Math Expressions for Modulated Waves

For the examples shown, they are all available in Audacity under effects. No programming needed at all. If you really need to do arbitrary math, you can use a plugin for Audacity.

Unless Golden Wave has a vast support network, I'd go with Audacity.

If you insist on using Golden Wave, the math shown there is quite trivial. Say you wanted a quadrature phase sine wave. If there is a hack to program each channel individually, one channel would be sin(2*pi*f*t) and the other cos(2*pi*f*t). T is presumably the dynamic variable that is incremented by the program based on the sample rate. F is frequency.

2*pi*f is angular frequency, i.e. omega.

You may want to check if the Audacity plug-ins work under windows. Most users are on linux. The basic Audacity program works under windows, Mac, and linux. Plugins are tbd.

Yes, Audacity has filters, and other named effects associated with sound processing, but I do not see any AM or FM functions in the drop downs. I want to use the program explicitly for signal generation.

What is the name of the Audacity plug-in you refer to? Unable to search-find it.

Apart from the above, I still need to know where to source a tutorial on the relevant algebraic expressions to get me started.

John Farrell

not sure, but wikipedia should give the two basic equations AM and FM, maybe even phase modulation, PM

AM signal(t) = ( (1+A*cos(wm*t) ) * cos(wc*t) /2 where A is modulation goes usually from 0 to 1, standard broadcast ??

0.25 ?? max?? wm is frequency of modulation that's 2 pi f wc is frequency of the carrier note if A==1, called suppressed carrier, because so overmodulated, the carrier disappears

FM signal(t) = cos(wc*(1+A*cos(wm*t))*t) where wm

Hi John, Well I know of no specific text/ tutorial that does waveform generation. And I'm not sure that it would be best. It's my firm belief that you will be much better served by doing the general theory.. but perhaps with an eye towards your application. You might start by looking at some basic trigonometry, the addition and multiplication of sine waves. If not a university text then go back to high school :^)

I find the whole subject becomes much easier with the introduction of phasors,

But that gets into complex numbers. Is that too much for you?

George H.

I don't know. I wish I had soundcards, SDR, and gnuradio radio when I was studying communications. Communications is very dry if you study it from a purely theoretical standpoint.

The modem chips I worked on all had secret hooks where you could see the eye pattern or constellation by adding external DACs and using secret test modes. It was substantially more informative than the pure math, especially when you could see noise kick a "blimp" into the next quadrant, or the constellation rotate after a noise or gain hit caused the recovered clock to be off a bit.

I was looking at a class syllabus at Berkeley where they were using the cheap rtlsdr dongle in their comm class. About the closest I ever came to doing something that cool in college was writing C code for radar analysis. But they just give you a signal to analyze and you tease out the data. That is hardly as cool as writing code to demodulate a live radio signal.

Try googling signal generation or something usefull. I searched signal generator sw and after awhile found some, but it took some work to find a good search phrase