Re: [Discuss-gnuradio] hi all, can I use one RX receive a wideband signal and then seperate it to many narrowband signals

[Tom Rondeau]

On Thu, Jan 20, 2011 at 10:30 PM, Marcus D. Leech <address@hidden> 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