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Mathematical technique used in data compression and analysis
a formal, mathematical definition of an orthonormal wavelet and of the integral wavelet transform. A function ψ ∈ L 2 ( R ) {\displaystyle \psi \,\in
Wavelet_transform
Transform in numerical harmonic analysis
a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage
Discrete_wavelet_transform
The complex wavelet transform (CWT) is a complex-valued extension to the standard discrete wavelet transform (DWT). It is a two-dimensional wavelet transform
Complex_wavelet_transform
Integral transform
In mathematics, the continuous wavelet transform (CWT) is a formal (i.e., non-numerical) tool that provides an overcomplete representation of a signal
Continuous_wavelet_transform
Function for integral Fourier-like transform
Spline wavelet Strömberg wavelet Complex Mexican hat wavelet fbsp wavelet Morlet wavelet Shannon wavelet Modified Morlet wavelet Chirplet transform Hermite
Wavelet
Prediction of digital video quality
c_{x}} is the complex wavelet transform of the signal x {\displaystyle x} and c y {\displaystyle c_{y}} is the complex wavelet transform for the signal
Structural similarity index measure
Structural_similarity_index_measure
(BQMF) Fast wavelet transform (FWT) Complex wavelet transform Non or undecimated wavelet transform, the downsampling is omitted Newland transform, an orthonormal
List of wavelet-related transforms
List_of_wavelet-related_transforms
Gaussian-windowed wavelet
Morlet wavelet (or Gabor wavelet) is a wavelet composed of a complex exponential (carrier) multiplied by a Gaussian window (envelope). This wavelet is closely
Morlet_wavelet
mathematics of signal processing, the harmonic wavelet transform, introduced by David Edward Newland in 1993, is a wavelet-based linear transformation of a given
Harmonic_wavelet_transform
Mathematical algorithm
The fast wavelet transform is a mathematical algorithm designed to turn a waveform or signal in the time domain into a sequence of coefficients based
Fast_wavelet_transform
Orthogonal wavelets
The Daubechies wavelets, based on the work of Ingrid Daubechies, are a family of orthogonal wavelets defining a discrete wavelet transform and characterized
Daubechies_wavelet
of wavelet transform called Complex wavelet transform (CWT) was developed. Similar to the 1-D complex wavelet transform, tensor products of complex wavelets
Wavelet for multidimensional signals analysis
Wavelet_for_multidimensional_signals_analysis
(SB-TS), also called wavelet packet decomposition (WPD; sometimes known as just wavelet packets or subband tree), is a wavelet transform where the discrete-time
Wavelet_packet_decomposition
First known wavelet basis
mathematics, the Haar wavelet is a sequence of rescaled "square-shaped" functions which together form a wavelet family or basis. Wavelet analysis is similar
Haar_wavelet
Discrete Fourier transform algorithm
"Fast approximate Fourier transform via wavelets transform". In Unser, Michael A.; Aldroubi, Akram; Laine, Andrew F. (eds.). Wavelet Applications in Signal
Fast_Fourier_transform
Functions used by the continuous wavelet transform
In numerical analysis, continuous wavelets are functions used by the continuous wavelet transform. These functions are defined as analytical expressions
Continuous_wavelet
Function used in signal processing
Gabor wavelets are wavelets invented by Dennis Gabor using complex functions constructed to serve as a basis for Fourier transforms in information theory
Gabor_wavelet
Topics referred to by the same term
wire tag, an animal tagging device Complex wavelet transform, an extension to the standard discrete wavelet transform used in image processing Constant
CWT
Short-time Fourier transform with variable resolution
Fourier transform and very closely related to the complex Morlet wavelet transform. Its design is suited for musical representation. The transform can be
Constant-Q_transform
