We have a "speaker", that can make a single frequency at a time (0 - 130k Hz). So we can play a tune by making it play a tone for 1 sec and then the next tone for 0.5 sec etc. We can change the length and frequency of the tones pretty quickly. But we can play any sound as they are typically a superposition of various frequencies (Fourier)... Or can we? Is there some algorithm to convert a sound signal into a sequence of sine waves.

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    $\begingroup$ Yes sound.stackexchange.com/q/45550 $\endgroup$
    – ZiglioUK
    Mar 5, 2021 at 21:25
  • $\begingroup$ "But we can play any sound as they are typically a superposition of various frequencies (Fourier)". Surely you mean you can not play any sound, because they are typically a superposition of various frequencies and amplitudes all being produced at the same time. Yes? $\endgroup$
    – TimWescott
    Mar 5, 2021 at 22:54
  • $\begingroup$ @ TimWescott. Yes of cause. Sorry. I think I was starting out as a question, but then changed it midway. :-/ $\endgroup$
    – DrDress
    Mar 6, 2021 at 15:05

1 Answer 1


Yes, as long as we are also allowed to vary the amplitude versus time and we're allowed any time period in which to change frequency. Any single valued waveform can also be described in terms of instantaneous frequency versus time, where the instantaneous frequency is the derivative of phase so in this case the rate of change in phase at any given point in time.

If the OP is referring to FM modulation itself (encoding the instantaneous amplitude of a real waveform to the frequency of a constant envelope sinusoid), then yes this is also done where the parameter that can be varied is the frequency deviation (linear mapping of waveform amplitude to frequency) resulting in the modulation index and ultimately the bandwidth required of the modulated signal. This modulated signal would need to be demodulated with a frequency discriminator to recover the original waveform.

  • $\begingroup$ That's a good idea. So we run the speaker at max freq 130kHz and modulate the amplitude. But FM radio is usually in the MHz range, so are there any rule of thump limit on how high freq sound we can play? $\endgroup$
    – DrDress
    Mar 6, 2021 at 15:11
  • $\begingroup$ Are you referring to normal audio speakers? They don’t go much past 15 KHz. To emulate any arbitrary waveform you want to be able to vary amplitude as well (unless you are encoding both amplitude and phase with FM modulation itself)? $\endgroup$ Mar 6, 2021 at 15:20
  • $\begingroup$ Well, it actually a high power pulsed CO2 laser. We can fire it at a given frequency and duty cycle. When it hits the target I assume it creates a shock wave for each pulse. At least we can hear high tones when we operate it. We think it would be fun (and very professional) to make it play sounds. But as I said, we can only quickly turn it on and off at a given frequency and duty cycle and then again at a different frequency and duty cycle and so on. I was wonder how to produce arbitrary sound from this. $\endgroup$
    – DrDress
    Mar 7, 2021 at 13:07
  • $\begingroup$ The frequency you refer to up to 180 KHz is the on.off keying of the laser, correct? I would think you wouldn’t hear anything if you operated it well above 20KHz which is the highest range of our hearing (closer to 15KHz for us older folks) $\endgroup$ Mar 7, 2021 at 13:47
  • $\begingroup$ Our hearing won’t demodulate FM so you are hearing sound waves that are produced within the range of our hearing (20Hz to 15 KHz). How those sounds are being produced if you keep your rate much higher is an interesting question $\endgroup$ Mar 7, 2021 at 13:50

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