1. Comparison of Wavelet and FFT Based Single Channel Speech Signal Noise Reduction Techniques
Ningping Fan, Radu Balan, Justinian Rosca
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SPIE Optics East 2004

2. Shot Time Discrete Fourier Transform in Frequency Presentation
k = 0
k = 1
k = 2
k = 3
k = 4
k = 5
k = 6
x(m, i)
x(m, i)
k = 7
m = 0, 1, 2, 3, 4, 5, 6, 7
X(k, i)
DFT
IDFT
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3. Shot Time Discrete Wavelet Transform in Time-Frequency Presentation2 h g ~
DWT
IDWT
x(m, i)
X(k, j)
Level 1
Level 2
Level 3
k = 0
j = i
k = 1
k = 2
j = i, i + 1
k = 3
j = i, i + 1, i + 2, i + 3
m = 0, 1, 2, 3, 4, 5, 6, 7
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4. Shot Time Discrete Wavelet Transform in Pseudo Frequency Presentation2 h g ~
DWT
IDWT
x(m,i)
X(k,i)
Level 1
Level 2
Level 3
k = 0
k = 1
k = 2, 3
k = 4, 5, 6, 7
m = 0, 1, 2, 3, 4, 5, 6, 7
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5. Shot Time Discrete Wavelet Packet Transform in Frequency Presentation2 h g ~
DWPT
IDWPT
x(m, i)
X(k, i)
Level 1
Level 2
Level 3
m = 0, 1, 2, 3, 4, 5, 6, 7
k = 0
k = 1
k = 2
k = 3
k = 4
k = 5
k = 6
k = 7
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6. Power Spectral Densities of Noise, Speech, and Noisy Speech
(a) Psd of DFT
(b) Psd of DWT in pseudo spectral presentation
(c) Psd of DWPT
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7. The Workflow of Single Channel Noise Reduction Operation
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8. Martin Noise Estimator - Noise Magnitude Tracking in Periodograms of STFT and DWT
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9. The Wiener Filter
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10. The Spectral Subtraction Filter
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11. The Wolfe-Godsill Filter - MAP Estimation of Amplitude and Phase
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12. The Ephraim-Malah Filter - MMS Estimation of Amplitude
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13. The transfer functions of the Wiener, Spectral Subtraction, Wolfe-Godsill, and Ephraim-Malah Filters
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14. Experiments
4 Speeches (male/female, conference/handset), 7 noises (background, fan, window, printer, etc.) are mixed in 4 ratios (28 per mixing ratio), Hz, 16 bits
STFT setting
x(m, I) sample with 40 overlap, and 56 zero padding
X(k, I) FFT
DWPT and DWT setting
x(m, I) samples with 96 overlap
X(k, I) - 8 levels
Battle-Lemarie (0), Burt-Adelson (1), Coiflet-6 (2), Daubechies-20 (3), Haar (4), Pseudo-coiflet-4 (5), and Spline-3-7 (6)
Objective Quality Measurements
Enhancement: global SNR (gSNR), segmental SNR (sSNR), frequency-weighted
segmental SNR (fwsSNR)
Distortion: Itakura-Saito distance (isD), and weighted spectral slope (WSS)
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15. Experimental Results for Spectral Subtractionqm
gSNR (dB)
sSNR (dB)
fwsSNR (dB)
isD
WSS
org
-0.1
2.31
5.9
