Time-frequency Representation of Musical Signals Using the Discrete Hermite Transform

Time-frequency Representation of Musical Signals Using the Discrete Hermite Transform
Author: Jacob Joseph Trombetta
Publisher:
Total Pages: 83
Release: 2011
Genre: Electrical engineering
ISBN:
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Time-frequency representations of musical signals help with the visualization and understanding of the building blocks of music. Difficulties with different representations limit the amount of information that can be extracted from the signal processing techniques used. The discrete Hermite transform has already proven to be an excellent choice in biomedical signal processing applications. We will show that the discrete Hermite transfrom is an excellent choice for the analysis of musical signals as well. The discrete Hermite basis functions are approximately sinusoidal with shorter function supports than the Fourier techniques. This gives them better frequency resolution than both classic Fourier transforms and current wavelet transforms for musical signals. We will show that the discrete Hermite transform and the time-frequency display it produces, the Hermitian distribution, will be an invaluable resource to the sign processing community.

Landscapes of Time-Frequency Analysis

Landscapes of Time-Frequency Analysis
Author: Paolo Boggiatto
Publisher: Springer
Total Pages: 358
Release: 2019-01-30
Genre: Mathematics
ISBN: 3030052109
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The chapters in this volume are based on talks given at the inaugural Aspects of Time-Frequency Analysis conference held in Turin, Italy from July 5-7, 2017, which brought together experts in harmonic analysis and its applications. New connections between different but related areas were presented in the context of time-frequency analysis, encouraging future research and collaborations. Some of the topics covered include: Abstract harmonic analysis, Numerical harmonic analysis, Sampling theory, Compressed sensing, Mathematical signal processing, Pseudodifferential operators, and Applications of harmonic analysis to quantum mechanics. Landscapes of Time-Frequency Analysis will be of particular interest to researchers and advanced students working in time-frequency analysis and other related areas of harmonic analysis.

Foundations of Time-Frequency Analysis

Foundations of Time-Frequency Analysis
Author: Karlheinz Gröchenig
Publisher: Springer Science & Business Media
Total Pages: 367
Release: 2013-12-01
Genre: Technology & Engineering
ISBN: 1461200032
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Time-frequency analysis is a modern branch of harmonic analysis. It com prises all those parts of mathematics and its applications that use the struc ture of translations and modulations (or time-frequency shifts) for the anal ysis of functions and operators. Time-frequency analysis is a form of local Fourier analysis that treats time and frequency simultaneously and sym metrically. My goal is a systematic exposition of the foundations of time-frequency analysis, whence the title of the book. The topics range from the elemen tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita tive methods in time-frequency analysis and the theory of pseudodifferential operators. This book is motivated by applications in signal analysis and quantum mechanics, but it is not about these applications. The main ori entation is toward the detailed mathematical investigation of the rich and elegant structures underlying time-frequency analysis. Time-frequency analysis originates in the early development of quantum mechanics by H. Weyl, E. Wigner, and J. von Neumann around 1930, and in the theoretical foundation of information theory and signal analysis by D.

Music Demixing with the Sliced Constant-Q Transform

Music Demixing with the Sliced Constant-Q Transform
Author: Sevag Hanssian
Publisher:
Total Pages: 0
Release: 2022
Genre:
ISBN:
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"Music source separation is the task of extracting an estimate of one or more isolated sources or instruments (for example, drums or vocals) from musical audio. The task of music demixing or unmixing considers the case where the musical audio is separated into an estimate of all of its constituent sources that can be summed back to the original mixture. Models for music demixing that use the Short-Time Fourier Transform (STFT) as their representation of music signals are popular and have achieved success in recent years. However, the fixed time-frequency resolution of the STFT, arising from the time-frequency uncertainty principle, requires a tradeoff in time-frequency resolution that can significantly affect music demixing results. The sliced Constant-Q Transform (sliCQT) is a time-frequency transform with varying time-frequency resolution that avoids the time-frequency tradeoff of the STFT. The model proposed by this thesis replaces the STFT with the sliCQT in a recent model for music demixing, to investigate the impact on the results"--

Biosignal Processing and Classification Using Computational Learning and Intelligence

