Re: [Discuss-gnuradio] CIC + halfband filter compensation

[Andy Walls]

> From: Geoffrey Mainland
> Date: Wed, 25 Apr 2018 16:39:11 -0400
> 
> I hope you will forgive a few naive signal processing questions :)
> 
> 1) What is the frequency response of the CIC and halfband filters in
> the
> USRP? This was addressed long ago on the mailing list
> (https://lists.gnu.org/archive/html/discuss-gnuradio/2007-05/msg00191
> .html),
> but the associated MATLAB script is no longer available now that the
> nabble archive is gone.

Attached are images generated from an Octave script, showing the
performance of the X310's CIC filter and 3 half-band filters,
filtering, decimating, and folding-in from the radio's 200 Msps down to
6.25 Msps.

The CIC filter is in blue.  It's droop hardly worth mentioning.

The Octave script is also attached.  It is far from generic.  It will
need significant modification if you have a different situation.


> 2) How do I design a filter to compensate appropriately?
>
> I know there are other methods for avoiding CIC droop, like
> oversampling, but I'd like to understand how to compensate with a
> filter
> as well.

As far as CIC compensation filters go:

http://lmgtfy.com/?q=cic+compensation+filter

:)

Seriously, there is plenty of reading material out there.

Regards,
Andy

> Thanks!
> Geoff
%
% (C) 2018 Andy Walls 
%

% The X310 DDC chain has 4 Integrator Stages  and 4 single delay Comb stages
% followed by a decimation stage.  We'll model that here, using the
% equations in https://www.altera.com/content/dam/altera-www/global/en_US/pdfs/literature/an/an455.pdf

M = 1; % differential delay
N = 4; % stages
R = 4; % decimation rate to go from 200 Msps down to 50 Msps
d = ones(1, R*M); % FIR filter coefficients before raising to N
  % Since it is like a cascade of N identical filters
[hd, wd] = freqz(d, [1], R*8*1024);
hd = hd .^ N;
hd = hd/hd(1);
wdturn = [wd(1:(R*8*1024/R))' wd((R*8*1024/R):-1:1)' ...
  wd(1:(R*8*1024/R))' wd((R*8*1024/R):-1:1)'] * 50/pi; % Fs = 200, fold into 0-50 multiple times

% The X310 DDC uses up to 3 x% Nyquist Half-band filters

% Coefficients from
% uhd/fpga-src/usrp3/top/x300/coregen_dsp/hb47.coe
% Generated with round((2^18-2)*halfgen_test(.21,12,1))
%  83% effective BW, 64dB to 85dB rolloff

a = [   -62, 0,194, 0,  -440, 0,   855, 0,  -1505, 0,  2478, 0, ...
  -3900, 0,   5990, 0, -9187, 0, 14632, 0, -26536, 0, 83009, ...
 131071, ...
  83009, 0, -26536, 0, 14632, 0, -9187, 0,   5990, 0, -3900, 0, ...
   2478, 0,  -1505, 0,   855, 0,  -440, 0,194, 0, -62];
b = a;

% Coefficients from
% uhd/fpga-src/usrp3/top/x300/coregen_dsp/hb63.coe
% Generated with round((2^18-2)*halfgen_test(.22,16,1))
%  88% effective BW, 64dB to 87dB rolloff
c = [ -35, 0, 95, 0, -195, 0, 352, 0, -582, 0, 907, 0, -1354, 0, 1953, 0, ...
  -2751, 0, 3813, 0, -5249, 0, 7264, 0, -10296, 0, 15494, 0, -27083, 0, ...
  83196, 131071, 83196, ...
  0, -27083, 0, 15494, 0, -10296, 0, 7264, 0, -5249, 0, 3813, 0, -2751, ...
  0, 1953, 0, -1354, 0, 907, 0, -582, 0, 352, 0, -195, 0, 95, 0, -35];

[ha,wa] = freqz(a, [1], 8*1024);
ha = ha/ha(1);
[hb,wb] = freqz(b, [1], 4*1024);
hb = hb/hb(1);
[hc,wc] = freqz(c, [1], 2*1024);
hc = hc/hc(1);

