Pitch Estimation and Voiced–Unvoiced Classification of Speech - Digital Speech: Coding for Low Bit Rate Communication Systems - page 156

10 4

2 × 1000

500 1.5

0 1

− 500 0.5

− 1000 0

50 100 150 200 4000

0 1000 2000 3000

(b) Frequency (Hz)

(a) Time (samples)

10 4

1 × 1

0.5 0.5

0 0

− 0.5 − 0.5

− 1 − 1

50 100 150

0 1000 2000 3000 4000

(c) Frequency (Hz)

(d) Lag (samples)

Figure 6.6 An example of (a) speech signal of T 0 8 kHz), (b)

magnitude spectrum, (c) zero-crossing spectrum, and (d) spectral autocorrelation

= 34 -sample ( F s =

M/T (u)

overlapping area) corresponding to very small ω τ ,i.e. + 0 . 5 ≤

0

ω τ << M/( 2 T 0 ) + 0 . 5 . Thus, the linear magnitude spectrum is used instead

of the logarithmic one.
Figure 6.6 shows an example illustrating the characteristics of SA. For a
speech segment in Figure 6.6a, the magnitude and its zero-crossing spectra
are shown in Figures 6.6b and 6.6c, respectively. Finally, the spectral autocor-
relation is shown in Figure 6.6d, indicating a prominent peak at the pitch lag.
The TA over a periodic signal produces high correlation for integer multiples
of the pitch period T 0 . This means that the spectral autocorrelation, R S (τ ) in
equation (6.19), has peaks for the integer submultiples of T 0 ,i.e. τ = T 0 /k ,

T 0 /T (l)

for 1 . Figure 6.7 shows an example featuring high SAs for

pitch period submultiples. Thus, the TA-based PDA may result in detecting
an unwanted pitch period multiple, and the SA-based PDA may result in
pitch-halving. The pitch period multiple and submultiple problems can be
compensated for by combining the two autocorrelation methods, TA and SA,
in an advantages way. Hence, the spectro-temporal autocorrelation (STA) is
defined as [19],

≤ k ≤

0

R ST (τ ) = αR T (τ ) + ( 1 − α)R S (τ ) (6.22)