Reverberation: Models, Estimation and Applications
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Reverberation: Models, Estimation and Applications Jimi Yung-Chuan Wen A Thesis submitted in fulfilment of requirements for the degree of Doctor of Philosophy of Imperial College London Signal Processing Group Department of Electrical and Electronic Engineering Imperial College London 2009 2 Abstract The use of reverberation models is required in many applications such as acoustic measurements, speech dereverberation and robust automatic speech recognition. The aim of this thesis is to investigate different models and propose a perceptually-relevant reverberation model with suitable parameter estimation techniques for different applications. Reverberation can be modelled in both the time and frequency domain. The model param- eters give direct information of both physical and perceptual characteristics. These characteristics create a multidimensional parameter space of reverberation, which can be to a large extent captured by a time-frequency domain model. In this thesis, the relationship between physical and perceptual model parameters will be discussed. In the first application, an intrusive technique is proposed to measure the reverberation or reverberance, perception of reverberation and the colouration. The room decay rate parameter is of particular interest. In practical applications, a blind estimate of the decay rate of acoustic energy in a room is required. A statistical model for the distribution of the decay rate of the reverberant signal named the eagleMax distribution is proposed. The eagleMax distribution describes the reverberant speech decay rates as a random variable that is the maximum of the room decay rates and anechoic speech decay rates. Three methods were developed to estimate the mean room decay rate from the eagleMax distributions alone. The estimated room decay rates form a reverberation model that will be discussed in the context of room acoustic measurements, speech dereverberation and robust automatic speech recognition individually. 3 Acknowledgment The viva Professor Filtra: No more globules Master SulfDiox: This anti-microbial agent is just right, Vinter Noah: Thank you gentlemen for the help. Now I can bottle it. After some time..... GREE CREE POP Master SulfDiox: Thank you Vinter Noah, but why does it taste of Capsicum? Professor Filtra: Also why does it taste of oxidation. Process Vinter Noah: A case of grapes arrived from the far east. It was not white nor red, but rather 54;100;139 for the skin and 139;102;139 for the must. It did not take crushing kindly as opening of the skin gives tannin with too much attitude. The ferments on the skin was strong. So I let it be and carefully modified my methods. Master SulfDiox do you remember the day of the Pigeage? Master SulfDiox: Yes, as a matter of fact, I enjoyed punching the cap that day. Good work out. Maybe it tastes of Capsicum, from the Naga I found in Dorset. (fell out of my pocket?) Vinter Noah: It was then at near frozen and fire in an Pao Ferro barrel. The Pao Ferro has a snappier attack than rosewood, with good sustain, and its warmer than Ebony. Natural aroma and is fragrant compared than oak, with oily pores that breathes. I think it is here when malic turns lactic and OH becomes COOl-! In lab test, testing Brix and Volatility different batches was blended. All permutation was validated by receptors and mixture of the five bases. Acknowledgment 4 Where? In the case, east and west, goes and comes. Marquetry, stem must seed juice, but skins anticipate and leverage papyrus support both absorbent and delicate; pigment applied by rounds or flats, overlapping small glazes of pure colour, washes and glazes, backruns and pouring colour Parquetry, clavelin hoch amber, but inside residing tingly fruit flavour followed by a long sweet finish, treacly thick grape must hit and tartness well rounded, along with zesty piquant In the case, nature, terroir, amplifying. Harmony between the atmo, litho and hydrosphere, Rhythm of oblique incident sun rays, Progression of elements, labile Ni P and pH K Melody improvisation, exploration of the solution space. Home Gnocchi it is not lumped nor knotted momo is too big, and Kreplach is too thin not fried like mandu but some kind of Jiaozi and almost Xiaolongbao unraised and unleavened, smooth and translucent, rather than white and fluffy. albumin coagulates to gelatine and stock this is mine, sauce + dumpling, taste that reflect and echo in upside down me Thank You Prof. Mark Sandler Mike Patrick Emanuël, Mark and level 8 and Armin Dad Mom Ruth 5 Contents Abstract 2 Acknowledgment 3 Contents 5 Chapter 1. Introduction 8 1.1 Context . 