% Fold freq axis to show aliasing into final passband
% Scale to original 50 Msps Fs
waturn = [wa(1:(8*1024/2))' wa((8*1024/2):-1:1)'] * 25/pi; % Fs = 50, fold 25-50 onto 25-0
wbturn = [wb(1:(4*1024/2))' wb((4*1024/2):-1:1)'] * 12.5/pi; % Fs = 25, fold 12.5-25 onto 12.5-0
wcturn = [wc(1:(2*1024/2))' wc((2*1024/2):-1:1)'] * 6.25/pi; % Fs = 12.5, fold 6.25-12.5 onto 6.25-0

clf;
plot( ...
 wdturn, 20*log10(abs(hd)), ';CIC filter 200 Msps folded to 50 Msps;', ...
 waturn, 20*log10(abs(ha)), ';1st HB filter 50 Msps folded to 25 Msps;', ...
 wbturn, 20*log10(abs(hb)), ';2nd HB filter 25 Msps folded to 12.5 Msps;', ...
 wcturn, 20*log10(abs(hc)), ';3rd HB filter 12.5 Msps folded to 6.25 Msps;');
title('X310 DDC CIC & Default Halfband Filters Alias Folding Performance');
ylabel('Gain (dB)');
xlabel('Frequency (MHz)');
grid on;
hold off;

% Passband droop at the final fold
% At Fs/2 = 6.25 MHz
worst_pass = ...
   20*log10(abs(hd(R*8*1024/32))) ...
 + 20*log10(abs(ha(8*1024/8))) ...
 + 20*log10(abs(hb(4*1024/4))) ...
 + 20*log10(abs(hc(2*1024/2)))
ideal_pass = ...
   20*log10(abs(hd(1))) ...
 + 20*log10(abs(ha(1))) ...
 + 20*log10(abs(hb(1))) ...
 + 20*log10(abs(hc(1)))
worst_droop = ideal_pass - worst_pass

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Re: [Discuss-gnuradio] CIC + halfband filter compensation

[CEL]

Hi Geoff,

might be a good idea to ask this on usrp-us...@lists.ettus.com, because
these CICs are not part of GNU Radio :)

Anyway: There's nothing much to interpret about CIC responses; they are
well-known. The length (and potentially order, as in exponent) of the
CIC used depends on your specific USRP model. (and, potentially, UHD
version)

It's rare that one actually designs an equalizing filter for the CIC –
in all USRPs, the CIC comes before the halfband filter(s), and thus,
you'd typically only see "the flattest part" of the frequency response
of the CIC.

Designing a compensating filter is mathematically impossible, but you
can alleviate certain aspects of the CIC impulse response. But this
would really require you to state what the target metric is over which
bandwidth. Also, it's almost certain that this filter would be
computationally much worse than just oversampling at the USRP end and
then decimating in software with a filter that fits what you need
better.

Notice that I very much believe that "what you need" is the critical
aspect here: Occam's razor tells me that unless you can define why the
CIC is your problem very well, then it's likely you're trying to solve
something that doesn't need solving (or that equalizing parts of the
CIC response isn't the answer you're looking for ;) ).

So, if you asked me: Describe what your system need is, and how you
came to the conclusion that the CIC is a problem! This mailing list is
very prone to having interesting discussions about real-world problems
where every party learns a lot.

Best regards,
Marcus

On Wed, 2018-04-25 at 16:39 -0400, Geoffrey Mainland wrote:
> I hope you will forgive a few naive signal processing questions :)
> 
> 1) What is the frequency response of the CIC and halfband filters in the
> USRP? This was addressed long ago on the mailing list
> (https://lists.gnu.org/archive/html/discuss-gnuradio/2007-05/msg00191.html),
> but the associated MATLAB script is no longer available now that the
> nabble archive is gone.
> 
> 2) How do I design a filter to compensate appropriately?
> 
> I know there are other methods for avoiding CIC droop, like
> oversampling, but I'd like to understand how to compensate with a filter
> as well.
> 
> Thanks!
> Geoff
> 
> 
> 
> ___
> Discuss-gnuradio mailing list
> Discuss-gnuradio@gnu.org
> https://lists.gnu.org/mailman/listinfo/discuss-gnuradio

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[Discuss-gnuradio] CIC + halfband filter compensation

[Geoffrey Mainland]

I hope you will forgive a few naive signal processing questions :)

1) What is the frequency response of the CIC and halfband filters in the
USRP? This was addressed long ago on the mailing list
(https://lists.gnu.org/archive/html/discuss-gnuradio/2007-05/msg00191.html),
but the associated MATLAB script is no longer available now that the
nabble archive is gone.

2) How do I design a filter to compensate appropriately?

I know there are other methods for avoiding CIC droop, like
oversampling, but I'd like to understand how to compensate with a filter
as well.

Thanks!
Geoff



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