Single Channel Blind Source Separation Biology Essay

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First of all, I would like to extend my utmost gratitude to my project supervisor, Mr Bryan Chong Fook Lim. His patience, understanding and continuous support truly inspired and motivated me to overcome the challenges I faced and helped to smoothen the progression and completion of this project.

My special thanks to Mr. Chai Yoon Yik who helped to suggest the technical ideas to initiate my project.  

I would like to gratefully acknowledge Mr. Gil-Jin Jang for sharing his literature, knowledge and assistance.  

Last but not least, I will always be indebted to my parents for their understanding, endless patience and encouragement when it was most required.

ABSTRACT:

The problem of separating conceptually distinct sources given only a single channel of mixture is known as the single channel blind source separation. In the developed algorithm, the separation of the mixture is carried out by employing a priori set of time-domain basis functions learnt by Independent Component Analysis (ICA). The basis functions and coefficients captured by ICA are an efficient representation of the statistical structure of the sound sources. Generalized Gaussian distribution was used to model the probability density functions of the source coefficients. The learning algorithm uses the maximum likelihood approach, which is maximizing the data likelihood, to separate the sources. The prototype system was tested on MATLAB R2011b and was successful in performing a two source separation from a single mixture. Experiments were carried out using speech signals and music signals. The accuracy of the extracted sources was measured using correlation to compare the similarity between the extracted signal and the original signal. Overall, the accuracy achieved from all the experiments carried out was 74.6%. A Graphical User Interface (GUI) was also designed for the system and tested to be fully functioning.

Table of Contents:

Declaration of Independent Work ………………………………………………………………………………………….

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I

Acknowledgement .………………………………………………………………………………………….…………………….

II

Abstract ………………………………………………………………………………………….……………………………………..

III

List of Figures ………………………………………………………………………………………….…………………………….

VI

List of Tables………………………………………………………………………………………….……………………………….

VII

List of Abbreviations………………………………………………………………………………………….……………………

VIII

Glossary………………………………………………………………………………………….………………………………………

VIII

Chapter 1.0 - Introduction ………………………………………………………………………………………….………….

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Chapter 2.0 - Literature Review ……………………………………………………………………………………………..

3

Chapter 3.0 - Materials and Methods ……………………………………………………………………………………

6

3.1.0 Materials ………………………………………………………………………………………….……………………………

6

3.2.0 Methods ………………………………………………………………………………………….…………………………..

6

3.2.1 General Overview ………………………………………………………………………………………….………………

6

3.2.2 Independent Component Analysis (ICA) Algorithm ………………………………………………………….

7

3.2.3 The Signal Representation Model ………………………………………………………………….……………….

8

3.2.4 Basis Filters ………………………………………………………………………………………….………………………

10

3.2.5 Generalized Gaussian Distribution ………………………………………………………………….………………

10

3.2.6 Separation Algorithm ………………………………………………………………….…………………………………

12

3.2.7 Original Single Channel BSS Algorithm ……………………………………….……………………………………

15

3.2.8 An Improved Single Channel BSS Algorithm ……………………………….……………………………………

17

3.2.9 Difference between Original and Improved Single Channel BSS Algorithm ……………………….

20

3.2.10 Extraction Steps for the Single Channel BSS Algorithm ……………………….…………………………

21

Chapter 4.0 - Results

25

4.1.0 Experiment setups …………………………………………………………………………………………………………

25

4.1.1 Experiment settings………………………………………………………………………………………………………

28

4.1.2 Results of the experiment using 8 kHz source signals ……………….……………………………………

29

4.1.3 Results of the experiment using downsampled source signals… ………………………………………

36

4.1.4 Results of the experiment using a mixture of 8 kHz source signals and downsampled source signals………………………………………………………………….…………………………………………….

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4.2.0 Basis Filters ……………………………………………………………………………………………………………………

50

4.3.0 Graphical User Interface (GUI) Implementation …………….………………………………………………

53

Chapter 5.0 - Discussion …………….………………………………………………….…………….…………………………

54

5.1.0 Improved Single Channel BSS algorithm ……………………………….…………….………………………….

54

5.1.1 Calculating Accuracy using Correlation ……………………………….…………….…………………………….

56

5.1.2 Filtering the High Frequency Noise Component ……………………………….…………….……………….

57

5.1.3 Using RMS value to determine the Actual Source ……………………………….…………….…………….

59

5.2.0 Evaluating the Average Spectral Plot ……………………………….…………….………………………………

59

5.2.1 Reason for Degraded Performance using the Downsampled Sources ………………………………

61

5.3.0 Execution Time of the Single Channel BSS Algorithm ……………………………….………………………

62

5.3.1 Overall Accuracy of the Single Channel BSS Algorithm ……………………………….……………………

63

5.4.0 Characteristics and Limitations of the Single Channel BSS Algorithm ………………………………

64

5.4.1 Summary ……………………………….……………………………….……………………………….…………………….

64

Chapter 6.0 - Conclusion ……………………………….……………………………….……………………………………

65

Chapter 7.0 - Recommendations for Future Work ……………………………….…………………………………

67

Chapter 8.0 - References ……………………………….……………………………….……………………………….…….

68

Appendix ……………………………….……………………………….……………………………….…………………………….

