Appendix B

Matlab Scripts for the Bandwidth Optimization Problem

B.1

This Matlab script was developed to provide a numerical proof of the fact that the phi-pulse is bandwidth-optimal among all pulses generated by SAS containing three adders.

ind=0;

for pp=2:256

 rr=1111111111111111111111;

 p=pp-1;

 x=zeros(p);

 for i =1:p

  np=p-i+1;

  for j=1:np

   m=np-j+1;

    a=boxcar(i);

   b=boxcar(j);

   c=boxcar(m);

   x=conv(conv(a,b),c);

   g=0;f=0;h=0;

   for k=2:p

    g=g+(x(k)-x(k-1))^2;

    h=h+(x(k)*x(k));

   end

   g=g+(x(p))^2+(x(1))^2;

   h=h+(x(1)*x(1));

   r=g-f*f/(pp);r=r/h;

   if(rr>r)

    xr=x;

    ir=i;

    jr=j;

    mr=m;

    rr=r;

   end

  end

end

exact=round(3*pp/8);

if(floor(0.375*pp)+0.5==(0.375*pp))

   exact=floor(0.375*pp); ...

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