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Amplitude modulation parameters


Anthocyanina

Question

Hi, So I'm trying to get the following waveform using amplitude modulation(the green one), Is the amplitude modulation equation used on waveforms the same as this one? 

s(t)= \left [ A_c+A_m\cos\left ( 2\pi f_mt \right ) \right ]\cos \left ( 2\pi f_ct \right )

as it is now, it seems(if using the same equation as above) that it is assumed that a, as shown in the desmos graph in red, is always assumed to be 1 and can't be changed. 

The modulated waveform i want to get is an arbitrary carrier being modulated by a sinusoid. Essentially i want to invert the carrier periodically and do so smoothly by sinusoidally changing its amplitude from 1x to -1x, so it would be like the purple equation, just multiply my arbitrary carrier by a sinusoid of any frequency i might need. I have tried doing this by getting the arbitrary data and multiplying it by the sinusoid on libreoffice calc, but for it to be low enough frequency for my purpose, i need to repeat the arbitrary points hundreds of times, so it doesn't fit in the wavegen memory. I tried doing it with the alter menu in the wave generator, but there is no way to tell it to fit the arbitrary waveform hundreds of times "under" the slow sinusoid, or not that i can find. I would like to know if there is currently a way to do this kind of modulation on waveforms, or if it would be possible to add an "a" setting to be able to achieve it in the way i do it on desmos.

Thank you!

(it seems the forum doesn't display TeX? at least not in the preview! 🙈)

graphs.png

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hi! @attila

no, that's the closest to what i want that i can currently see how to do on waveforms. What i would like is to be able to also make that "+1" term, that appears in the amplitude modulation equation, variable, where we could have Ac[1+u cos(2*pi*fm*t)]*cos(2*pi*fc*t) such that not only allowed us to edit Ac, u, fm,fc (with Ac being the carrier amplitude, u being the modulation index, fm, and fc being the modulation and carrier frequencies respectively), but also allowed us to change that first constant "1" treating it now like a user selectable variable. In this video is shown what i want to do but don't see how i can on waveforms, and when b is equal to 0, we get the waveform i want to produce, and essentially, if we make A1, and u equal to 1, and b equal to cero, what we get is just cos(2*pi*fm*t)*cos(2*pi*fc*t), or for an arbitrary carrier, cos(2*pi*fm*t)*arb(2*pi*fc*t)

to summarize, I would like to know if there's a way to either make all parameters of the amplitude modulation variable, or if there's a way to multiply any waveform of any frequency by any other waveform of any other frequency, or if this could be added. Thank you!

 

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