be either of real or complex type. Shannon wavelet is not well-localized (noncompact) in the time domain, but its Fourier transform is band-limited (compact
Shannon_wavelet
Time-frequency transform in geophysics
is a generalization of the short-time Fourier transform (STFT), extending the continuous wavelet transform and overcoming some of its disadvantages. For
S_transform
Function in discrete mathematics
discrete wavelet transform with the discrete Fourier transform. Companion matrix DFT matrix Fast Fourier transform FFTPACK Fastest Fourier Transform in the
Discrete_Fourier_transform
Special case of the short-time Fourier transform
further details. Gabor filter Gabor wavelet Gabor atom Time-frequency representation S transform Short-time Fourier transform Wigner distribution function E
Gabor_transform
Method for detecting a signal's fractal dimension
The wavelet transform modulus maxima (WTMM) is a method for detecting the fractal dimension of a signal. More than this, the WTMM is capable of partitioning
Wavelet transform modulus maxima method
Wavelet_transform_modulus_maxima_method
wavelet transform, expand the signal in terms of wavelet functions which are localised in both time and frequency. Thus the wavelet transform of a signal
Time–frequency_representation
Mathematical transform that expresses a function of time as a function of frequency
the transform is a complex valued function of frequency. The term Fourier transform refers to both the mathematical operation and to this complex-valued
Fourier_transform
Types of wavelets
different wavelets are known by the name Poisson wavelet. In one context, the term "Poisson wavelet" is used to denote a family of wavelets labeled by
Poisson_wavelet
Continuous wavelets
In mathematics, Cauchy wavelets are a family of continuous wavelets, used in the continuous wavelet transform. The Cauchy wavelet of order p {\displaystyle
Cauchy_wavelet
mathematics, the complex Mexican hat wavelet is a low-oscillation, complex-valued, wavelet for the continuous wavelet transform. This wavelet is formulated
Complex_Mexican_hat_wavelet
Branch of mathematics
in wavelet transforms and chirplet transforms, with the wavelet analog of the (continuous) Fourier transform being the continuous wavelet transform. The
Fourier_analysis
Fourier-related transform for signals that change over time
transforms: Cone-shape distribution function Constant-Q transform Fractional Fourier transform Gabor transform Newland transform S transform Wavelet transform
Short-time_Fourier_transform
Multiresolution Fourier Transform is an integral fourier transform that represents a specific wavelet-like transform with a fully scalable modulated window
Multiresolution Fourier transform
Multiresolution_Fourier_transform
Number with a real and an imaginary part
control theory, systems are often transformed from the time domain to the complex frequency domain using the Laplace transform. The system's zeros and poles
Complex_number
Signal representation
Reciprocal space Short-time Fourier transform Time–frequency representation Time–frequency analysis Wavelet Wavelet transform – digital image processing, signal
Frequency_domain
transforms. Integral transform Wavelet transform Fourier-transform spectroscopy Harmonic analysis List of transforms List of mathematic operators Bispectrum
List of Fourier-related transforms
List_of_Fourier-related_transforms
Mathematical signal manipulation by computers
analysis, a discrete wavelet transform is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage
Digital_signal_processing
wavelet Haar wavelet Morlet wavelet Mexican hat wavelet Complex Mexican hat wavelet Hermitian wavelet Discrete wavelet transform Continuous wavelet Continuous
List of functional analysis topics
List_of_functional_analysis_topics
applied mathematics, fbsp wavelets are frequency B-spline wavelets. These frequency B-spline wavelets are complex wavelets whose spectrum are spline.
