2. Communications & Multimedia Signal Processing Frequency Kalman Noise Reduction Esfandiar Zavarehei Department of Electronic and Computer Engineering Brunel University 28 July, 2004

3. Communications & Multimedia Signal Processing Residual Noise Y(e jw ) = X(e jw ) + N(e jw ) |Y(e jw )| 2 = |X(e jw )| 2 + |N(e jw )| 2 + +2 |X(e jw )| |N(e jw )|cos(∆θ) Assuming ∆θ=0 → |Y(e jw )|= |X(e jw )|+ |N(e jw )| which is the assumption in Spectral Subtraction that causes the cross-product to remain in the signal. This remaining noise is called Residual Noise

4. Communications & Multimedia Signal Processing Phase difference

5. Communications & Multimedia Signal Processing Noise Model Variations, Another source of Residual Noise The noise has some fluctuations around its mean

6. Communications & Multimedia Signal Processing Signal to Residual Noise Ratio (SNR Residue )

7. Communications & Multimedia Signal Processing Distribution of Residual Noise This figure is the histogram of the residual noise for each frequency bin all together plotted as an image

8. Communications & Multimedia Signal Processing Distribution of Residual Noise We assume that the distribution of the residual noise is Gaussian and use Kalman Filter to reduce its effect. The figure shows the mean of all histograms across frequency that looks like a Gaussian distribution

9. Communications & Multimedia Signal Processing Goal Fluctuations of frequency trajectory centred around f = 761Hz (bin number 20) across time for the clean and noisy signal.

10. Communications & Multimedia Signal Processing Kalman Filter

11. Communications & Multimedia Signal Processing Advantages of Kalman Kalman uses the Variance of the noise. It can use the data in neighbour frequency trajectories for enhanced prediction    f t=k A C B D E

12. Communications & Multimedia Signal Processing Results so far SNR results do not show the perceptual quality of the output

13. Communications & Multimedia Signal Processing Results so far (cont.)

14. Communications & Multimedia Signal Processing Results so far (cont.) Noisy Spectral Subtraction Nonlinear Spectral Subtraction SS Kalman SS Kalman with VAD

15. Communications & Multimedia Signal Processing Results so far (cont.) The same method could be applied to Mel-Spectrum for recognition purposes

16. Communications & Multimedia Signal Processing Challenges and future work The transition from vowels to consonants and vice versa is not modelled so the Filter might be distracted More sophisticated use of the neighbourhood information and better ways of predicting the values

17. Communications & Multimedia Signal Processing Thanks!