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Discrete fourier transform expressed as a matrix
applied mathematics, a DFT matrix is a square matrix as an expression of a discrete Fourier transform (DFT) as a transformation matrix, which can be applied
DFT_matrix
Function in discrete mathematics
space, the DFT expression can also be written in terms of a DFT matrix. When scaled appropriately, it becomes a unitary matrix, and the DFT can thus be
Discrete_Fourier_transform
Generalisation of Fourier transform to any ring
\\v_{n-1}\end{bmatrix}}.} The matrix for this transformation is called the DFT matrix. Similarly, the matrix notation for the inverse Fourier transform
Discrete Fourier transform over a ring
Discrete_Fourier_transform_over_a_ring
Discrete Fourier transform algorithm
factorizing the DFT matrix into a product of sparse (mostly zero) factors. As a result, it manages to reduce the complexity of computing the DFT from O ( n
Fast_Fourier_transform
Matrix of geometric progressions
discrete Fourier transform is defined by a specific Vandermonde matrix, the DFT matrix, where the x i {\displaystyle x_{i}} are chosen to be nth roots
Vandermonde_matrix
Most widely known generalized inverse of a matrix
{\displaystyle {\mathcal {F}}} be the Discrete Fourier Transform (DFT) matrix; then C = F ⋅ Σ ⋅ F ∗ , C + = F ⋅ Σ + ⋅ F ∗ . {\displaystyle
Moore–Penrose_inverse
Linear algebra matrix
Toeplitz matrices, so the DFT coefficients are asymptotically uncorrelated for stationary data. For a symmetric circulant matrix C {\displaystyle C} one
Circulant_matrix
Matrix with shifting rows
In linear algebra, a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to
Toeplitz_matrix
Discrete Fourier transform for prime sizes
algorithm that computes the discrete Fourier transform (DFT) of prime sizes by re-expressing the DFT as a cyclic convolution (the other algorithm for FFTs
Rader's_FFT_algorithm
Fast Fourier Transform algorithm
Cooley–Tukey algorithm breaks the DFT into smaller DFTs, it can be combined arbitrarily with any other algorithm for the DFT. For example, Rader's or Bluestein's
Cooley–Tukey_FFT_algorithm
Change of basis applied in quantum computing
as a unitary matrix (or quantum gate) acting on quantum state vectors, where the unitary matrix F N {\displaystyle F_{N}} is the DFT matrix F N = 1 N [
Quantum_Fourier_transform
are coefficients of a discrete Fourier transform (DFT) matrix. Each row or column of the DFT matrix provides an orthogonal CI spreading code which spreads
Carrier_interferometry
Method of analysis of unbalanced three-phase power systems
non-linear power systems. It can be seen that the transformation matrix A above is a DFT matrix, and as such, symmetrical components can be calculated for any
Symmetrical_components
Form of radar used to create images of landscapes
new variants. Each multidimensional DFT computation is expressed in matrix form. The multidimensional DFT matrix, in turn, is disintegrated into a set
Synthetic-aperture_radar
Mathematical transform that expresses a function of time as a function of frequency
Fourier transform with variable resolution DFT matrix – Discrete fourier transform expressed as a matrix Discrete Fourier transform – Function in discrete
Fourier_transform
Generalization of the discrete Fourier transform
the unitary DFT, note that as defined above D F T . D F T ∗ = S {\displaystyle DFT.DFT^{*}=S} , where S {\displaystyle S} is a diagonal matrix consisting
Fourier transform on finite groups
Fourier_transform_on_finite_groups
Transform in numerical harmonic analysis
transform, consider the DWT and DFT of the following sequence: (1,0,0,0), a unit impulse. The DFT has orthogonal basis (DFT matrix): [ 1 1 1 1 1 − i − 1 i 1
Discrete_wavelet_transform
Computational quantum mechanical modelling method to investigate electronic structure
Density functional theory (DFT) is a computational quantum mechanical modeling method used in physics, chemistry and materials science to investigate
Density_functional_theory
Transform in mathematics
the discrete Fourier transform (DFT), but using a purely real matrix. It is equivalent to the imaginary parts of a DFT of roughly twice the length, operating
Discrete_sine_transform
Algorithmic determination of wave cycle parts
References). Here we consider 1-D discrete Fourier transform (DFT) phase retrieval problem. The DFT of a complex signal f [ n ] {\displaystyle f[n]} is given
Phase_retrieval
be determined accordingly. Generalizations of Pauli matrices DFT matrix Circulant matrix Weyl, H. (1927). "Quantenmechanik und Gruppentheorie". Zeitschrift
Generalized_Clifford_algebra
Involutive change of basis in linear algebra
first column element of the matrix is denoted by ( H n ) 0 , 0 {\textstyle (H_{n})_{0,0}} . H1 is precisely the size-2 DFT. It can also be regarded as
Hadamard_transform
Technique used in signal processing and data compression
sequence whereas DFTs are related to Fourier series coefficients of only periodically extended sequences. DCTs are equivalent to DFTs of roughly twice
Discrete_cosine_transform
Two-dimensional group theory table
character table for general cyclic groups is (a scalar multiple of) the DFT matrix. Another example is the character table of S 3 {\displaystyle S_{3}} :
Character_table
