Spectral flatness

About: Spectral flatness is a research topic. Over the lifetime, 292 publications have been published within this topic receiving 7030 citations. The topic is also known as: tonality coefficient & Wiener entropy.

Linear Prediction of Speech

Abstract: 1. Introduction.- 1.1 Basic Physical Principles.- 1.2 Acoustical Waveform Examples.- 1.3 Speech Analysis and Synthesis Models.- 1.4 The Linear Prediction Model.- 1.5 Organization of Book.- 2. Formulations.- 2.1 Historical Perspective.- 2.2 Maximum Likelihood.- 2.3 Minimum Variance.- 2.4 Prony's Method.- 2.5 Correlation Matching.- 2.6 PARCOR (Partial Correlation).- 2.6.1 Inner Products and an Orthogonality Principle.- 2.6.2 The PARCOR Lattice Structure.- 3. Solutions and Properties.- 3.1 Introduction.- 3.2 Vector Spaces and Inner Products.- 3.2.1 Filter or Polynomial Norms.- 3.2.2 Properties of Inner Products.- 3.2.3 Orthogonality Relations.- 3.3 Solution Algorithms.- 3.3.1 Correlation Matrix.- 3.3.2 Initialization.- 3.3.3 Gram-Schmidt Orthogonalization.- 3.3.4 Levinson Recursion.- 3.3.5 Updating Am(z).- 3.3.6 A Test Example.- 3.4 Matrix Forms.- 4. Acoustic Tube Modeling.- 4.1 Introduction.- 4.2 Acoustic Tube Derivation.- 4.2.1 Single Section Derivation.- 4.2.2 Continuity Conditions.- 4.2.3 Boundary Conditions.- 4.3 Relationship between Acoustic Tube and Linear Prediction.- 4.4 An Algorithm, Examples, and Evaluation.- 4.4.1 An Algorithm.- 4.4.2 Examples.- 4.4.3 Evaluation of the Procedure.- 4.5 Estimation of Lip Impedance.- 4.5.1 Lip Impedance Derivation.- 4.6 Further Topics.- 4.6.1 Losses in the Acoustic Tube Model.- 4.6.2 Acoustic Tube Stability.- 5. Speech Synthesis Structures.- 5.1 Introduction.- 5.2 Stability.- 5.2.1 Step-up Procedure.- 5.2.2 Step-down Procedure.- 5.2.3 Polynomial Properties.- 5.2.4 A Bound on |Fm(z)|.- 5.2.5 Necessary and Sufficient Stability Conditions.- 5.2.6 Application of Results.- 5.3 Recursive Parameter Evaluation.- 5.3.1 Inner Product Properties.- 5.3.2 Equation Summary with Program.- 5.4 A General Synthesis Structure.- 5.5 Specific Speech Synthesis Structures.- 5.5.1 The Direct Form.- 5.5.2 Two-Multiplier Lattice Model.- 5.5.3 Kelly-Lochbaum Model.- 5.5.4 One-Multiplier Models.- 5.5.5 Normalized Filter Model.- 5.5.6 A Test Example.- 6. Spectral Analysis.- 6.1 Introduction.- 6.2 Spectral Properties.- 6.2.1 Zero Mean All-Pole Model.- 6.2.2 Gain Factor for Spectral Matching.- 6.2.3 Limiting Spectral Match.- 6.2.4 Non-uniform Spectral Weighting.- 6.2.5 Minimax Spectral Matching.- 6.3 A Spectral Flatness Model.- 6.3.1 A Spectral Flatness Measure.- 6.3.2 Spectral Flatness Transformations.- 6.3.3 Numerical Evaluation.- 6.3.4 Experimental Results.- 6.3.5 Driving Function Models.- 6.4 Selective Linear Prediction.- 6.4.1 Selective Linear Prediction (SLP) Algorithm.- 6.4.2 A Selective Linear Prediction Program.- 6.4.3 Computational Considerations.- 6.5 Considerations in Choice of Analysis Conditions.- 6.5.1 Choice of Method.- 6.5.2 Sampling Rates.- 6.5.3 Order of Filter.- 6.5.4 Choice of Analysis Interval.- 6.5.5 Windowing.- 6.5.6 Pre-emphasis.- 6.6 Spectral Evaluation Techniques.- 6.7 Pole Enhancement.- 7. Automatic Formant Trajectory Estimation.- 7.1 Introduction.- 7.2 Formant Trajectory Estimation Procedure.- 7.2.1 Introduction.- 7.2.2 Raw Data from A(z).- 7.2.3 Examples of Raw Data.- 7.3 Comparison of Raw Data from Linear Prediction and Cepstral Smoothing.- 7.4 Algorithm 1.- 7.5 Algorithm 2.- 7.5.1 Definition of Anchor Points.- 7.5.2 Processing of Each Voiced Segment.- 7.5.3 Final Smoothing.- 7.5.4 Results and Discussion.- 7.6 Formant Estimation Accuracy.- 7.6.1 An Example of Synthetic Speech Analysis.- 7.6.2 An Example of Real Speech Analysis.- 7.6.3 Influence of Voice Periodicity.- 8. Fundamental Frequency Estimation.- 8.1 Introduction.- 8.2 Preprocessing by Spectral Flattening.- 8.2.1 Analysis of Voiced Speech with Spectral Regularity.- 8.2.2 Analysis of Voiced Speech with Spectral Irregularities.- 8.2.3 The STREAK Algorithm.- 8.3 Correlation Techniques.- 8.3.1 Autocorrelation Analysis.- 8.3.2 Modified Autocorrelation Analysis.- 8.3.3 Filtered Error Signal Autocorrelation Analysis.- 8.3.4 Practical Considerations.- 8.3.5 The SIFT Algorithm.- 9. Computational Considerations in Analysis.- 9.1 Introduction.- 9.2 Ill-Conditioning.- 9.2.1 A Measure of Ill-Conditioning.- 9.2.2 Pre-emphasis of Speech Data.- 9.2.3 Prefiltering before Sampling.- 9.3 Implementing Linear Prediction Analysis.- 9.3.1 Autocorrelation Method.- 9.3.2 Covariance Method.- 9.3.3 Computational Comparison.- 9.4 Finite Word Length Considerations.- 9.4.1 Finite Word Length Coefficient Computation.- 9.4.2 Finite Word Length Solution of Equations.- 9.4.3 Overall Finite Word Length Implementation.- 10. Vocoders.- 10.1 Introduction.- 10.2 Techniques.- 10.2.1 Coefficient Transformations.- 10.2.2 Encoding and Decoding.- 10.2.3 Variable Frame Rate Transmission.- 10.2.4 Excitation and Synthesis Gain Matching.- 10.2.5 A Linear Prediction Synthesizer Program.- 10.3 Low Bit Rate Pitch Excited Vocoders.- 10.3.1 Maximum Likelihood and PARCOR Vocoders.- 10.3.2 Autocorrelation Method Vocoders.- 10.3.3 Covariance Method Vocoders.- 10.4 Base-Band Excited Vocoders.- 11. Further Topics.- 11.1 Speaker Identification and Verification.- 11.2 Isolated Word Recognition.- 11.3 Acoustical Detection of Laryngeal Pathology.- 11.4 Pole-Zero Estimation.- 11.5 Summary and Future Directions.- References.