10.31
-3.12
-0.71
2.95
7.44
1.51
4.85
9.64
15.18
0.46
0.32
0.2
0.12
43.3 34
24.56
16.03
spectral subtraction
fft
1.44
4.63
7.96
11.01
-0.7
2.16
5.24
8.2
3.9
6.75
9.63
12.4
0.41
0.29
0.13
41.64
32.31
23.63
15.96
wp0
1.03
4.05
6.61
9.52
-1.51
1.37
6.93
3.12
6.83
8.04
10.62
0.47
0.25
0.14
41.56
32.46
24.61
16.68
wp1
0.84
3.79
7.64
11.29
-1.76
1.04
4.78
8.3
2.83
6.43
10.25
13.39
0.51
0.34
0.11
42.39
33.27
23.65
15.84
wp2
1.01 4
7.68
11.54
-1.54
1.31
4.91
8.63
3.09
6.77
11.18 15
0.48
0.19
41.67
32.63
23.81
15.91
wp3
1.02
4.04
6.29
9.25
-1.5
1.36
3.56
6.69
6.82
7.91
10.6
0.27
0.15
41.42
32.44
25.53
17.43
wp4
3.77
7.35
-1.8
4.46
8.03
2.79
6.38
9.89
13.06
0.56
0.37
0.21
42.4
33.43
24.28
16.29
wp5
0.96
3.93
7.43
11.31
-1.6
1.22
4.62
8.39 3
10.82
14.7
0.49
0.33
41.51
32.59
24.3
16.24
wp6
0.94
6.56
9.47
-1.71
1.13
3.85
6.88
2.86
6.63
10.61
0.31
42.22
33.05
24.75
16.76
wt0
0.81
3.71
7.23
10.86
-1.82
4.37
2.74
6.28
9.76
12.89
0.5
42.35
33.41
24.38
16.3
wt1
0.67
3.51
7.05
10.74 -2
0.74
4.18
7.78
2.55
6.06
12.83
0.52
0.35
0.22
42.44
33.57
24.58
16.49
wt2
0.78
3.66
7.19
10.85
-1.87
0.91
4.34
7.9
2.72
9.8
12.93
42.32
33.37
wt3
0.79
7.27
10.93
-1.84
0.97
4.41
7.98
2.76
6.37
9.88
13.04
33.4
24.35
wt4
0.65
7.06
10.76
-2.02
4.19
7.79
2.51
6.02
9.66
12.88
0.57
0.23
42.68
33.75
24.72
16.61
wt5
3.65
7.12
10.72
-1.83
4.28
2.73
9.75
12.84
42.21
24.51
16.51
wt6
0.61
3.39
6.92
-2.11
7.65
2.34
5.82
9.44
12.61
42.95
34.04
25.05
16.93
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16. Experimental Results for Wiener Filterqm
gSNR (dB)
sSNR (dB)
fwsSNR (dB)
isD
WSS
org
-0.1
2.31
5.9
10.31
-3.12
-0.71
2.95
7.44
1.51
4.85
9.64
15.18
0.46
0.32
0.2
0.12
43.3 34
24.56
16.03
Wiener filter
fft
1.6
4.78
8.17
11.47
-0.35
2.47
5.55
8.69
4.12
7.17
10.41
13.74
0.43
0.3
0.13
42.03
32.82
24.03
16.19
wp0
1.09
4.09
7.59
11.24
-1.37
1.47
4.73
8.25
3.17
6.98
10.19
13.32
0.47
0.31
42.27
32.84
23.76
15.89
wp1
0.9
3.84
7.64
11.49
-1.62
1.17
4.86
8.59
2.87
6.62
11.14
14.98
0.52
0.33
0.19
0.11
42.81
33.45
23.88
15.94
wp2
1.07
4.04
6.58
9.47
-1.4
1.42
3.88
6.89
3.14
6.93
8.03
10.58
0.48
0.25
0.14
42.25
32.93
24.55
16.63
wp3
1.08
4.07
7.62
11.25
-1.36
4.77
8.27
3.18 7
10.21
13.31
32.78
23.61
15.81
wp4
3.83
7.67
11.52
-1.66
1.13
4.9
8.61
2.83
6.55
11.18
0.57
0.37
33.61
23.75
15.87
wp5
1.02
3.96
6.33
9.28
-1.46
1.32
3.58
6.69
3.05
6.82
8.12
10.78
0.18
41.96
32.83
25.96
17.9
wp6
0.98
3.9
7.31
10.94
-1.59
1.2
4.42
7.96
2.88
6.66
9.91
13.05
0.45
0.22
42.49
33.1
24.48
16.5
wt0
0.87
3.76
7.32
11.16
1.1
4.54
2.8
6.44
10.61
14.43
0.5
42.22
33.36
24.31
16.24
wt1
0.73
7.15
11.06
-1.84
0.89
4.36
8.16
2.6
6.21
10.44
14.33
0.54
0.35
0.21
42.34
33.51
24.5
16.4
wt2
0.84
3.73
7.28
11.15
-1.69
4.51
2.78
6.46
10.67
14.51
0.51
42.15
33.29
16.23
wt3
0.86
3.79
7.36
11.23
-1.65
1.14
4.6
8.36
2.84
6.57
10.77
14.63
33.34
24.26
16.16
wt4
3.61
7.18
11.07
-1.85
0.92
4.38
2.57
6.19
10.4
14.3
0.6
0.38
42.67
33.77
24.67
16.53
wt5
0.85
3.69
7.19
11.02
-1.68
1.05
4.44
8.15
2.79
14.42
0.34
42.05
33.38
16.45
Wt6
0.59
3.37
6.96
10.88
-2.04
0.67
4.17
7.99
2.27
