A novel algorithm for computing the 1-D discrete Hartley transform

An efficient split algorithm for calculating the one-dimensional discrete Hartley transforms, by using a special partitioning in the frequency domain, is introduced. The partition determines a fast paired transform that splits the 2^r-point unitary Hartley transform into a set of 2^r-n-point odd-frequency Hartley transforms, n=1:r. A proposed method of calculation of the 2^r-point Hartley transform requires 2^r-1(r-3)+2 multiplications and 2^r-1(r+9)-r²-3r-6 additions.