if you could help me with the math required, i would be very grateful.
I think what they're talking about here (single side-band modulation)
works this way. We take our original spectrum which has two sides,
each the conjugate of the other.
/\ /
___//_____|____/_/___
we get rid of one side, to get the complex representation
/\
__________|____/_/___
In the time domain this is a complex valued signal. To shift all the frequencies by a certain amount we convolve in the frequency domain by an impulse given by the fourier transform of e^(2*pi*i*f) where f is the frequency to shift by. This looks like, in the frequency domain:
|
__________|__|________
Convolution in the frequency domain (with a single sided spectrum) shifts all the frequencies to the right. Conv. in the frequency domain is the same as multiplication in the time domain. So we can do this operation as complex multiplication of our two complex signals. Resulting spectrum
/\
__________|______/_/\_
Then, just throw away the imaginary part and multiply by two, and there you have a real-valued signal. Let's see here...I got a little patch put together for demonstration purposes, using hilbert~ Don't rightly know why it won't work well with the osc~ set to 0? Chuck