Fbsp_wavelet
Image compression standard and coding system
(created in 1992), which is based on a discrete cosine transform (DCT), with a newly designed, wavelet-based method. The standardized filename extension is
JPEG_2000
Method of detecting shapes within images
in C. scikit-image Hough-transform for line, circle and ellipse, implemented in Python. [1] Hough transform based on wavelet filtering, to detect a circle
Hough_transform
Gabor filter was modified by Morlet to form an orthonormal continuous wavelet transform. Although the Gabor filter achieves a sense of optimality in terms
Log_Gabor_filter
Signal analysis tool
can be compared with other analysis methods such as Fourier transform and Wavelet transform. Using the EMD method, any complicated data set can be decomposed
Hilbert–Huang_transform
Visual representation of the spectrum of frequencies of a signal as it varies with time
optical spectrometer, a bank of band-pass filters, by Fourier transform or by a wavelet transform (in which case it is also known as a scaleogram or scalogram)
Spectrogram
Technique used in signal processing and data compression
this product is added to the final image. Discrete wavelet transform JPEG - Discrete cosine transform - Contains a potentially easier to understand example
Discrete_cosine_transform
Compact encoding of digital data
cosine transform Discrete sine transform Discrete wavelet transform Embedded zerotrees of wavelet transforms Fractal compression Lapped transform Line spectral
Data_compression
Feature detection algorithm in computer vision
The scale-invariant feature transform (SIFT) is a computer vision algorithm to detect, describe, and match local features in images, invented by David
Scale-invariant feature transform
Scale-invariant_feature_transform
Polynomial sequence
sequence. The polynomials arise in: signal processing as Hermitian wavelets for wavelet transform analysis probability, such as the Edgeworth series, as well
Hermite_polynomials
Integral transform
"Linear Canonical Transforms: Theory and Applications", Springer, New York 2016. J.J. Ding, "Time–frequency analysis and wavelet transform course note", the
Linear canonical transformation
Linear_canonical_transformation
Linear filter used for texture analysis
cos θ + y * sin θ y' = -x * sin θ + y * cos θ i = 0 :+ 1 Gabor transform Gabor wavelet Gabor atom Log Gabor filter Gabor, D. (1946). "Theory of communication"
Gabor_filter
Signal analysis to extract information from electroencephalography (EEG) data
less complex equipment compared to conventional frequency analysis. Time-frequency analysis is typically performed using the Wavelet Transform (WT),
EEG_analysis
Subfield of control engineering
utilizing methods like spectral analysis, wavelet analysis, wavelet transform, short term Fourier transform, Gabor Expansion, Wigner-Ville distribution
Fault_detection_and_isolation
Method of data analysis
analysis, visualization and data preprocessing. The data are linearly transformed onto a new coordinate system such that the directions (principal components)
Principal_component_analysis
data, or a seismogram, may be considered as a convolution of the source wavelet, the reflectivity and noise. Its deconvolution is usually implemented as
Multidimensional seismic data processing
Multidimensional_seismic_data_processing
Method of encoding digital data on multiple carrier frequencies
research, a wavelet transform is introduced to replace the DFT as the method of creating orthogonal frequencies. This is due to the advantages wavelets offer
Orthogonal frequency-division multiplexing
Orthogonal_frequency-division_multiplexing
Method of encoding digital data on multiple carrier frequencies
can consider Wavelet N-OFDM. N-OFDM has become a technique for power-line communications (PLC). In this area of research, a wavelet transform is introduced
Non-orthogonal frequency-division multiplexing
Non-orthogonal_frequency-division_multiplexing
Integral expressing the amount of overlap of one function as it is shifted over another
"Reducing the Computational Complexity of Image Processing Using Wavelet Transform Based on the Winograd Method". Pattern Recognition and Image Analysis
Convolution
Type of artificial neural network
networks, fuzzy inference networks, complex neural networks, wavelet networks, Fourier transform, Laplacian transform, etc. Due to its different learning
Extreme_learning_machine
Type of image noise
dealing with speckle to a known tractable case. Recently, the use of wavelet transform has led to significant advances in image analysis. The main reason
Speckle_(interference)
Type of data compression
