path: root/macros/intfilt.sci

function [h, a]= intfilt(R, L, freqmult)


    // This function estimate Interpolated FIR Filter Design.
    // Calling Sequence
    // h=intfilt(R,L,freqmult)
    // [h a]=intfilt(R,L,freqmult)

    // Parameters
    // R: Samples. It should be numeric
    // L: bandlimited interpolation samples. It must be nonzero.
    // freqmult: bandlimitedness of ALPHA times the Nyquist frequency, IT can be numeric or character ('B' or 'L', B is length
    //   (N+1)*L-1 for N odd and (N+1)*L for N even)

    // h:  linear phase FIR filter.

    // Examples
    // h=intfilt(20,10,'l')     // The output of this example has 220 columns ,so it is difficult to write it here.
    // h=intfilt(20,10,1)     // The output of this example has 220 columns ,so it is difficult to write it here.

    //h1=intfilt(2,3,'l');
    //OUTPUT :
    //               - 0.0625    0.    0.5625    1.    0.5625    0.  - 0.0625

    //h2=intfilt(4,1,1);
    //OUTPUT :
    //               0.3001054    0.6366198    0.9003163    1.    0.9003163    0.6366198    0.3001054

    // See also
    // Authors
    // Jitendra Singh

funcprot(0);
[lhs,rhs]=argn(0);

if (rhs~=3) then
	error ("Wrong number of input arguments.")
end

if (lhs<1 | lhs>2) then
	error ("Wrong number of input arguments.")
end

    if or(type(R)==10) | or(type(L)==10) then
              error ('Argument R and L must be numeric.')

              else




         if argn(2)==3 then
                   if type(freqmult)==10 then
                             typ=freqmult;
                             n=L;
                   else
                             freqmult=double(freqmult);
                             typ='b';
                             end

     end

     if freqmult==0 then
         h=repmat(%nan,[1,(2*R*L-1)])
         a=1;
         else


     //typ(1)=='b' | typ(1)=='B'

         if convstr(typ(1), 'u') =='B' then
                   n=2*R*L-1;


                   if freqmult==1 then
                             M=[R R 0 0];
                             F= [0 1/(2*R) 1/(2*R) 0.5];
                   else
                             M=R*[1 1];

                  if type(freqmult)==10 then
               F=[0 98/2/R];
           else
               F=[0 freqmult/2/R]
               end

        for f=(1/R):(1/R):.5,

            if type(freqmult)==10 then
            F=[F f-(98/2/R) f+(98/2/R)];
        else
            F=[F f-(freqmult/2/R) f+(freqmult/2/R)];
            end

            M=[M 0 0];
        end;

        if (F(length(F))>.5),
            F(length(F))=.5;
        end;
    end
        N=n-1; F=F*2; M=M


if (max(F)>1) | (min(F)<0)
    error('Frequencies in F must be in range [0,1]')
end




if ((length(F)-fix(length(F)./2).*2)~=0)
    error('Argument F should of even length');
end

if (length(F) ~= length(M))
    error('The input arguments F & A must have same length');
end


    W = ones(length(F)/2,1);
    ftype = '';


    ftype = 0;  differ = 0;


N = N+1;

F=F(:)/2;  M=M(:);  W=sqrt(W(:));
dF = diff(F);

if (length(F) ~= length(W)*2)
    error('There should be one weight per band.');
end


if or(dF<0),

    error('F frequency must be increasing')

end



if and(dF(2:2:length(dF)-1)==0) & length(dF) > 1,
    band = 1;
else
    band = 0;
end
if and((W-W(1))==0)
    weights = 1;
else
    weights = 0;
end

L=(N-1)/2;

Nodd = N-fix(N./2).*2;


    if ~Nodd
        m=(0:L)+.5;
    else
        m=(0:L);
    end


    k=m';
    need_matrix = (~band) | (~weights);




    if need_matrix

        I1=k(:,ones(size(m,1),size(m,2)))+m(ones(size(k,1),size(k,2)),:);
        I2=k(:,ones(size(m,1),size(m,2)))-m(ones(size(k,1),size(k,2)),:);
        G=zeros(size(I1,1),size(I1,2));
    end

    if Nodd
        k=k(2:length(k));
        b0=0;
    end;
    b=zeros(size(k,1),size(k,2));

    dd=diff(F);

    if or(dd==0) & R==1 then

        h=repmat(%nan,[1,n])
        a=1

        else
    for s=1:2:length(F),


        m=(M(s+1)-M(s))/(F(s+1)-F(s));
        b1=M(s)-m*F(s);
        if Nodd
            b0 = b0 + (b1*(F(s+1)-F(s)) + m/2*(F(s+1)*F(s+1)-F(s)*F(s)))* abs(W((s+1)/2)^2) ;
        end

      b=b(:)
        b = b+(m/(4*%pi*%pi)*(cos(2*%pi*k*F(s+1))-cos(2*%pi*k*F(s)))./(k.*k))* abs(W((s+1)/2)^2);



        b = b' + (F(s+1)*(m*F(s+1)+b1)*sinf(2*k*F(s+1))- F(s)*(m*F(s)+b1)*sinf(2*k*F(s)))* abs(W((s+1)/2)^2);
        if need_matrix



               mat=matrix((.5*F(s+1)*(sinf(2*I1*F(s+1))+sinf(2*I2*F(s+1)))- .5*F(s)*(sinf(2*I1*F(s))+sinf(2*I2*F(s))) ) * abs(W((s+1)/2)^2),size(G,1),size(G,2)) ;
                mat=mat';
                G=G+mat;


        end
    end;


    if Nodd
        b=[b0; b'];
    end;

    if need_matrix
        a=G\b;
    else
        a=(W(1)^2)*4*b;
        if Nodd
            a(1) = a(1)/2;
        end
    end
    if Nodd
        h=[a(L+1:-1:2)/2; a(1); a(2:L+1)/2].';
    else
        h=.5*[flipud(a); a].';
    end;
     end;

  //typ(1)=='l' | typ(1)=='L'



       elseif convstr(typ(1), 'u') =='L'  then

            if n==0 then
                      h=ones(1,R)
                      return
                      end

        t=0:n*R+1;
        l=ones(n+1,length(t));

        for i=1:n+1
                  for j=1:n+1
                            if (j~=i) then
                                      l(i,:)=l(i,:).*(t/R-j+1)/(i-j);
                            end
                  end
        end

        h=zeros(1,(n+1)*R);

        for i=0:R-1
        for j=0:n
                  h(j*R+i+1)=l((n-j)+1,round((n-1)/2*R+i+1));
        end
end



if h(1) == 0,
        h(1) = [];
    end

else
          error ('This type of filter is not recognized.')


         end
         a=1;


 end
 end

endfunction



////// Supplementary function

function y=sinf(x)

     for i=1:length(x)
               if x(i)==0 then
                         y(i)=1;
                         else

               y(i)=sin(%pi*x(i))/(%pi*x(i));
               end

               end

          y=y';
endfunction