Frequency-domain Approaches
In the frequency domain, polyphonic detection is possible, usually utilizing the periodogram to convert the signal to an estimate of the frequency spectrum . This requires more processing power as the desired accuracy increases, although the well-known efficiency of the FFT, a key part of the periodogram algorithm, makes it suitably efficient for many purposes.
Popular frequency domain algorithms include: the harmonic product spectrum; cepstral analysis and maximum likelihood which attempts to match the frequency domain characteristics to pre-defined frequency maps (useful for detecting pitch of fixed tuning instruments); and the detection of peaks due to harmonic series.
To improve on the pitch estimate derived from the discrete Fourier spectrum, techniques such as spectral reassignment (phase based) or Grandke interpolation (magnitude based) can be used to go beyond the precision provided by the FFT analysis. Another phase-based approach is offered by Brown and Puckette
Read more about this topic: Pitch Detection Algorithm
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