VC-1 Wavelet compression Motion JPEG 2000 Dirac Sorenson video codec Modified discrete cosine transform (MDCT) Dolby Digital (AC-3) Adaptive Transform Acoustic
Lossy_compression
sensors and development of the FPGA system for QRS complex detection based on Integer Wavelet Transform. Stojanović's professional activities include the
Radovan_Stojanović
Techniques and methods in signal processing
time–frequency distributions, such as: Short-time Fourier transform (including the Gabor transform), Wavelet transform, Bilinear time–frequency distribution function
Time–frequency_analysis
Sequence of data points over time
techniques: Fast Fourier transform Continuous wavelet transform Short-time Fourier transform Chirplet transform Fractional Fourier transform Chaotic analysis
Time_series
Combining multiple images to create one
transform and the premier ones, discrete wavelet transform, shift-invariant wavelet transform (SIDWT), and discrete cosine harmonic wavelet transform
Multi-focus_image_fusion
Mathematical transform
(2017-08-29). "Graph Fourier Transform" (PDF). Hammond, David K.; Vandergheynst, Pierre; Gribonval, Rémi (2011-03-01). "Wavelets on graphs via spectral graph
Graph_Fourier_transform
Mathematical function, inverse of an exponential function
York: John Wiley & Sons, p. 98, ISBN 978-0-470-31983-3 Chui, C.K. (1997), Wavelets: a mathematical tool for signal processing, SIAM monographs on mathematical
Logarithm
Digital video coder/decoder
encoding process. The most popular encoding transform is the 8x8 DCT. Codecs that make use of a wavelet transform are also entering the market, especially
Video_codec
Type of artificial neural network architecture
Motor Imagery Electroencephalogram Classification Based on Adaptive Wavelet Transform Kolmogorov–Arnold Networks". IEEE Transactions on Consumer Electronics
Kolmogorov–Arnold_Networks
Variation in the time intervals between heartbeats
which is based on the Hilbert transform of the RR data. A newly used HRV index,[citation needed] which depends on the wavelet entropy measures, is an alternative
Heart_rate_variability
Type of vector space in math
Bachman, George; Narici, Lawrence; Beckenstein, Edward (2000), Fourier and wavelet analysis, Universitext, Berlin, New York: Springer-Verlag, ISBN 978-0-387-98899-3
Hilbert_space
Study of classical optics using Fourier transforms
optics. To put it in a slightly complex way, similar to the concept of frequency and time used in traditional Fourier transform theory, Fourier optics makes
Fourier_optics
Theory of stochastic processes
a complex of statistical variables into principal components". Journal of Educational Psychology. 24 (6): 417–441. doi:10.1037/h0071325. A wavelet tour
Kosambi–Karhunen–Loève theorem
Kosambi–Karhunen–Loève_theorem
Weiss, Guido (1996). A First Course on Wavelets. CRC Press. ISBN 978-0-8493-8274-1. Mallat, Stéphane (2008), A Wavelet Tour of Signal Processing: The Sparse
Riesz_sequence
Measure of covariance of components of a random vector
called principal component analysis (PCA) and the Karhunen–Loève transform (KL-transform). The covariance matrix plays a key role in financial economics
Covariance_matrix
Examination of the heart's electrical activity
events. Common methods Steps Step 1: Preprocessing Signal Denoising: Use wavelet denoising, band-pass filtering (0.5–50 Hz), or Principal Component Analysis
Electrocardiography
Covariance and correlation
{\mathcal {F}}} denotes the Fourier transform, and an f ¯ {\displaystyle {\overline {f}}} again indicates the complex conjugate of f {\displaystyle f}
Cross-correlation
Tool for digital signal processing
Olivier; Laligant, Olivier; Truchetet, Frederic (2002). "Discrete wavelet transform implementation in Fourier domain for multidimensional signal". Journal
Filter_bank
Function of propagation delay and Doppler frequency
Ambigüedad". 2 National Taiwan University, Time-Frequency Analysis and Wavelet Transform 2021, Professor of Jian-Jiun Ding, Department of Electrical Engineering
Ambiguity_function
Software program
Eero (2000). "A parametric texture model based on joint statistics of complex wavelet coefficients". International Journal of Computer Vision. 40: 49–70
DeepDream
Method of image retrieval
Integrating Pixel Cluster Indexing, histogram intersection and discrete wavelet transform methods. Potential uses for CBIR include: Architectural and engineering
Content-based_image_retrieval
Measure of the joint variability
understood as a normalized version of covariance.) The covariance between two complex random variables Z , W {\displaystyle Z,W} is defined as cov ( Z , W
Covariance
Foundational principle in quantum physics
Gaussian-shaped pulse (Gabor wavelet) [For the un-squared Gaussian (i.e. signal amplitude) and its un-squared Fourier transform magnitude σ t σ f = 1 / 2
