filtering - Adding signals and separate them using MATLAB -


i have 2 signals m(t) = exp(-100*abs(t)) , c(t) = cos(2*pi*1000*t). need add them , separate them using low pass filter (lpf) , band pass filter (bpf) , plot figures.

i wrote code :

fs = 100*1000; ts = 1/fs; t = -0.1:ts:0.1-ts; no = length(t);  m = exp(-100*abs(t)); c = cos(2*pi*1000*t); g = m + c;  y = abs(g);  cutoff = 200; [a b]= butter(5,2*cutoff*ts);  z = filter(a,b,y);  figure(1) plot(t,m,t,z);  legend('input signal','output signal') xlabel('time')  ylabel('amplitude') title('case study')

note used lpf [a b] = butter(5,2*cutoff*ts);

the problem plot shifted , think because of dc component. can me edit code , fix shift? , should use bpf? if yes, how?

the offset getting using abs value of g. if instead of filtering y filter g better result. offset comes dc component of abs(c) since not centered on zero, , low pass filter maintain offset


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