Generation of very flat optical frequency combs from continuous-wave lasers using cascaded intensity and phase modulators driven by tailored radio frequency waveforms

Abstract: We demonstrate a scheme based on a cascade of lithium niobate intensity and phase modulators driven by specially tailored RF waveforms to generate an optical frequency comb with very high spectral flatness. In this Letter, we demonstrate a 10 GHz comb with 38 comb lines within a spectral power variation below 1 dB. The number of comb lines that can be generated is limited by the power handling capability of the phase modulator, and this can be scaled without compromising the spectral flatness. Furthermore, the spectral phase of the generated combs in our scheme is almost purely quadratic, which, as we will demonstrate, allows for high-quality pulse compression using only single-mode fiber.

Asymptotic formalism for ultraflat optical frequency comb generation using a Mach-Zehnder modulator.

Abstract: We theoretically prove that a conventional Mach-Zehnder modulator can generate an optical frequency comb with excellent spectral flatness. The modulator is asymmetrically dual driven by large amplitude sinusoidal signals with different amplitudes. The driving condition to obtain spectral flatness is analytically derived and optimized, yielding a simple formula. This formula also predicts the conversion efficiency and bandwidth of the generated frequency comb.

Generation of very flat optical frequency combs from continuous-wave lasers using cascaded intensity and phase modulators driven by tailored radio frequency waveforms

Abstract: We demonstrate a scheme, based on a cascade of lithium niobate intensity and phase modulators driven by specially tailored radio frequency waveforms to generate an optical frequency comb with very high spectral flatness. In this work we demonstrate a 10 GHz comb with ~40 lines with spectral power variation below 1-dB and ~60 lines in total. The number of lines that can be generated is limited by the power handling capability of the phase modulator, and this can be scaled without compromising the spectral flatness. Furthermore, the spectral phase of the generated combs in our scheme is almost purely quadratic which, as we will demonstrate, allows for very high quality pulse compression using only single mode fiber.

The Theory of Linear Prediction

Abstract: Linear prediction theory has had a profound impact in the field of digital signal processing. Although the theory dates back to the early 1940s, its influence can still be seen in applications today. The theory is based on very elegant mathematics and leads to many beautiful insights into statistical signal processing. Although prediction is only a part of the more general topics of linear estimation, filtering, and smoothing, this book focuses on linear prediction. This has enabled detailed discussion of a number of issues that are normally not found in texts. For example, the theory of vector linear prediction is explained in considerable detail and so is the theory of line spectral processes. This focus and its small size make the book different from many excellent texts which cover the topic, including a few that are actually dedicated to linear prediction. There are several examples and computer-based demonstrations of the theory. Applications are mentioned wherever appropriate, ut the focus is not on the detailed development of these applications. The writing style is meant to be suitable for self-study as well as for classroom use at the senior and first-year graduate levels. The text is self-contained for readers with introductory exposure to signal processing, random processes, and the theory of matrices, and a historical perspective and detailed outline are given in the first chapter. Table of Contents: Introduction / The Optimal Linear Prediction Problem / Levinson's Recursion / Lattice Structures for Linear Prediction / Autoregressive Modeling / Prediction Error Bound and Spectral Flatness / Line Spectral Processes / Linear Prediction Theory for Vector Processes / Appendix A: Linear Estimation of Random Variables / B: Proof of a Property of Autocorrelations / C: Stability of the Inverse Filter / Recursion Satisfied by AR Autocorrelations