Uncertainty_principle
ISBN 0-8493-8481-8. Mitrea, M. (1994), Singular Integrals, Hardy Spaces and Clifford Wavelets, Lecture Notes in Mathematics, vol. 1575, Springer Verlag, ISBN 0-387-57884-6
Clifford_analysis
Irregular beating of the atria of the heart
focus would not be established. In multiple wavelet theory, a wavefront will break into smaller daughter wavelets when encountering an obstacle, through a
Atrial_fibrillation
Measure of the long-range dependence of a time series
Magnar (1998-09-01). "Determination of the Hurst exponent by use of wavelet transforms". Physical Review E. 58 (3): 2779–2787. arXiv:cond-mat/9707153. Bibcode:1998PhRvE
Hurst_exponent
Library for numerical analysis in C and C++
fitting Physical constants IEEE floating-point arithmetic Discrete wavelet transform Since the GSL is written in C, it is straightforward to provide wrappers
GNU_Scientific_Library
Type of stochastic process
order, time-frequency analysis (e.g., Wavelet transform, Wigner distribution function, or Short-time Fourier transform) can be employed to isolate and suppress
Stationary_process
Role of coherent states
F(b,a)=\langle b,a|\varphi \rangle \,,} is called the continuous wavelet transform of the signal φ {\displaystyle \varphi } . This concept can be extended
Coherent states in mathematical physics
Coherent_states_in_mathematical_physics
Generalized function whose value is zero everywhere except at zero
Engineering Sciences: Distributional and fractal calculus, integral transforms, and wavelets, Birkhäuser, ISBN 978-0-8176-3924-2 Schwartz, L. (1950), Théorie
Dirac_delta_function
Signal processing technique
non-periodic functions fall into the category of Fourier analysis. The Fourier transform of a function produces a frequency spectrum which contains all of the
Spectral_density_estimation
Correlation of a signal with a time-shifted copy of itself, as a function of shift
[S(f)]\end{aligned}}} where IFFT denotes the inverse fast Fourier transform. The asterisk denotes complex conjugate. Alternatively, a multiple τ correlation can
Autocorrelation
Array of logic gates that are reprogrammable
of hardware solutions optimized for complex tasks, such as 3D MRI image segmentation, 3D discrete wavelet transform, tomographic image reconstruction,
Field-programmable_gate_array
Application of radar which is used to create two-dimensional images
direction and receives the backscattering from the targets which will be transformed to a radar image from the received signals. Usually the reflected pulse
Imaging_radar
Estimator for quality of a statistical model
directly compare the AIC values of the two models. Instead, we should transform the normal cumulative distribution function to first take the logarithm
Akaike_information_criterion
Quantity derived from seismic data
Fourier transform, continuous wavelet transform, Wigner-Ville distribution, matching pursuit, among many others. Once each trace has been transformed into
Seismic_attribute
Probabilistic problem-solving algorithm
computer simulations. They can provide approximate solutions to problems too complex for mathematical analysis. The name comes from the Monte Carlo Casino in
Monte_Carlo_method
Concept in radio communication
communication systems usually employ multi-carrier modulations (such as OFDM or wavelet OFDM) to avoid the intersymbol interference that multipath propagation
Multipath_propagation
Optical imaging technique
A wavelet transform (WT) approach may also be considered. Using both a series of function localized in both real and Fourier space from the complex window
Spectroscopic optical coherence tomography
Spectroscopic_optical_coherence_tomography
Special mathematical function defined as sin(x)/x
Technique in signal processing List of mathematical functions Shannon wavelet Sinc filter – Ideal low-pass filter or averaging filter Sinc numerical
Sinc_function
Equation in Fourier analysis
Fourier transform Explicit formulae for L-functions Stein and Weiss, p 251 Pinsky, M. (2002), Introduction to Fourier Analysis and Wavelets., Brooks
Poisson_summation_formula
Statistical measure of variability
67449\sigma .} This form is used in, e.g., the probable error. In the case of complex values (X+iY), the relation of MAD to the standard deviation is unchanged
Median_absolute_deviation
COMPLEX WAVELET-TRANSFORM
COMPLEX WAVELET-TRANSFORM
Surname or Lastname
English
English : habitational name from Coppull in Lancashire, recorded in the 13th century as Cophill, from Old English copp ‘peak’ + hyll ‘hill’.English : nickname from Old French curt peil ‘short hair’.Probably an Americanized spelling of German and Jewish Koppel or German and Dutch Kappel.
