Speech feature extraction using linear Chirplet transform and its applications*

Figures & data

Figure 1. Illustration of the Linear Chirplet Transform with three main steps. In step $\mathrm{\#}$1, the blue line is rotated by an angle θ, then becomes the green line. In step $\mathrm{\#}$2, the green line is shifted by $\alpha t_0$ to be the red line. At the final step, the red line is transformed with STFT.

Figure 2. Linear Chirplet Transform with chirp rate $\alpha =0$. In this case, LCT performs equivalent with the Fourier transform.

Figure 3. Linear Chirplet Transform with positive chirp rate $\alpha =5$. In the TF plane, the signal is highlighted with red color when the frequency achieving high energy increases over time.

Algorithm 1. Speech feature extraction using Linear Chirplet Transform

1. procedure Feature-Extraction($T,\mathrm{\Omega },\alpha ,\sigma ,s(t)$)

2. $z(t)\leftarrow s(t)+j\mathcal{H}[s(t)]$

3. $Feature\leftarrow [,]$

4. for $t_0\in T$ do

5.  for $\omega \in \mathrm{\Omega }$ do

6.   $z_{t_0,\omega }(t)\leftarrow z(t)w_{(\sigma )}(t-t_0)$

7.   $z_{t_0,\omega }^R(t)\leftarrow z_{t_0,\omega }(t){\mathrm{\Phi }}_{\alpha }^R(t)$

8.   $z_{t_0,\omega }^{R,M}(t)\leftarrow z_{t_0,\omega }^R(t){\mathrm{\Phi }}_{\alpha }^M(t,t_0)$

9.   $Feature[t_0,\omega ]\leftarrow {\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}{z}_{t_0,\omega }^{R,M}(t)\exp (-j\omega t)\mathrm{d}t$

10.  return Feature

Figure 4. Illustration of 3D time-frequency representation returned by Linear Chirplet Transform for input audio with the content ‘There was a change now’, said a woman.

Table 1. Some statistics in TIMIT and VIVOS.

Information	TIMIT	VIVOS
Male (recorders)	438	34
Female (recorders)	192	31
Total recorders	630	65
Total dialects	8	3
Total audio files	6300	12420
Total length (hours)	5.4	15.7

Table 2. Some statistics in LibriSpeech.

Information	Amount
Male (recorders)	1210
Female (recorders)	1128
Total recorders	2338
Dialects	Not mention
Total length (hours)	960
# words	977.000

Table 3. Speaker gender recognition in TIMIT and VIVOS.

Feature	TIMIT	TIMIT	VIVOS	VIVOS
	Error_Rate(%)	$f_1$_ Score	Error_Rate(%)	$f_1$_ Score
Spectrogram	7.59	93.34	5.99	94.23
Mel-Spectrogram	8.62	93.02	3.51	96.55
MFCC	5.10	95.29	3.61	96.25
LCT ($\alpha =0.5$)	4.44	95.87	2.72	97.36
LCT ($\alpha =-0.5$)	4.39	95.89	2.52	97.42

Table 4. Speaker dialect recognition in TIMIT and VIVOS.

Feature	TIMIT	TIMIT	VIVOS	VIVOS
	Error_Rate(%)	$f_1$_ Score	Error_Rate(%)	$f_1$_ Score
Spectrogram	4.50	95.28	5.85	94.42
Mel-Spectrogram	4.21	95.52	4.10	95.86
MFCC	2.17	97.82	2.66	97.18
LCT ($\alpha =0.5$)	2.01	97.98	2.68	97.15
LCT ($\alpha =-0.5$)	1.95	98.02	2.69	97.37

Table 5. Speech recognition with different features for English (E) in LibriSpeech and Vietnamese (V) in VIVOS.

Feature	T-C (E)	Transducer (E)	T-C (V)	Transducer (V)
	WER(%)	WER(%)	WER(%)	WER(%)
Spectrogram	8.65	8.02	25.87	34.65
Mel-Spectrogram	7.09	8.11	26.14	33.26
MFCC	6.47	6.45	23.73	28.08
LCT ($\alpha =0.5$)	6.38	6.47	23.91	29.28
LCT ($\alpha =-0.5$)	6.29	6.76	22.52	28.10