I

List of Figures:

Figure 1: Frequency ranges of musical instruments and the human voice

1

Figure 2: Frequency ranges of musical instruments and the human voice

4

Figure 3: Types of kurtosis

8

Figure 4: Single channel mixing model -

8

Figure 5: Decomposition of mixture signal

8

Figure 6: Decomposition of source signal

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Figure 7: Rotating the data to minimize Gaussianity

10

Figure 8: Effect of varying mean on distribution

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Figure 9: Effect of varying standard deviation on distribution -

11

Figure 10: Effect of varying q or ß parameter on distribution

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Figure 11: Generating output coefficients from data and basis filter

12

Figure 12: Block diagram of separation algorithm

14

Figure 13: Steps in Training Phase of the Original Single Channel BSS Algorithm

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Figure 14: Steps in Separation Phase of the Original Single Channel BSS Algorithm -

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Figure 15: Steps in Separation Phase of the Improved Single Channel BSS Algorithm

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Figure 16: Steps in sub section of the Separation Phase of the Improved Single Channel BSS Algorithm

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Figure 17: Steps in main Separation Phase of the Improved Single Channel BSS Algorithm

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Figure 18: Flow of the Improved Single Channel BSS Algorithm

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Figure 19: Histograms of the sources

26

Figure 20: Spectrograms of the sources

27

Figure 21: List of experiments conducted

28

Figure 22: Basis filter for rock music

50

Figure 23: Basis filter for jazz music

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Figure 24: Basis filter for male speech

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Figure 25: Basis filter for female speech

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Figure 26: Basis filter for piano music

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Figure 27: Basis filter for guitar music

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Figure 28: Basis filter for epic music

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Figure 29: GUI designed for Single Channel BSS Algorithm

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Figure 30: Comparison between results (graph) from original and improved algorithm

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Figure 31: Comparison between results (histogram) from original and improved algorithm

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Figure 32: Rate of convergence

56

Figure 33: Correlation scale of accuracy

56

Figure 34: Positive and negative correlation

57

Figure 35: Before(left) and after(right) passing through the high pass filter (Rock Music)

57

Figure 36: Noise component present above 3.7 kHz before filtering (left) and after filtering (left)

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Figure 37: Design of low pass filter using FDA tools

58

Figure 38: Average spectral plot for all sources

60

Figure 39: Average spectral plot for piano, guitar and epic music

60

Figure 40: Spectrogram plots for piano, guitar and epic music

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Figure 41: Occurrence of aliasing

62

Under Appendix

Figure A1: Overview of GUI

I

Figure A2: Warning for insufficient audio signals being loaded

I

Figure A3: Warning for insufficient audio signals for learning basis

I

Figure A4: Warning for basis not being loaded before proceeding to extraction process

II

Figure A5: Selecting the number of sources

II

Figure A6: Selecting audio files

III

Figure A7: Information on Source Signals

III

Figure A8: Plotting graphs and histograms of source signals

IV

Figure A9: Plotting graph of mixture

IV

Figure A10: Learning basis

V

Figure A11: Basis Filters learnt

V

Figure A12: Loading basis into environment

V

Figure A13: Status of GUI

VI

Figure A14: First stage separation results

VI

Figure A15: Execution time, Status of GUI and accuracy results of extracted sources - VI

VI

Figure A16: Graph plots of extracted source signals

VII

Figure A17: Saving extracted source signals

VII

Figure A18: Help file for GUI

VIII

List of Tables:

Table 1: Technical Objectives

2

Table 2: Correlation results for the 8 kHz signals

29

Table 3: Average correlation results for the 8 kHz signals

30

Table 4: Extracted music signals

31

Table 5: Extracted speech signals

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Table 6: Extracted speech and music signals

34

Table 7: Extracted speech and music signals

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Table 8: Correlation results for the downsampled signals

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Table 9: Average correlation results for the downsampled signals

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Table 10: Extracted music signals

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Table 11: Extracted music signals

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Table 12: Correlation results for the mixture of 8 kHz and downsampled signals

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Table 13: Average correlation results for the mixture of 8 kHz and downsampled signals

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Table 14: Average correlation results for the mixture of 8 kHz and downsampled signals

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Table 15: Extracted music signals

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Table 16: Extracted music signals

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Table 17: Extracted music signals

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Table 18: Extracted speech and music signals

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Table 19: Extracted speech and music signals

48

Table 20: Extracted speech and music signals

49

Table 21: Extracted speech and music signals

50

Table 22: Status of Technical Objectives -

66

List of Abbreviations:

BSS: Blind Source Separation

CASA : Computationary Auditory Scene Analysis

GUI: Graphical User Interface

ICA : Independent Component Analysis

ISA: Independent Subspace Analysis

PCA: Principal Component Analysis

PDF : Probability Density Function

RMS : Root-Mean-Square

Glossary :

Correlation: Measure of similarity between signals

Data Likelihood : Probability of the data

8 kHz signals : Source signals with sampling rate of 8 kHz

Downsampled signals: Source signals that have been downsampled from 44.1 kHz

Gradient Ascent : Method used to obtain the maximum likelihood of data

Maximum a posteriori : Method to maximize the posterior distribution

Maximum likelihood : Method to maximize the probability of the data

Leptokurtic : Distributions with high kurtosis value (super-Gaussian)

Mesokurtic : Normal distribution

Platykurtic : Distributions with low kurtosis value (sub-Gaussian)

Overdetermined : A case where there are less sources than sensors/mixtures.

Underdetermined : A case where there are more sources than sensors/mixtures.