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1.1. Steps in the initial auditory processing. 4 2 THE TIME-FREQUENCY ENERGY REPRESENTATION 2.1. Short-time spectrum of a steady-state Iii. 9 2.2. Smoothed short-time spectra. 9 2.3. Short-time spectra of linear chirps. 13 2.4. Short-time spectra of /w /'s. 15 2.5. Wide band spectrograms of /w /'s. 16 Spectrograms of rapid formant motion. 2.6. 17 2.7. Wigner distribution and spectrogram. 21 2.8. Wigner distribution and spectrogram of cos wot. 23 2.9. Concentration ellipses for transform kernels. 28 2.10. Concentration ellipses for complementary kernels. 42 42 2.11. Directional transforms for a linear chirp. 47 2.12. Spectrograms of /wioi/ with different window sizes. 2.13. Wigner distribution of /wioi/. 49 2.14. Time-frequency autocorrelation function of /wioi/. 49 2.15. Gaussian transform of Iwioi/. 50 2.16. Directional transforms of lwioi/. 52 3 TIME-FREQUENCY FILTERING 3.1. Recovering the transfer function by filtering. 57 3.2. Estimating 'aliased' transfer function. 61 3.3. T-F autocorrelation function of an impulse train. 70 3.4. T-F autocorrelation function of LTI filter output. 70 Windowing recovers transfer function. 3.5. 72 3.6. Shearing the time-frequency autocorrelation function. 75 3.7. T-F autocorrelation function for FM filter. 76 3.8. T-F autocorrelation function of FM filter output. 77 3.9. Windowing recovers transfer function. 79 4 THE SCHEMATIC SPECTROGRAM Problems with pole-fitting approach.
Communication & Signal Processing involving topics such as: Communications Theory and Techniques, Communications Protocols and Standards, Telecommunication Systems, Modulation and Signal Design, Coding Compression and Information Theory, Communication Networks, Wireless Communication, Optical Communication, Wireless Sensor Networks, MIMO Systems, MIMO Communications, Signal Processing for Communications e-Learning. Digital Signal Processing, Multiresolution Analysis, Wavelets, Smart Antennas, Adaptive Antennas, Theory and Practice of Signal Processing, Digital Signal Processing, Speech, Image, Video Signal Processing, Person Authentication, Biometry, Medical Imaging, Remote Sensing Analysis, Image Indexation, Image compression, Data Fusion and Pattern Recognition, Parallel Computing, Artificial Intelligence, Information Retrieval.
Because most real-world signals, including speech, sonar, communication, and biological signals, are non-stationary, traditional signal analysis tools such as Fourier transforms are of limited use because they do not provide easily accessible information about the localization of a given frequency component. A more suitable approach for those studying non-stationary signals is the use of time frequency representations that are functions of both time and frequency. Applications in Time-Frequency Signal Processing investigates the use of various time-frequency representations, such as the Wigner distribution and the spectrogram, in diverse application areas. Other books tend to focus on theoretical development. This book differs by highlighting particular applications of time-frequency representations and demonstrating how to use them. It also provides pseudo-code of the computational algorithms for these representations so that you can apply them to your own specific problems. Written by leaders in the field, this book offers the opportunity to learn from experts. Time-Frequency Representation (TFR) algorithms are simplified, enabling you to understand the complex theories behind TFRs and easily implement them. The numerous examples and figures, review of concepts, and extensive references allow for easy learning and application of the various time-frequency representations.
Presents a wide range of graphical representations of some speech signals and allows current speech analysis techniques to be assessed and directly compared. Describes time-frequency representations, auditory modeling, neural networks, pitch and multi-channel analysis. The study of over 40 different analyses of speech is represented in myriad images found throughout.
The concept of time and frequency representation of signals dates back to the first notation for music. From a mathematical viewpoint we can associate the time function to its Fourier transform. This book introduces a useful representation of signals simultaneously in time and frequency.
Understand the methods of modern non-stationary signal processing with authoritative insights from a leader in the field.
This work addresses two related questions. The first question is what joint time-frequency energy representations are most appropriate for auditory signals, in particular, for speech signals in sonorant regions. The quadratic transf for the representation: (1) shift-invariance, (2) positivity, (3) superposition, (4) locality, and (5) smoothness. The second question addressed is how to obtain a rich, symbolic description of the phonetically relevant features om these time-frequency energy surfaces, the so-called schematic spectrogram Time-frequency ridges, the 2-D analog of spectral peaks, are one feature that is proposed. If non-oriented kernels are used for the energy representation, then the ridge tops can be identified with zero-crossings in the inner project of the gradient vector and the direction of greatest downward curvature. If oriented kernels are used, the method can be generalized to give better orientation selectivity (e.g., intersecting ridges) at the cost of poorer time-frequency locality.
Because most real-world signals, including speech, sonar, communication, and biological signals, are non-stationary, traditional signal analysis tools such as Fourier transforms are of limited use because they do not provide easily accessible information about the localization of a given frequency component. A more suitable approach for those studying non-stationary signals is the use of time frequency representations that are functions of both time and frequency. Applications in Time-Frequency Signal Processing investigates the use of various time-frequency representations, such as the Wigner distribution and the spectrogram, in diverse application areas. Other books tend to focus on theoretical development. This book differs by highlighting particular applications of time-frequency representations and demonstrating how to use them. It also provides pseudo-code of the computational algorithms for these representations so that you can apply them to your own specific problems. Written by leaders in the field, this book offers the opportunity to learn from experts. Time-Frequency Representation (TFR) algorithms are simplified, enabling you to understand the complex theories behind TFRs and easily implement them. The numerous examples and figures, review of concepts, and extensive references allow for easy learning and application of the various time-frequency representations.
Featuring traditional coverage as well as new research results that, until now, have been scattered throughout the professional literature, this book brings together—in simple language—the basic ideas and methods that have been developed to study natural and man-made signals whose frequency content changes with time—e.g., speech, sonar and radar, optical images, mechanical vibrations, acoustic signals, biological/biomedical and geophysical signals. Covers time analysis, frequency analysis, and scale analysis; time-bandwidth relations; instantaneous frequency; densities and local quantities; the short time Fourier Transform; time-frequency analysis; the Wigner representation; time-frequency representations; computation methods; the synthesis problem; spatial-spatial/frequency representations; time-scale representations; operators; general joint representations; stochastic signals; and higher order time-frequency distributions. Illustrates each concept with examples and shows how the methods have been extended to other variables, such as scale. For engineers, acoustic scientists, medical scientists and developers, mathematicians, physicists, and mangers working in the fields of acoustics, sonar, radar, image processing, biomedical devices, communication.