1. Apparatus for analyzing periodic signals, comprising: means for dividing said signal into consecutive segments; means for calculating a super-resolution decomposition of said segments into frequency values, frequency decay rates, initial amplitudes; means for pruning said list of frequencies so as to produce a list vector of frequency values {right arrow over (L)} having n elements; a frequency sorter for ordering the elements of said list vector {right arrow over (L)} so as to produce an ordered frequency list vector {right arrow over (F)}; a column duplicator for forming a matrix F, having as each column said frequency list vector {right arrow over (F)}; a candidate generator for forming a matrix of candidate fundamentals D from said matrix F and said frequency list vector {right arrow over (F)} according to D={right arrow over (F)}−F T ; a pre-validator for forming a candidate fundamental list vector {right arrow over (D)} whose m elements are chosen from the positive elements of D that are greater than a minimum value; a group averager for producing both a vector of averaged groupings of fundamentals, {right arrow over (G)}, and an associated count vector, {right arrow over (C)}, from said fundamental list vector {right arrow over (D)}; an average fundamental selector for processing said vector of averaged groupings of fundamentals, {right arrow over (G)}, and said associated count vector, {right arrow over (C)} so as to produce a count threshold c and an initial fundamental estimate α 0 ; a sub-harmonic searcher for producing a pre-refined fundamental estimate, φ 0 , by computing a sub-harmonic candidate vector {right arrow over (S)} from said initial fundamental estimate α 0 and said frequency list vector {right arrow over (F)} according to {right arrow over (S)}={right arrow over (F)}−0.5α 0 {right arrow over (1)}; a fundamental refiner for producing a refined fundamental estimate, f 0 , by computing a first error vector {right arrow over (E)} −1 , according to {right arrow over (E)} −1 ={right arrow over (F)}−f 0 (−1)·{right arrow over (1)} and by computing a second error vector {right arrow over (E)} according to {right arrow over (E)}={right arrow over (F)}−φ k 1; and a harmonic refiner for producing a refined harmonic estimate, h k , by recomputing said first error vector {right arrow over (E)} −1 according to {right arrow over (E)} −1 ={right arrow over (F)}−h k (−1)·{right arrow over (1)} and by recomputing said second error vector {right arrow over (E)} according to {right arrow over (E)}={right arrow over (F)}−φ k {right arrow over (1)}, where k=kf 0 , and where the integer k is greater than 1; and where h k (−1) is the refined harmonic estimate from the previous signal segment.