Typically, the bandwidth of the audio allowed to drive the transmitter is limited to ~3000Hz, this is strictly due to the spacing of the AM channels which is 10KHz; so why limit the audio bandwidth to 3Khz? Because when the radio frequency (the carrier) is modulated by the audio frequency, it results in producing additional radio frequencies, called sidebands, these sidebands are simultaneously created that are the carrier frequency plus the audio frequency, and the carrier frequency minus the audio frequency. So a 3Khz tone driving an AM transmitter transmitting on a carrier frequency of 1,000,000 Hz, actually creates sidebands that are transmitting at 1,003,000 Hz and 997,000 Hz. But the sidebands are of no consequence to the AM receiver, they are just a byproduct of modulating one signal with another; the audio bandwidth is limited because of the desire to have AM channels spaced 10Khz apart and limit interference from adjacent channels.

If you wanted to increase the audio bandwidth of AM radio to approach FM fidelity, you would have an AM transmitter that could modulate the transmitter at up to +/-20Khz, the limiting factor to quality then would be the power output ratio between the unmodulated carrier and the maximum power the transmitter could be driven to by the modulating audio, and your proximity to the transmitter; this is because the "loudness" of the signal received is determined by the strength of the signal, and the dynamic range is determined by the ratio of the strongest to weakest signal detectable by the receiver. To be clear, a weak signal wouldn't necessarily mean a lower frequency range, it would mean a less loud station with lower dynamic range, and maybe not even being able to hear the quieter parts of the audio. (Try listening to a distant AM station playing music, you'll hear what I'm talking about.)

However, this proximity to the transmitter is not nearly as much of a problem for FM, this is because FM is not dependent on any relative, or ratio of signal strength in demodulating the audio signal. In the case of FM, the "loudness" of the audio is translated into how far the carrier frequency deviates from the center (carrier) frequency; and the actual audio frequency reproduction is a result of the rate/frequency that the deviation of the carrier occurs. In other words, an FM carrier signal being allowed to deviate +/-3Khz, determines it's dynamic range (loud to softness ratio), but because the audio and transmitted carrier are limited to +/-3Khz and so that bandwidth isn't exceeded during modulation. Commercial FM radio stations are spaced at 200Khz, so having a transmitter do +/-19Khz for greater audio frequency reproduction, causes no problem with interference with an adjacent station, and obviously having that wide of a bandwidth means that dynamic range can be greater as well.

Finally, remember that in analog electronic audio, there are always two facets that need to be reproduced, frequency and loudness, and in any analog modulation scheme, both will be represented somehow, although it may not be obvious to you at first glance.

The spread-spectrum issue is well covered in other posts.

• I really don't see that being the implied question. Nov 5, 2022 at 23:25
• But the sidebands are of no consequence to the AM receiver, they are just a byproduct of modulating one signal with another That is incorrect. You're trying to talk away the fact that modulatio causes bandwidth; that's the point. The sidebands are not of "no consequence to the receiver": On the contrary, they contain 100% of the information. The unmodulated carrier contains 0 information. How could it? It has 0 bandwidth. So, your math is off here. Nov 5, 2022 at 23:29
• Your 20 kHz bandwidth argument makes no sense to me – what you mean with "FM fidelity" is probably a broadcast FM transmitter, which would, according to the Carson Bandwidth Rule, would need ca 170 kHz bandwidth to reproduce a 20 kHz wide audio signal. So, is your argument "AM cannot be as good, it uses less bandwidth"? Because that doesn't work that way: If you have more bandwidth, you have more noise, and hence, with a fixed transmit power, your SNR goes down, not up. Nov 5, 2022 at 23:34
• Then you say a weak signal wouldn't necessarily mean a lower frequency range, it would mean a less loud station with lower dynamic range, and maybe not even being able to hear the quieter parts of the audio that's not true. Linearity holds. You can amplify a weak signal as much as you need, no problem there. We're not even close to the quantum world, where there's really a point of "some effect or no effect, nothing in between". Amplification, however, will not increase your SNR. SNR is the limiting factor, always, never the absolute power you receive! Nov 5, 2022 at 23:34
• So, as much as I like the discussion you kick off with this, most of this is wrong / bad math, and it doesn't actually address the question asked. Neither the explicitly asked one, is FM spread-spectrum?, nor what you imply would be the question, why does FM sound better than AM?. Nov 5, 2022 at 23:36