5.82
10.16
14.1
42.96
34.05
25.02
16.82
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17. Experimental Results for Wolfe-Godsill Filterqm
gSNR (dB)
sSNR (dB)
fwsSNR (dB)
isD
WSS
org
-0.1
2.31
5.9
10.31
-3.12
-0.71
2.95
7.44
1.51
4.85
9.64
15.18
0.46
0.32
0.2
0.12
43.3 34
24.56
16.03
Wolfe-Godsill
fft
1.5
4.67
7.8
10.66
-0.48
5.18
7.96
3.78
6.31
9.07
11.86
0.44
0.23
0.15
42.22
32.98
24.39
16.62
wp0
0.79
3.55
7.39
11.23
-1.69
0.9
4.58
8.31
2.77
5.35
10.74
14.59
0.59
0.41
0.21
41.61
33.2
24.49
16.45
wp1
3.24
6.47
9.3
-2.01
0.52
3.73
6.7
2.49
5.1
7.92
10.43
0.65
0.25 43
34.4
24.98
17.23
wp2
0.77
3.51
7.49
11.11
-1.74
0.83
4.63
8.13
2.73
5.32
10.14
13.24
41.91
33.47
23.85
16.07
wp3
7.52
11.35
-1.7
0.89
4.74
8.45
2.78
11.04
14.85
0.11
41.6
23.95
16.09
wp4
3.3
6.57
9.59
-2.02
0.53
3.71
6.83
2.56
5.25
8.06
0.74
0.51
0.13
42.9
34.71
25.59
17.71
wp5
0.72
3.45
11.21
-1.82
4.59
8.2
2.63
5.23
10.25
13.42
0.6
41.76
33.5
24.12
16.21
wp6
0.78
3.46
7.5
11.41
-1.9
0.63
4.69
8.49
2.51
5.24
11.05
14.95
0.36
0.19
43.36
34.51
24.1
16.16
wt0
0.58
3.17
6.16
-2.13
6.59
5.13
7.94
10.59
0.61
0.43
0.26
43.1
34.21
25.27
17.13
wt1
0.45
2.98
6.02
9.04
-2.29
3.31
6.55
2.39
5.06
8.03
10.82
0.64
0.27
0.16
43.22
34.42
25.53
17.48
wt2
0.56
3.15
6.15
9.1
-2.16
0.38
6.61
2.52
5.17
8.01
10.68
43.04
34.11
25.2
17.1
wt3
0.54
6.21
9.18
-2.17
6.67
8.04
0.62
43.11
34.17
25.23
17.02
wt4 3
6.09
9.16
-2.33
3.37
6.63
2.38
8.26
11.1
0.5
0.31
0.18
43.44
34.87
25.96
17.79
wt5
0.57
3.11 6
8.79
-2.12
0.37
3.34
6.34
5.11
7.84
10.41
42.99
34.27
25.51
17.65
wt6
0.47
2.91
5.91
8.94
-2.26
3.21
6.43
2.36
5.03
7.98
10.7
0.39
0.14
43.64
34.85
26.12
18.07
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18. CPU Time Consumption for FFT, DWPT, and DWT
Abr.
transforms
Implementation
CPU Time (time of STFT)
fft
Shot time Fourier transform
Custom implementation of FFT 1
wp0
Battle-Lemarie wavelet packet
UBC Imager Wavelet Package
10.304
wp1
Burt-Adelson wavelet packet
3.016
wp2
Coiflet-6 wavelet packet
7.779
wp3
Daubechies-D20 wavelet packet
8.608
wp4
Haar wavelet packet
0.949
wp5
Pseudo-coiflet-4 wavelet packet
4.745
wp6
Spline-3-7 wavelet packet
4.356
wt0
Battle-Lemarie wavelet transform
2.458
wt1
Burt-Adelson wavelet transform
0.882
wt2
Coiflet-6 wavelet transform
1.898
wt3
Daubechies-D20 wavelet transform
UBC Imager Wavelet Package
2.084
wt4
Haar wavelet transform
0.390
wt5
Pseudo-coiflet-4 wavelet transform
1.255
wt6
Spline-3-7 wavelet transform
1.153
wt7
Custom implementation
0.067
wt8
Daubechies-D4 wavelet transform
0.085
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19. Conclusion
All methods can reduce noise in SNR sense, and more specifically
STFT is the best, DWPT the second, and DWT the last
STFT and DWPT can reduce distortion
DWPT has less distortion and is better with high SNR signals
Further research
Try other incomplete transforms of DWPT and DWT
Adapt Martin noise estimator for each frequency due to different sample length
Test other wavelet bases
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