All submatrices of a discrete Fourier transform matrix of prime length are invertible
{\displaystyle \Omega } is non-zero. Equivalently, all submatrices of a DFT matrix of prime length are invertible. In signal processing, the theorem was
Chebotarev theorem on roots of unity
Chebotarev_theorem_on_roots_of_unity
A complex Hadamard matrix is any complex N × N {\displaystyle N\times N} matrix H {\displaystyle H} satisfying two conditions: unimodularity (the modulus
Complex_Hadamard_matrix
Binomial transform Discrete Fourier transform, DFT Fast Fourier transform, a popular implementation of the DFT Discrete cosine transform Modified discrete
List_of_transforms
matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries
List_of_named_matrices
spectrum Discrete Fourier series Non-uniform discrete Fourier transform DFT matrix Entropy influence conjecture Fast cosine transform Fast Fourier transform
List of Fourier analysis topics
List_of_Fourier_analysis_topics
Physical property that measures stiffness of material
inverse quantity is referred to as elastic modulus. Density functional theory (DFT) provides reliable methods for determining several forms of elastic moduli
Elastic_modulus
High-performance algorithm
5-step FFT, 6-step FFT, etc. The Bailey FFT is typically used for computing DFTs of large datasets, such as those used in scientific and engineering applications
Bailey's_FFT_algorithm
outwards to infinity in all four directions. This is analogous to the DFT matrix but, in this case, is continuous and infinite in extent. The value of
Fourier_operator
Fourier-related mathematical transform
discrete Fourier transform (DFT), with analogous applications in signal processing and related fields. Its main distinction from the DFT is that it transforms
Discrete_Hartley_transform
Describes the range of energies of an electron within the solid
well reproduced by DFT. But there are also systematic errors in DFT bands when compared to experiment results. In particular, DFT seems to systematically
Electronic_band_structure
Family of block-oriented display terminals and printers made by IBM
controller through a poll, is translated by the controller into EBCDIC. For DFT (Distributed Function Terminal) type displays, most of the 3270 data stream
IBM_3270
solving for the Kohn-Sham eigenstates as normal DFT codes do, CONQUEST solves for the one particle density matrix, ρ ( r , r ′ ) {\displaystyle \rho (\mathbf
CONQUEST
Algorithm used for frequency estimation and radio direction finding
of manifolds. MUSIC outperforms simple methods such as picking peaks of DFT spectra in the presence of noise, when the number of components is known
MUSIC_(algorithm)
Strategy for business processes
flow technology (DFT) is a strategy for defining and deploying business processes in a flow, driven in response to customer demand. DFT is based on a set
Demand_flow_technology
Method in physics
method (LAPW) is an implementation of Kohn-Sham density functional theory (DFT) adapted to the simulation of a wide range of properties of periodic materials
Linearized augmented-plane-wave method
Linearized_augmented-plane-wave_method
to be self-consistent, as explained below. In density functional theory (DFT) calculations of electronic energies of materials, the eigenvalue equation
Rayleigh theorem for eigenvalues
Rayleigh_theorem_for_eigenvalues
Heat treatment technique used to increase the yield strength of malleable materials
symmetry of the supercells and it suits well with the currently available DFT methods. In this way, some researchers have developed strategies to screen
Precipitation_hardening
Mathematical operation in signal processing
the DFT. The premise behind circular convolution is to take the DFTs of the input signals, multiply them together, and then take the inverse DFT. Care
Multidimensional discrete convolution
Multidimensional_discrete_convolution
Class of artificial neural networks
traditional quantum chemistry methods such as density functional theory (DFT) is the reduction in computational cost from O(n³) to O(n), enabling simulations
Graph_neural_network
Class of chemical compounds
(2015-05-12). "Electronic Properties of Zigzag Graphene Nanoribbons Studied by TAO-DFT". Journal of Chemical Theory and Computation. 11 (5): 2003–2011. Bibcode:2015JCTC
Acene
Filters used in signal processing that are optimal in some sense
method is, in fact, a simple version of the discrete Fourier transform (DFT). The DFT takes an N {\displaystyle N} -valued complex input and correlates it
Matched_filter
Computational chemistry software package
calculations, such as Hartree–Fock, density functional theory (DFT) including time-dependent DFT (TDDFT), Møller–Plesset perturbation theory (MP2), coupled
Q-Chem
Periodicity computation method
the same frequency as separate sinusoids). The relationship between the DFT and the approximation of trigonometric functions using the least-squares
Least-squares spectral analysis
Least-squares_spectral_analysis
Function used in signal processing
(DTFT) such as the DFTs in Fig 2 only reveals the leakage into the DFT bins from a sinusoid whose frequency is also an integer DFT bin. The unseen sidelobes
Window_function
Quantum chemistry software program
energies and analytical polarizabilities and hyperpolarizabilities for HF and DFT wavefunctions. An efficient vectorized Gaussian integral package allowing