8 1.1.1 Reverberation . 8 1.1.2 Application for Telecomunications and others . 9 1.2 Research Aim and Thesis Structure . 11 1.2.1 Research statement . 11 1.2.2 Thesis Structure . 11 1.3 Scope and Original Contributions . 12 Chapter 2. Review 14 2.1 Introduction . 14 Brief History of Reverb . 14 2.2 Physics of Reverberation . 16 2.2.1 Modal and Statistical Models . 17 2.2.2 Room Transfer Function . 18 2.2.3 Simulating Room Impulse Responses . 20 2.2.4 Implementation of Reverberators . 22 2.3 Subjective Listening Tests . 23 2.4 Perception of Reverberation . 25 2.4.1 Reverberance . 25 2.4.2 Spatial Perception . 26 2.4.3 Perceptual Effects of Early Echoes: Colouration . 27 2.4.4 Perceptual Effects of the Late Reverberation: Reverberation Tail . 28 2.5 Application . 28 2.5.1 Measurement . 28 2.5.2 Enhancement . 29 2.5.3 Recognition . 32 2.5.4 Evaluation . 33 2.6 Review Summary . 38 Chapter 3. Reverberation Modelling 39 3.1 Introduction . 39 Contents 6 3.2 Time-Frequency Room Model . 40 3.2.1 Frequency-Domain Statistical Room Model . 40 3.2.2 Time and Time-Frequency Domain Statistical Room Model . 41 3.2.3 Concept of Energy Decay Curve and Energy Decay Relief . 42 3.2.4 STFT Statistical Room Model . 43 3.2.5 Synthesis of STFT Room Model . 44 3.2.6 Comparison . 45 3.3 A novel signal based measurement . 48 3.4 Reverberation Decay Tail measure: RDT ....................... 50 3.4.1 Reverberation Tail Concept . 50 3.4.2 End-points and Flat Regions . 53 3.4.3 Results for RDT ................................ 54 3.5 Colouration measure: Rcol .............................. 57 3.5.1 Onsets Detection and Rcol formulation . 58 3.5.2 Experiments for Rcol ............................. 60 3.5.3 Results for Rcol ................................ 61 3.6 Perceptual Significance Experiments . 64 3.6.1 Perception of Reverberation (Tail) . 65 3.6.2 Colouration Space . 68 3.7 Summary . 75 Chapter 4. Blind Estimation 76 4.1 Introduction . 76 4.2 State of the art . 77 4.3 Methodology . 79 4.4 Statistical Decay Rate Modelling of Room Acoustics and Anechoic Speech . 80 4.4.1 Review of Statistical Speech Models . 81 4.4.2 Decay Rate . 82 4.4.3 Anechoic Speech . 83 4.4.4 Room Decay Rate . 84 4.5 Decay Rate of Reverberant Speech . 84 4.5.1 Convolution as Max Approximation . 85 4.5.2 EagleMax Distribution Formulation . 88 4.5.3 Empirical EagleMax Modelling . 90 4.6 Parameter Estimation from eagleMax distribution . 92 4.6.1 Exact Calculation . 94 4.6.2 Maximum Likelihood Estimation . 95 4.6.3 Statistical Features Mapping . 96 4.7 Mean Estimation Experiments . 98 4.7.1 A Priori Knowledge Uncertainty . 99 4.7.2 Order Selection and Fitting Range . 100 4.7.3 Non-Gaussianality . 101 4.7.4 Special Case with µH < 0 . 101 4.7.5 Batch Estimation . 102 4.8 Summary . 104 Chapter 5. Application 106 5.1 Introduction . 106 5.2 Methodology . 106 Contents 7 5.3 Acoustic Measurement . 107 5.3.1 Maximum Likelihood Estimation . 108 5.3.2 Statistical Features Mapping . 109 5.3.3 Implementation . 109 5.3.4 Decay Rate vs Reverberation Time vs Early Decay Time . 112 5.3.5 Experiments for Real RIRs and Real World Signals . 114 5.4 Speech Enhancement . 116 5.4.1 Review of Underlying Algorithm . 117 5.4.2 Experiments and Results . 117 5.5 Automatic Speech Recognition . 118 5.5.1 Review of Underlying Algorithms . 119 5.5.2 Combined Approach . 121 5.5.3 Blind Approach . 124 5.5.4 Variance Mask . 124 5.5.5 Experiments . 126 5.5.6 Summary for ASR . 131 5.6 Chapter Summary . 132 Chapter 6. Conclusion 133 6.1 Résumé . 133 6.2 Conclusion and Future Directions . 134 6.3 Publications ..