Re: [Discuss-gnuradio] Frequency multiplexing at baseband -filters introduce 'DDDDDDDDDDD'

[Marcus Müller]

Hi Damindra,

basically, you'll have to parameterize the PFB channelizer with a
prototype filter – imagine you had just one channel centered at 0 Hz in
your input band, and design a low-pass filter that would select that.

To illustrate: You've got something like

            ^S
    -----   |   -----   
   /     \  |  /     \
  /       \ | /       \
 /         \|/         \
------------+----------->
            0           f

so, channel 0 and 1 centered at - and +f_sample/4, respectively.

Imagine some shifted your signal so that channel 0 was exactly at 0 Hz
(that's especially easy to imagine and to implement; that's a frequency
shift by multiplication with exp(j*2pi * (f_sample/4)/f_sample *
n)=exp(j*2pi /4 *n)=exp(j*pi/2*n)=1, j, -1, -j, 1, j, …)

            ^ S
 - -      --|--      - -
    .    /  |  \    ,
     .  /   |   \  ,
      ./    |    \, 
------------+----------->
            0           f

You should be able to design a LPF to select that channel alone.

Now, using that filter, the PFB channelizer calculates a filterbank that
is essentially nothing more than the even and the odd taps of that
filter, applied each to half of the input signal, and then, with a 2-FFT
(yeah, that's kind of a boring FFT) transformed back into being elements
of a sensible signal. That's basically two filters for the cost of one +
one FFT.

Cheers,
Marcus