Nyquist and FM and Signal Mixing....

[kostoglotov]

In an assignment I have, we are told to implement a Frequency Modulating function without using any of MATLAB's in-built functions, and not to use it's integration function either (use cumsum instead).

I've been getting a lot of problems trying to solve these assignment problems without telling MATLAB to generate insanely too large vectors that exceed memory...

Thing is, under Australian law, LPON transmitters are allocated 85 Mhz to 88 Mhz.

To create a time vector that correctly represents waveforms at those frequencies means creating very dense time vectors. Our monitoring signal is 72 seconds long, and to sample the oscillator correctly during modulation (fm_mod) means trying to create too large a time vector. I could use interp1() to match the less dense message vector to the 8x.x MHz oscillator waveform vector...except of course, not enough memory.

My question is, do we need to adhere to Nyquists Theorem when mixing our oscillator with our message signal during modulation, or can we apply that 2*pi*fc*t to a time vector that contains WAY fewer points than would be needed to properly represent a 8x.x MHz waveform?

 

[sophiecentaur]

I have no idea about the particular situation you are discussion but sub Nyquist sampling of a signal is quite feasible if there is a 'line structure' to the spectrum of the original sampled signal and the sample frequency is chosen to fold the aliases back down into identifiable gaps in between the baseband spectral lines. This requires the sampled signal not to change significantly over a short time - so the sidebands of the basic lines leave plenty of room between them.
For an LPON system, there will probably be guard bands between the used channels and aliases could probably be placed in those spaces.