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

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 Siemens Corporate Research

Shot Time Discrete Wavelet Transform in Time-Frequency Presentation 2 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 Siemens Corporate Research

Shot Time Discrete Wavelet Transform in Pseudo Frequency Presentation 2 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 Siemens Corporate Research

Shot Time Discrete Wavelet Packet Transform in Frequency Presentation 2 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 Siemens Corporate Research

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 Siemens Corporate Research

The Workflow of Single Channel Noise Reduction Operation Siemens Corporate Research

Martin Noise Estimator - Noise Magnitude Tracking in Periodograms of STFT and DWT Siemens Corporate Research

The Wiener Filter Siemens Corporate Research

The Spectral Subtraction Filter Siemens Corporate Research

The Wolfe-Godsill Filter - MAP Estimation of Amplitude and Phase Siemens Corporate Research

The Ephraim-Malah Filter - MMS Estimation of Amplitude Siemens Corporate Research

The transfer functions of the Wiener, Spectral Subtraction, Wolfe-Godsill, and Ephraim-Malah Filters Siemens Corporate Research

Experiments 4 Speeches (male/female, conference/handset), 7 noises (background, fan, window, printer, etc.) are mixed in 4 ratios (28 per mixing ratio), 16000 Hz, 16 bits STFT setting x(m, I) - 200 sample with 40 overlap, and 56 zero padding X(k, I) - 256 FFT DWPT and DWT setting x(m, I) - 256 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) Siemens Corporate Research

Experimental Results for Spectral Subtraction qm 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 The best The second Siemens Corporate Research

Experimental Results for Wiener Filter qm 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 The best The second Siemens Corporate Research

Experimental Results for Wolfe-Godsill Filter qm 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 The best The second Siemens Corporate Research

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 Siemens Corporate Research

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 Siemens Corporate Research