Chapter 2 Background
4.1 Proposed Robust Speech Analysis Method
4.1.2 Noise analysis and reduction
classified, as shown in Figs. 4.3(e) and 4.3(f). The estimated formants are the average of the closely located peaks.
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Figure 4.3: Spectral envelopes and their peaks
We tested the MEMD-based speech analysis method under noisy conditions [35]. Our method could be robust inF0 estimation compared with the LP and CEP-based methods.
However, the spectral envelope and formant estimation were not robust. Therefore, we proposed the two-stage speech analysis for noisy conditions, where the first stage exploits the common mode alignment property of MEMD for noise decomposition in the frequency domain. The second stage is the MEMD-based speech analysis method.
The limitation of this analysis was that it was only robust to white noise but not to others such as pink noise. As we know, the power spectral density (PSD) of pink noise is inversely proportional to the frequency, unlike the PSD of white noise, which is flat in the frequency domain. The flat shape of the PSD of white noise is the slowest oscillating component that is decomposed into the last IMF by using MEMD. However, the PSD of pink noise gradually changes in a high frequency range and quickly changes in a low-frequency range. Consequently, the components of the PSD of pink noise spread into all of the IMFs, i.e., the quickly changing components are in the low IMF orders, whereas the slowly changing ones are in the high IMF orders. On the basis of this limitation, we decided to propose the noise reduction stage in the time domain with MEMD. The modified speech analysis method is shown in Fig. 4.4, where there are conceptually two stages of noise reduction and speech analysis. We still exploit the common mode alignment property of MEMD for the decomposition of noise on the basis of the assumption that noise is stationary and the speech signal is not stationary in a long-time analysis frame.
MEMD-based noise decomposition
IMF selection
F0 estimation
Voiced/unvoiced classification Spectral subtraction
Formant and spectral envelope estimations ݕሺݐሻ
Results
Figure 4.4: Block diagram of the speech analysis framework in noisy conditions voiced/unvoiced classification or voice activity detection (VAD). The second step uses this VAD for SS to reduce the remaining noise in the frequency range of the speech signals.
Consider the observed noisy speech signal, y(t), which can be represented as the sum of a clean speech signal s(t) and the background noise w(t), i.e., y(t) = s(t) +w(t).
When y(t) is decomposed into IMFs by using MEMD, we assume that the effects of noise dominate in some IMFs and the speech signals dominate in the other IMFs. Thus, y(t) can be redefined as
y(t) =
A
X
k=1
ck(t)
| {z } noise
+
B
X
k=A+1
ck(t)
| {z } speech
+
K
X
k=B+1
ck(t)
| {z } noise
, (4.1)
whereAandB are the orders of IMF that separate IMFs into groups of noise and speech.
Due to the overlap between the frequency bands of IMFs, it is hard to separate the noises and speech completely when the frequency components of noises are distributed into the whole frequency range like white and pink noise. However, MEMD can reduce the degree of mixing by decomposition. The remaining task is to find IMFs that the speech signals or noise dominate. On the basis of the assumption that noise is stationary but the speech signal is not stationary in a long-time analysis frame, 0.5 to 1 s, the power envelope of noise should fluctuate slowly, and the power envelope of speech should fluctuate faster.
Therefore, the comparing power envelopes should be helpful in detecting the IMFs of noise.
If we dividey(t) into framesy1(t),y2(t), andy3(t), we can form the multivariate signal
y1(t) y
2(t) y
3(t)
c 1 c 2 c 3 c 4 c 5 c 6 c 7 c 8 c 9 c 10 c 11 c 12 c 13 c 14 c 15
Time (s)
0 0.2 0.4 0.6 0.8
c 16
Time (s)
0 0.2 0.4 0.6 0.8
Time (s)
0 0.2 0.4 0.6 0.8
Figure 4.5: Input signals (first row), IMFs of input signals (ck), and power envelopes of IMFs (red).
by using them, y(t) = [y1(t), y2(t), y3(t)]. MEMD takes y(t) as an input and decomposes y1(t), y2(t), and y3(t) simultaneously into IMFs, as shown in Fig. 4.5, where the first row contains y1(t), y2(t), and y3(t). The IMFs of each frame are denoted as ck(t) in the associated column. Let the power envelope of an IMF is defined as
pk(t) =p
LPF[|ck(t) +jHilbert(ck(t))|2] (4.2) where pk(t) is the power envelope ofck(t), LPF[·] is a low pass filtering, and Hilbert[·] is the Hilbert transform. Since noise is stationary, it is common to y1(t), y2(t), and y3(t).
MEMD aligns common noise in the same order of IMFs which can be identified by using the similarity of the power envelopes. Noise IMFs should have power envelopes that are high in similarity, but those of the speech signals should be low in similarity.
The power envelopes of IMFs are shown by the red lines in Fig. 4.5. The normalized Euclidean distance between the power envelopes when the orders of IMF are the same is shown in Fig. 4.6(a) by the blue line, where the Euclidean distance is averaged from three pairs of columns and the horizontal axis is the order of IMFs. A low value of Euclidean distance indicates the orders of IMFs for which noise dominates, whereas those with a high value of Euclidean distance indicate the IMFs of speech signals. Therefore, we can
discard IMFs having a low Euclidean distance to reduce noise, as shown by the red line in Fig. 4.6(a). The clean, noisy, and enhanced speech signals are shown in Figs. 4.6(b) – 4.6(d).
After noise reduction by using MEMD, the F0 is estimated. VAD is constructed by using the standard deviation of the estimated F0, as shown in Fig. 4.7, where the noisy speech signal in Fig. 4.7(a) is interfered with pink noise. The estimated F0 is shown in Fig. 4.7(b). The standard deviation (STD) of the estimated F0 is shown in Fig. 4.7(c).
The STD ofF0 was calculated by using 20 values equivalent to 20 frames when the frame shift was 1 ms. The resulting VAD is shown as the blue line in Fig. 4.7(d) and is based on the threshold value of 10 Hz of the STD in Fig. 4.7(c). Ten Hz is the allowable variation of F0 during voiced sections. Since this approach may fail to detect unvoiced sections as shown with the beginning of the speech signal in Fig. 4.7(d). We alleviate this error by widening the detected voiced sections as follows. First, the detected narrow-width voiced sections, which should not be voiced sections, were eliminated, as shown in Fig. 4.7(e), on the basis of shortest vowel sound of human speech. Second, the detected wide-width voiced sections were extended to a certain range, as shown in Fig. 4.7(f). On the basis of this VAD, the remaining noise was reduced by using SS. The improved spectral envelope is shown in Fig. 4.8.
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Figure 4.6: Euclidean distance, signals, and estimated F0: (d) – (e) estimated F0 of (a) is the blue line and those red lines are of (b) and (c). (f) blue, red, and orange lines associate with three pairs of column of IMFs in Fig. 4.5.
Amplitude -0.1
0 0.1
F0 (Hz) 200 400 600
STD of F0 (Hz)
50 100 150
Amplitude
-0.1 0 0.1
Amplitude
-0.1 0 0.1
Time (s)
0.5 1 1.5 2 2.5 3
Amplitude
-0.1 0 0.1
(a)
(b)
(c)
(d)
(e)
(f)
Figure 4.7: VAD using estimated F0