I have a signal that consists of N frequencies all with unknown phase and frequency(N) = frequency(N-1) + 2Hz. I would like to selectively scale the amplitudes of some of those signals in such a way that I can change which frequencies to scale and how much to scale them on the fly.
Is this possible? How complex of a circuit would this be?
Analog? Digital? or Both?
Where should I start?
Thanks
To expand on Brian, making a filter with analog components that has a very small passband with a fast transition into the stop band is nearly impossible, while this is very very easy with a digital system.
You will have to sample at-least twice as fast as the fastest signal. I would suggest making sure you are at-least 2.1 times faster.
For will need to design one gigantic filter that changes each frequency by the amount you want.
If you want to control the magnitude of each signal separately then you will have to make N digital filters, create N datasets, apply the N different gains, and then recombine the signals, if you filtering is good you will just be able to sum to recombine. Do not take too much solace in this as it is the only easy step.
The sharper you want your transitions the more data-points the filter will need. There is no way around this, it has been proven mathematically.
Let me know in a comment if I can add more to help.
For that many passbands, you can take your signal, chunk it into windows, then FFT the window. (You will need a huge window for a million bins.) Then scale the magnitude of each frequency bin as desired, then do the inverse FFT, then reassemble the chunks into a continuous stream.
This will scramble phase a little bit, but it works well enough in many applications.
It would need to be digital for any good number of N. Start with a basic digital filter book.
You will probably need to use digital signal processing.
Check out http://www.dspguide.com/ for a primer on DSP.
