On Thu, Jan 20, 2011 at 10:30 PM, Marcus D. Leech <mle...@ripnet.com> wrote: > On 01/20/2011 10:22 PM, James Jordan wrote: >> Marcus, Thanks for reply. >> That is make sense, so the point become how to convert the signal to >> baseband. > Oh, that's relatively easy--you multiply it with a complex signal at the > same frequency--that's > exactly how it's done in hardware, and it works equally-well in software. > > The Gnu Radio channelizer likely is more sophisticated than that, using > different > mathematical tricks to improve efficiency, etc. > > When you multiply two sinusoids of Xhz and Yhz, you end up with a mixed > sinusoid-- > Xhz+YHz and XHz-Yhz. > > In direct-conversion, you mix (multiply) it with a signal of the same > center frequency, and you get > the baseband frequencies, but since this is baseband, you need to use > complex representation, otherwise > the + and - frequencies "fold" around each other.
Yes, the polyphase filterbank is a bit more clever than that. It'll sound like magic when you first hear about it, but what you are doing using (or abusing) the concept of aliasing. What happens is that you decimate the signal before you filter it. The decimation process folds all of the Nyquist zones down to baseband, but now they are aliased on top of each other. You filter the signal at this point, but that doesn't get rid of the aliases, of course. That's where the "despinning" operation comes in. See, when you've brought all of the signals to baseband, you filter them with different phases, so in the complex plane, each alias has a specific phase rotation. You despin these according to what channel you want to pull out. For this, you rotate all of the other channels such that when you sum up the outputs of the filters, these channels cancel. For the channel you want, you rotate them in a way that summing them up adds the signals together. So the output is to suppress all of the other channels and reinforce the channel you've asked for. So it's a series of multiply and adds. If you want all channels together, these multiply and adds looking amazingly like an FFT, which is how we normally implement this operation. It's a lot more efficient doing it this way than filtering each channel and downconverting it to baseband. If you really want to know more, read fred harris' "Multirate Signal Processing for Communication Systems." Tom _______________________________________________ Discuss-gnuradio mailing list Discuss-gnuradio@gnu.org http://lists.gnu.org/mailman/listinfo/discuss-gnuradio
