Improved Algorithm for ODCT Computation of a Running Data Sequence

Algorithm 1

root2 = sqrt(2.0);N = 8,r = 2,sign = −1;

root_2N = sqrt(2.0 * N − 1.0);a = 2.0/root_2N;

for k = 0: N − 1;

if (mod(k, N)==0)

  pk = 1.0/root2;

else pk = 1.0;

end;

M = N + N − 1;

theta = 2 * r * k * pi/M;Ar = cos(theta);Br = sin(theta);

sign = −sign;

p1 = 0.0;p2 = 0.0;p3 = 0.0;p4 = 0.0;p5 = 0.0

 for  x = 0 : r − 1;

     angle1 = (x + x + 1) * k * pi/M;

     angle2 = (x + x) * k * pi/M;

     sin 1 = sin(angle1);

     sin 2 = sin(angle2);

     cos 1 = cos(angle1);

     cos 2 = cos(angle2);

 if  (x==0)

           pk1 = 1.0/root2;

else

           pk1 = 1.0;

 end;

 p1 = p1 + pk1  * (fnew(r − x)) * sin 2;

 p2 = p2 + (fold(r − x)) * sin 1;

 p3 = p3 + (−fold(2 *  r − x) + Ar * fold(r − x)) * cos 1;

 p4 = p4 + (fnew(2 *  r − x) − pk1  * Ar * fnew(r − x)) * cos 2;

 end;

p5 = (1.0/sqrt(2.0) − 1) * sign * (f(N) − fnew(r) * Ar + fnew(2 * r));

term1 = a  *  pk  * (−sign * Br * p1 + Br * p2 + p3 + sign * p4 + p5);

C_NEW(k + 1) = 2 * Ar * C(k + 1) − C_old(k + 1) + term1

end;