> 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 <a...@silverblocksystems.net> % % 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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