Comparison of Wavelet and FFT Based Single Channel Speech Signal Noise Reduction Techniques

1. 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

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) IDFT DFT Siemens Corporate Research

3. 2 2 2 2 2 2 Level 3 Level 3 ~ k = 0 j = i 2 h h Level 2 Level 2 ~ k = 1 j = i ~ 2 g 2 h g h Level 1 Level 1 ~ k = 2 j = i, i + 1 ~ 2 g 2 h g h k = 3 j = i, i + 1, i + 2, i + 3 ~ 2 g g x(m, i) X(k, j) x(m, i) m = 0, 1, 2, 3, 4, 5, 6, 7 DWT IDWT Shot Time Discrete Wavelet Transform in Time-Frequency Presentation Siemens Corporate Research

4. 2 2 2 2 2 2 Level 3 Level 3 ~ k = 0 2 h h Level 2 Level 2 ~ k = 1 ~ 2 g 2 h g h Level 1 Level 1 ~ k = 2, 3 ~ 2 g 2 h g h k = 4, 5, 6, 7 ~ 2 g g x(m,i) X(k,i) x(m,i) m = 0, 1, 2, 3, 4, 5, 6, 7 DWT IDWT Shot Time Discrete Wavelet Transform in Pseudo Frequency Presentation Siemens Corporate Research

5. Level 3 Level 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ~ k = 0 2 h h Level 2 Level 2 ~ k = 1 ~ 2 g 2 h g h Level 1 Level 1 ~ ~ k = 2 ~ 2 g 2 h 2 h g h h k = 3 ~ 2 g g ~ k = 4 2 h h ~ k = 5 ~ 2 g 2 h g h ~ k = 6 ~ ~ 2 g 2 g 2 h g g h x(m, i) x(m, i) k = 7 ~ 2 g g m = 0, 1, 2, 3, 4, 5, 6, 7 X(k, i) DWPT IDWPT Shot Time Discrete Wavelet Packet Transform in Frequency Presentation Siemens Corporate Research

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 Siemens Corporate Research

7. The Workflow of Single Channel Noise Reduction Operation Siemens Corporate Research

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

9. The Wiener Filter Siemens Corporate Research

10. The Spectral Subtraction Filter Siemens Corporate Research

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

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

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

14. 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

15. Experimental Results for Spectral Subtraction The best The second Siemens Corporate Research

16. Experimental Results for Wiener Filter The best The second Siemens Corporate Research

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

18. transforms Implementation CPU Time (time of STFT) Abr. 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 UBC Imager Wavelet Package 3.016 wp2 Coiflet-6 wavelet packet UBC Imager Wavelet Package 7.779 wp3 Daubechies-D20 wavelet packet UBC Imager Wavelet Package 8.608 wp4 Haar wavelet packet UBC Imager Wavelet Package 0.949 wp5 Pseudo-coiflet-4 wavelet packet UBC Imager Wavelet Package 4.745 wp6 Spline-3-7 wavelet packet UBC Imager Wavelet Package 4.356 wt0 Battle-Lemarie wavelet transform UBC Imager Wavelet Package 2.458 wt1 Burt-Adelson wavelet transform UBC Imager Wavelet Package 0.882 wt2 Coiflet-6 wavelet transform UBC Imager Wavelet Package 1.898 wt3 Daubechies-D20 wavelet transform UBC Imager Wavelet Package 2.084 wt4 Haar wavelet transform UBC Imager Wavelet Package 0.390 wt5 Pseudo-coiflet-4 wavelet transform UBC Imager Wavelet Package 1.255 wt6 Spline-3-7 wavelet transform UBC Imager Wavelet Package 1.153 wt7 Haar wavelet transform Custom implementation 0.067 wt8 Daubechies-D4 wavelet transform Custom implementation 0.085 CPU Time Consumption for FFT, DWPT, and DWT Siemens Corporate Research

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 Siemens Corporate Research