Explain pitch period estimation using short-time autocorrelation

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(i) The discrete time auto-correlation function of a deterministic signal is given by $ \phi (k) = \sum_{m-w}^{w} x(m)x(m+k) $

(ii) For random or periodic signal is auto-correlation function is given as $$ \phi(k) = \lim_{n \to w} \,\, \frac{1}{2N+1} \sum_{m-w}^{w}x(m)x(m+k) $$

(iii) When the signal is periodic with a …

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