Efficient phase-only frequency estimation

Techniques that estimate frequency and chirp rate as weighted sums of phase differences have received attention because they can be simple to implement. The novel contributions in this paper include the efficient implementation of these estimates through recursive structuring of the computation and trapezoidal approximation of the weighting functions. A multirate cascade structure for the trapezoidal weighting is given that allows frequency and chirp rate estimates to be formed for multiple analysis window lengths with little extra computation. The techniques described are particularly well suited to hardware implementation because they virtually eliminate multiplications while having little impact on performance