Boy/Male
Tamil
Poornan | பூரà¯à®¨à®¾à®¨
Complete
Poornan | பூரà¯à®¨à®¾à®¨
Girl/Female
Bengali, Indian
Good Complex
Surname or Lastname
English
English : habitational name, probably from Comley in Shropshire or Combley on the Isle of Wight; both are named with Old English cumb ‘valley’ + lēah ‘woodland clearing’.
Boy/Male
British, English
Meadow of Quivering Aspens
Girl/Female
Arabic, Muslim
Complex; Zigzag; Curling
Surname or Lastname
English
English : variant spelling of Wakeley.
Surname or Lastname
English
English : habitational name from Wakeley in Hertfordshire, named from the Old English byname Waca, meaning ‘watchful’ (see Wake) + Old English lēah ‘woodland clearing’.
Surname or Lastname
English
English : unexplained.Americanized form of German Koppler.
Boy/Male
Anglo, British, English
From the Damp Meadow
Male
French
Pet form of Norman French Ace, ACELET means "noble at birth."
Boy/Male
British, English
From the Damp Meadow
Boy/Male
English
From Wake's meadow.
Girl/Female
Muslim
Complex, Zigzag, Curling
Boy/Male
Anglo, Australian, British, English
Meadow of Quivering Aspens
Girl/Female
Tamil
Complete
Female
Hebrew
(×ַיֶּלֶת) Hebrew name derived from a name for the morning star, AYELET means "deer; gazelle."
Girl/Female
Hindu, Indian
Complex
Surname or Lastname
English
English : variant of Wakeley.
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : habitational name from any of various places called Copley, for example in County Durham, Staffordshire, and Yorkshire, from the Old English personal name Coppa (apparently a byname for a tall man) or from copp ‘hilltop’ + lēah ‘woodland clearing’.
COMPLEX WAVELET-TRANSFORM
COMPLEX WAVELET-TRANSFORM
Biblical
a meadow of waters; a brother of waters
Boy/Male
Hindu
Head of the monkey army
Boy/Male
Dutch American
Laughter.
Female
Italian
(Russian ТатьÑна): Feminine form of Latin Tatianus, probably TATIANA means "father." In use by the Italians, Portuguese, Romanians, Russians and Spanish.
Girl/Female
Indian
Hope; Love; Firm Heart; Warm
Girl/Female
Muslim/Islamic
Princess
Boy/Male
Tamil
Bharddwaj | பாரà¯à®¤à¯à®¤à¯à®µà®¾à®œ
A Lucky bird, A sage
Boy/Male
Hindu
To merge
Boy/Male
Indian, Tamil
Son of Clouds
Girl/Female
Hindu
Insight, Intelligence, Mind
COMPLEX WAVELET-TRANSFORM
COMPLEX WAVELET-TRANSFORM
COMPLEX WAVELET-TRANSFORM
COMPLEX WAVELET-TRANSFORM
COMPLEX WAVELET-TRANSFORM
a.
Intricate; entangled; complicated; complex.
n.
A complex; an aggregate of parts; a complication.
v. t.
To bring to a state in which there is no deficiency; to perfect; to consummate; to accomplish; to fulfill; to finish; as, to complete a task, or a poem; to complete a course of education.
a.
Not complex; uncompounded; simple.
a.
Free from waves; undisturbed; not agitated; as, the waveless sea.
imp. & p. p.
of Couple
imp. & p. p.
of Compile
a.
Complex, complicated.
a.
One of the pairs of plates of two metals which compose a voltaic battery; -- called a voltaic couple or galvanic couple.
n.
One who couples; that which couples, as a link, ring, or shackle, to connect cars.
a.
See Couple-close.
n.
Composed of two or more parts; composite; not simple; as, a complex being; a complex idea.
imp. & p. p.
of Comply
a.
Finished; ended; concluded; completed; as, the edifice is complete.
pl.
of Couple-close
a.
Repeatedly compound; made up of complex constituents.
n.
One who compiles; esp., one who makes books by compilation.
n.
A little wave; a ripple.
n.
One who complies, yields, or obeys; one of an easy, yielding temper.
adv.
In a complex manner; not simply.