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Basic waveforms with FM

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Hello all,

so I am the proud owner of a preenFM2 now... And I try to get accommodated with its FM-synthesis (this is not the first FM-capable synthesizer I use, btw...), so I thought it would be fun to do what I have done on many FM-synths before: creating baisc waveforms with FM (saw, tri, square, pulse) to get an understanding of it's parameter-range and response...

But whatever I try I can not even come close to a synthesized 2-OP approximation of a sawtooth-waveform?!? hmm,... The spectrum looks right, so I guess there is some sort of phase-delay inside the operators, maybe?

BTW: just curious, but what was the reason for not using phasemodulation but real FM?

many thanks,


after some further experiments... Could it be that there is a highpass-filter in-between the carriers and the modulators (in-between every modulator-carrier-link... so there should be quite a lot of them)? This could explain the observed phase-shift. And if so, this would effectively implement phase modulation instead of frequency modulation because of using the derivative of the modulation-signal, then.. wouldn't it?

If I'm not missing a point here, wouldn't it be "better" in this case to directly use PM and to save some CPU-cycles by avoiding the HP-filters (maybe to increase sample rate or polyphony or for allowing feedback)?

all the best,

Hello again,

I have made a measurement of the preenFM2-output (noise is due to digital amplification to make it fit the simulated data in gnuplot. Despite a 13-16 kHz whine at -60dB -- the OLED? -- the output is dead clean) and compared it to

a) a 3OP-PM sawtooth-approximation without a phase-shift in between the carriers and the modulators


b) a 3OP-PM sawtooth-approximation with a phase-shift of pi*0.5

One clearly can see, that (b) is quite close to the output of the preenFM2. The differences -- I think -- mostly come from the frequency response of my audio-equipment which will of course distort the signal a little bit.

This should clarify what I meant with "phase-delay" in the last postings.

To explicitly say this: Both variants (whith and without the phase-difference) absolutely sound the same and have the same spectral distribution. Only the waveform on the oscilloscope will differ from the expected result. So, basically this is nothing to worry about...

On the other hand side: This result makes me really think that it might be a good idea to (maybe via a flag for backwards-compatibility?) switch the preen over to use PM (as most (all??) other "FM" synths do). It's using PM anyways, now...
With this change it would produce the expected waveforms from the various tutorials and it would (most probably) save some CPU-time to calculate...

For me personally it was just irritating. The sound and the flexibility of this nice little monster is outstanding! I love it, so many thanks Xavier!

all the best,


--- Quote from: SMF on July 11, 2019, 02:03:30 PM ---BTW: just curious, but what was the reason for not using phasemodulation but real FM?

--- End quote ---

The reason is that the preenfm started as a simple FM attemp and turned into a synthetiser over time.
I was even not aware at that time that other synths used Phase modulation.
Phase modulation avoid a pitch shifting when cascading 3 operators or more without any CPU impact. And i think that the reason why 80s synth used it.
FM needs a low pass (EDITED :!!!!TYPO <= It's a HIGH PASS) (few HZ) after operators to avoid this pitch shifting.

I don't remember the maths, but PM/FM spectral diferrences should be obvious when cascading at least 3 operators.

Thanks for the nice words...
but i don't have any plan to PM to the preenfm2 ;)


Hi Xavier,

--- Quote from: Xavier on August 04, 2019, 10:42:18 AM ---FM needs a low pass (few HZ) after operators to avoid this pitch shifting.

--- End quote ---

when I read this for the first time (in an older thread), I assumed it was a typo, but as you repeatedly say it's a low-pass filter, I am curious now... because for all what I recall, it is a high-pass filter which is required to get rid of the DC-component of the resulting spectrum in case of FM (PM does get rid of the DC-component inherently)...

So, if you really use a low-pass filter in between the operators, then I assume that it might be used to isolate (integrate over) the DC-component from the signal and then subtracting it from the next modulator-input? If so, then you turned the low-pass into a high-pass in this way...

But I may be misunderstanding what you actually do there.

all the best,


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