Pitch Estimation and Voiced–Unvoiced Classification of Speech - Digital Speech: Coding for Low Bit Rate Communication Systems - page 148

Lag Values

0 40 80 120 0 40 80 120 0 40 80 120 0 40 80 120

AMDF
Function

Speech
Signal

0 160 320 480 640

Samples

Figure 6.1 AMDF and speech signal: the minima of the AMDF corresponding to the
pitch values are indicated by circles

Autocorrelation Method
The direct distance measurement is the most popular criterion examining the
similarity between two waveforms; it can be expressed as,

N − 1

1
N

+ τ) ] 2 E(τ ) = [ s(n) − s(n (6.2)

n = 0

Equation (6.2) assumes that the average signal level is fixed. However, at
speech onsets and offsets this is not true, hence, the use of the normalized
similarity criterion which considers the effect of nonstationarity of speech
signals,

−

N 1

1
N

τ) ] 2 E(τ ) = [ s(n) − βs(n + (6.3)

n = 0

where β is a scaling factor, or the pitch gain, controlling the changes in signal
level. Under the assumption that the signal is stationary (i.e. s(n) = s(n + τ) ),