Grigoryan Brief Notes in Advanced DSP

Fourier Analysis with MATLAB
1. Auflage 2010
ISBN: 978-1-4398-0138-3
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 354 Seiten

Based on the authors’ research in Fourier analysis, Brief Notes in Advanced DSP: Fourier Analysis with MATLAB® addresses many concepts and applications of digital signal processing (DSP). The included MATLAB® codes illustrate how to apply the ideas in practice.

The book begins with the basic concept of the discrete Fourier transformation and its properties. It then describes lifting schemes, integer transformations, the discrete cosine transform, and the paired transform method for calculating the discrete Hadamard transform. The text also examines the decomposition of the 1D signal by so-called section basis signals as well as new forms of 2D signal/image representation and decomposition by direction signals/images. Focusing on Fourier transform wavelets and Givens–Haar transforms, the last chapter discusses the problem of signal multiresolution.

This book presents numerous interesting problems and concepts of unitary transformations, such as the Fourier, Hadamard, Hartley, Haar, paired, cosine, and new signal-induced transformations. It aids readers in using new forms and methods of signals and images in the frequency and frequency-and-time domains.

Autoren/Hrsg.

Grigoryan, Artyom M.

Grigoryan, Merughan

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Bildsignalverarbeitung
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Signalverarbeitung, Bildverarbeitung, Scanning
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Drahtlostechnologie

Inhaltsverzeichnis

Discrete Fourier Transform
Properties of the discrete Fourier transform
Fourier transform splitting
Fast Fourier transform
Codes for the paired FFT
Paired and Haar transforms
Integer Fourier Transform
Reversible integer Fourier transform
Lifting schemes for DFT
One-point integer transform
DFT in vector form
Roots of the unit
Codes for the block DFT
General elliptic Fourier transforms

Cosine Transform
Partitioning the DCT
Paired algorithm for the N-point DCT
Codes for the paired transform
Reversible integer DCT
Method of nonlinear equations
Canonical representation of the integer DCT

Hadamard Transform
The Walsh and Hadamard transform
Mixed Hadamard transformation
Generalized bit and transformations
T-decomposition of Hadamard matrices
Mixed Fourier transformations
Mixed transformations: continuous case

Paired Transform-Based Decomposition
Decomposition of 1D signals
2D paired representation

Fourier Transform and Multiresolution
Fourier transform
Representation by frequency-time wavelets
Time-frequency correlation analysis
Givens–Haar transformations
References
Index