Tom, thanks very much. though I still not fully understand it I will read the book u suggested.
Regards! On Sun, Jan 23, 2011 at 1:04 AM, Tom Rondeau <trondeau1...@gmail.com> wrote: > 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 >
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