Biosignal Processing and Classification Using Computational Learning and Intelligence
Author: Alejandro A. Torres-García
Publisher: Academic Press
Total Pages: 538
Release: 2021-09-18
Genre: Science
ISBN: 0128204281
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Biosignal Processing and Classification Using Computational Learning and Intelligence: Principles, Algorithms and Applications posits an approach for biosignal processing and classification using computational learning and intelligence, highlighting that the term biosignal refers to all kinds of signals that can be continuously measured and monitored in living beings. The book is composed of five relevant parts. Part One is an introduction to biosignals and Part Two describes the relevant techniques for biosignal processing, feature extraction and feature selection/dimensionality reduction. Part Three presents the fundamentals of computational learning (machine learning). Then, the main techniques of computational intelligence are described in Part Four. The authors focus primarily on the explanation of the most used methods in the last part of this book, which is the most extensive portion of the book. This part consists of a recapitulation of the newest applications and reviews in which these techniques have been successfully applied to the biosignals’ domain, including EEG-based Brain-Computer Interfaces (BCI) focused on P300 and Imagined Speech, emotion recognition from voice and video, leukemia recognition, infant cry recognition, EEGbased ADHD identification among others. Provides coverage of the fundamentals of signal processing, including sensing the heart, sending the brain, sensing human acoustic, and sensing other organs Includes coverage biosignal pre-processing techniques such as filtering, artifiact removal, and feature extraction techniques such as Fourier transform, wavelet transform, and MFCC Covers the latest techniques in machine learning and computational intelligence, including Supervised Learning, common classifiers, feature selection, dimensionality reduction, fuzzy logic, neural networks, Deep Learning, bio-inspired algorithms, and Hybrid Systems Written by engineers to help engineers, computer scientists, researchers, and clinicians understand the technology and applications of computational learning to biosignal processing

Foundations of Signal Processing

Foundations of Signal Processing
Author: Martin Vetterli
Publisher: Cambridge University Press
Total Pages: 745
Release: 2014-09-04
Genre: Technology & Engineering
ISBN: 1139916572
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This comprehensive and engaging textbook introduces the basic principles and techniques of signal processing, from the fundamental ideas of signals and systems theory to real-world applications. Students are introduced to the powerful foundations of modern signal processing, including the basic geometry of Hilbert space, the mathematics of Fourier transforms, and essentials of sampling, interpolation, approximation and compression The authors discuss real-world issues and hurdles to using these tools, and ways of adapting them to overcome problems of finiteness and localization, the limitations of uncertainty, and computational costs. It includes over 160 homework problems and over 220 worked examples, specifically designed to test and expand students' understanding of the fundamentals of signal processing, and is accompanied by extensive online materials designed to aid learning, including Mathematica® resources and interactive demonstrations.

The Analytical Theory of Heat

The Analytical Theory of Heat
Author: Jean-Baptiste-Joseph Fourier
Publisher:
Total Pages: 534
Release: 1878
Genre: Heat
ISBN:
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Advanced Digital Signal Processing and Noise Reduction

Advanced Digital Signal Processing and Noise Reduction
Author: Saeed V. Vaseghi
Publisher: John Wiley & Sons
Total Pages: 544
Release: 2008-12-23
Genre: Science
ISBN: 0470740167
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Digital signal processing plays a central role in the development of modern communication and information processing systems. The theory and application of signal processing is concerned with the identification, modelling and utilisation of patterns and structures in a signal process. The observation signals are often distorted, incomplete and noisy and therefore noise reduction, the removal of channel distortion, and replacement of lost samples are important parts of a signal processing system. The fourth edition of Advanced Digital Signal Processing and Noise Reduction updates and extends the chapters in the previous edition and includes two new chapters on MIMO systems, Correlation and Eigen analysis and independent component analysis. The wide range of topics covered in this book include Wiener filters, echo cancellation, channel equalisation, spectral estimation, detection and removal of impulsive and transient noise, interpolation of missing data segments, speech enhancement and noise/interference in mobile communication environments. This book provides a coherent and structured presentation of the theory and applications of statistical signal processing and noise reduction methods. Two new chapters on MIMO systems, correlation and Eigen analysis and independent component analysis Comprehensive coverage of advanced digital signal processing and noise reduction methods for communication and information processing systems Examples and applications in signal and information extraction from noisy data Comprehensive but accessible coverage of signal processing theory including probability models, Bayesian inference, hidden Markov models, adaptive filters and Linear prediction models Advanced Digital Signal Processing and Noise Reduction is an invaluable text for postgraduates, senior undergraduates and researchers in the fields of digital signal processing, telecommunications and statistical data analysis. It will also be of interest to professional engineers in telecommunications and audio and signal processing industries and network planners and implementers in mobile and wireless communication communities.

Mathematics of the Discrete Fourier Transform (DFT)

Mathematics of the Discrete Fourier Transform (DFT)
Author: Julius O. Smith
Publisher: Julius Smith
Total Pages: 323
Release: 2008
Genre: Fourier transformations
ISBN: 097456074X
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"The DFT can be understood as a numerical approximation to the Fourier transform. However, the DFT has its own exact Fourier theory, and that is the focus of this book. The DFT is normally encountered as the Fast Fourier Transform (FFT)--a high-speed algorithm for computing the DFT. The FFT is used extensively in a wide range of digital signal processing applications, including spectrum analysis, high-speed convolution (linear filtering), filter banks, signal detection and estimation, system identification, audio compression (such as MPEG-II AAC), spectral modeling sound synthesis, and many others. In this book, certain topics in digital audio signal processing are introduced as example applications of the DFT"--Back cover