... 67
5.3 NoiseReductionwithWavelets 68
5.3.1 WaveletTransformofaNoisyAudioSignal 68
5.3.2 Orthogonal WaveletTransform and Thresholding . . 69
5.3.3 Nonorthogonal WaveletTransform and Thresholding ... the construction of fast algorithms for
the analysis and synthesis with wavelets and even the definition ofwavelet bases. Finally, it allows a
review of the fast wavelettransformof Section 1.5 ... 152
Table of Contents
List of Figures xix
List of Tables xxii
Notation xxiii
0 Introduction 1
I Wavelet Theory and Practice 5
1 Wavelets 7
1.1 Introduction 7
1.2 Historic Outline . . 8
1.3 TheWaveletTransform...
... function to
Transforms
Fourier transformof :
Wavelet transformof with respect to :
Approximation of at the scale
Detail of at the scale
Misc
DCT Discrete cosine transform
WT Wavelet transform
Hz ... fundamentals of the wavelet theory: We discuss the time–frequency resolution
of the wavelettransform and compare it to the common short–time Fourier transform. The multiscale
property of the dyadic wavelet ... SAMPLING GRID OF THE WAVELETTRANSFORM 17
around is
The energy spread of a wavelet atom is thus centered at and of size along time and
along frequency. [Mal98]
The area of the Heisenberg box of uncertainty...
... between input and output of the forward transform is expressed as
Discrete Wavelet Transforms - A Compendium of New Approaches and Recent Applications4
Figure 13. Derivation of double non separable ... level of the standard
separable DWTs of JPEG 2000. It means that the finite word length problem peculiar to the
Discrete Wavelet Transforms - A Compendium of New Approaches and Recent Applications2 2
ulation ... 0.986
Table 1. Average PSNR and correlation of proposed method and Y. Wang method [8].
Discrete Wavelet Transforms - A Compendium of New Approaches and Recent Applications3 8
s
1
s
3
s
2
s
4
=
k ⋅s
1
0
0
(k...
... exist outside
the discrete series setting. In 1992, Mallat and Zhong [92] constructed a
transform related to the original continuous wavelet transform, called the
dyadic wavelet transform. Starting ... systematic construction ofwavelet transforms.
The book departs from a few basic realizations: Any wavelet transform
V
η
is a unitary equivalence between π and a subrepresentation of λ
G
,theleft
regular ... some
suitable subspace of L
2
(G). Indeed, in the case of the original wavelets arising
from the ax + b-group, the focus of interest is on the action of that group
on the real line by affine transformations,...
... F. Warshofsky, and the Editors of Time-Life Books,
Sound and Hearing, Life Science Library, Time-Life Books, Alexandria, VA, 1965, p.
173.
DRAFT of “Mathematics of the Discrete Fourier Transform ... the expected value of any
function f (v) of a random variable v is given by
E{f (v)}
∆
=
∞
−∞
f(x)p
v
(x)dx
DRAFT of “Mathematics of the Discrete Fourier Transform (DFT),” by J.O.
Smith, CCRMA, ... study a variety of practical spectrum analysis exam-
ples, using primarily Matlab to analyze and display signals and their
spectra.
DRAFT of “Mathematics of the Discrete Fourier Transform (DFT),”...
... pages
doi:10.1155/2010/191085
Research Article
Eigenvectors of the Discrete Fourier Transform Based on
the Bilinear Transform
Ahmet Serbes and Lutfiye Durak-Ata (EURASIP Member)
Department of Electronics and Communications ... orthonormal eigenvectors of the DFT matrix, which is closer to the samples of Hermite-Gaussian functions, is crucial
in the definition of the discrete fractional Fourier transform. In this work, ... aliasing in the discrete z-domain, it is appropriate to use it
in the discretization of the eigenfunctions of the Fourier transform. We obtain Hermite-Gaussian-like eigenvectors of the DFT
matrix....
... shape of the waveform being decomposed.
Chapter 8- The Discrete Fourier Transform 145
Type ofTransform Example Signal
Fourier Transform
Fourier Series
Discrete Time Fourier Transform
Discrete ... Digital Signal
Processing, such as: Fourier transform, Laplace transform, Z transform,
Hilbert transform, Discrete Cosine transform, etc. Just what is a transform?
To answer this question, remember ... French mathematician). Transforms are not limited to any specific
type or number of data. For example, you might have 100 samples of discrete
data for the input and 200 samples ofdiscrete data for...
... window,
but may also include any number of the zeros. This has the effect
169
CHAPTER
9
Applications of the DFT
The Discrete Fourier Transform (DFT) is one of the most important tools in Digital ... width of the peak) and spectral leakage (the
amplitude of the tails).
To explore the theoretical aspects of this in more detail, imagine an infinitely
long discrete sine wave at a frequency of 0.1 ... DFT of the
impulse response provides samples of this continuous curve. If youN/2 %1
make the DFT longer, the resolution improves, and you obtain a better idea of
Chapter 9- Applicationsof the...
... Theory and Applicationsof OFDM
Ahmad R. S. Bahai and Burton R. Saltzberg
Principles of Digital Transmission: With Wireless Applications
Sergio Benedetto and Ezio Biglieri
Simulation of Communication ... convolution of two signals of length
N is a sequence of length N so the inter-block interference issue is
resolved.
Proper windowing of OFDM blocks, as shown later, is important to
mitigate the effect of ... combination of transmit and receive
filters, is Nyquist, with the roll-off factor assumed to be less than 1.
Figure 1.7. OFDM modulation concept: Real and Imaginery components of
an OFDM symbol...
... Methods of the study 4
Part II: Development.
Chapter 1: Theoretical background.
I. An overview of English morpheme
I.1. Definition of Morpheme 5
I.2. Type of morpheme 6
II. An overview of Vietnamese ... different form of the same word
19
English morpheme system Luong Thuan & Kim Phuong
OUTLINE
Part I: Introduction.
1. Rationale (reasons of the study) 3
2. Aims of the study 3
3. Scope of the study ... system Luong Thuan & Kim Phuong
hội trưởng (president of association) đội trưởng (head of group)
nhóm trưởng (head of group) tổ trưởng (head of small
group)
Many morphemes in this type may be...
... converted into a finite set. The next step of encoding maps the
finite set ofdiscrete time, continuous amplitude signals into a finite set ofdiscrete time, discrete
amplitude signals.
A signal x(n) ... If the range
of x(t) is the set of integers Z, then x(t) is said to be a continuous time, discrete amplitude signal. In
contrast, a discrete time signal x(n) has Z as its domain. A discrete time, ... R as its range. A discrete time, discrete amplitude signal has Z as its range. Here, the focus is
on discrete time signals. Quantization is the process of approximating any discrete time, continuous
amplitude...