TSTE16: Filter order as function of transition band

Just a small, trivial MATLAB script to illustrate analog filter order as function of transition band width and signal bandwidth. This example illustrates well how, for example, the analog reconstruction filter after a DAC has to be dimensioned to attenuate the images.

For illustration purposes, we have chosen Butterworth filter approximation, eventhough it is not the best one. What the graph shows is that the filter order increases dramatically for narrow transition bands, and eventhough we step away 10 MHz from a 500-kHz bandwidth, the filter order is still two or more.


fp = 500e3;
Wp = 2*pi*fp;

deltafs = logspace(1,7);
deltaWs = 2*pi*deltafs;

for m = 1:length(deltafs)
deltaW = deltaWs(m);
[N, Wn] = buttord(Wp, Wp + deltaW, ...
0.1, 60, 's');
M(m) = N;
end;

sl = loglog(deltafs/1000, M);
xlabel('Transition band width [kHz]');
ylabel('Butterworth filter order');
title('Filter order as function of transition band width');
set(sl,'LineWidth',8);

print('-dpng','-r200','mspsSimulatedFilterOrder.png')

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