Plucked/Struck String Pitch Estimation

• Take FFT of middle third of plucked string tone
• Detect spectral peaks
• Form histogram of peak spacing $\Delta f_i$
• Pitch estimate ${\hat f}_0\mathrel{\stackrel{\Delta}{=}}$ most common spacing $\Delta f_i$
• Refine ${\hat f}_0$ with gradient search using harmonic comb:
  $$\begin{eqnarray*} {\hat f}_0 &\mathrel{\stackrel{\Delta}{=}}& \arg\max_{{\hat f}... ...hat f}_0} \prod_{i=1}^K \left\vert X(k_i{\hat f}_0)\right\vert \end{eqnarray*}$$
  

  where

  $$\begin{eqnarray*} K &=& \mbox{number of peaks, and}\\ k_i &=& \mbox{estimated h... ...f $i$th peak}\\ && \mbox{(valid method for non-stiff strings)} \end{eqnarray*}$$
  

Must skip over any missing harmonics,
i.e., omit $k_i$ whenever $\vert X(k_i{\hat f}_0)\vert\approx 0$.

References: For pointers to research literature, see http://ccrma.stanford.edu/~jos/jnmr/Model_Parameter_Estimation.html