PQS_(software)
Computational chemistry software package
system is calculated at each time step using density functional theory (DFT), Hartree-Fock (HF), or other electronic structure calculation methods. The
Car–Parrinello molecular dynamics
Car–Parrinello_molecular_dynamics
Array of antennas creating a steerable beam
are processed using a DFT. The DFT introduces multiple different discrete phase shifts during processing. The outputs of the DFT are individual channels
Phased_array
service.gov.uk/government/uploads/system/uploads/attachment_data/file/851465/dft-traffic-signs-manual-chapter-6.pdf http://www.trl.co
LinSig
Chemistry program for Intel-compatible x86, x86-64 processors
Quantum Chemistry Speed Test, Firefly's DFT code came second (losing only to commercial QChem), beating other free DFT codes by a large margin. Firefly's unique
Firefly_(computer_program)
Problem in Fourier analysis
measured by the spectral concentration. The discrete Fourier transform (DFT) U(f) of a finite series w t {\displaystyle w_{t}} , t = 1 , 2 , 3 , 4 ,
Spectral concentration problem
Spectral_concentration_problem
Fourier-related transform for signals that change over time
window, then the STFT may be more efficiently evaluated using a sliding DFT algorithm. The STFT is invertible, that is, the original signal can be recovered
Short-time_Fourier_transform
Branch of chemistry
implementations of DFT typically scale as O ( N 3 ) {\displaystyle {\mathcal {O}}(N^{3})} , mainly due to the need to diagonalize the Kohn-Sham matrix. The diagonalization
Computational_chemistry
theory (DFT) calculations exists. These databases have proven their utility in high-throughput material screening and discovery. Some common DFT databases
Materials_informatics
Multidimensional fast Fourier transform algorithm
(MD) discrete Fourier transform (DFT) down into successively smaller MD DFTs until, ultimately, only trivial MD DFTs need to be evaluated. The most common
Vector-radix_FFT_algorithm
Category of computational quantum chemistry technique
noniterative step which scales as N7. Hybrid Density functional theory (DFT) methods using functionals which include Hartree–Fock exchange scale in a
Ab initio quantum chemistry methods
Ab_initio_quantum_chemistry_methods
Model of human decision-making
Decision field theory (DFT) is a dynamic-cognitive approach to human decision making. It is a cognitive model that describes how people actually make
Decision_field_theory
use of a linear combination of numerical atomic orbitals makes SIESTA a DFT code. SIESTA can produce very fast calculations with small basis sets, allowing
SIESTA_(computer_program)
Electronic design automation method
incorporate any Design For Testability (DFT) scheme. However, these test generators, combined with low-overhead DFT techniques such as partial scan, have
Automatic test pattern generation
Automatic_test_pattern_generation
Mathematical operation
with the output samples. When an FFT is used to compute the 824 unaffected DFT samples, we don't have the option of not computing the affected samples,
Circular_convolution
Theorem in quantum chemistry
the ground electronic states solved by one-particle methods (such as HF or DFT) already imply configuration interaction of the ground-state configuration
Brillouin's_theorem
Interaction between electronic and nuclear vibrational motion in a molecule
"First-order nonadiabatic coupling matrix elements between excited states: A Lagrangian formulation at the CIS, RPA, TD-HF, and TD-DFT levels". The Journal of Chemical
Vibronic_coupling
Simplified model in condensed matter physics
based simulations using density functional theory (DFT). The inclusion of the Hubbard term in DFT simulations is important as this improves the prediction
Hubbard_model
Antenna arrays with smart signal processing algorithms
antenna arrays with multi channels, use the digital beamforming, usually by DFT or FFT. Two of the main types of smart antennas include switched beam smart
Smart_antenna
written as ∇ {\displaystyle \nabla } .) det – determinant of a matrix or linear transformation. DFT – discrete Fourier transform. dim – dimension of a vector
List of mathematical abbreviations
List_of_mathematical_abbreviations
distributions. FreeON performs Hartree–Fock, pure density functional, and hybrid HF/DFT calculations (e.g. B3LYP) in a Cartesian-Gaussian LCAO basis. All algorithms
FreeON
Type of defect in crystalline materials
Structural and Electronic Properties of Hybrid 2D Materials Using Complementary DFT and Machine Learning Approaches". Advanced Theory and Simulations. 2 1800128
Stacking_fault
Chemical compound
Chertihin, George V.; Andrews, Lester (13 September 2002). "Matrix infrared spectra and DFT calculations of the reactive MHx (x = 1, 2, and 3), (H2)MH2
Scandium(III)_hydride
Software library for computing discrete Fourier transforms
(FFTW) is a software library for computing discrete Fourier transforms (DFTs) developed by Matteo Frigo and Steven G. Johnson at the Massachusetts Institute
Fastest Fourier Transform in the West
Fastest_Fourier_Transform_in_the_West
Method for finding largest (or smallest) eigenvalues
Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is a matrix-free method for finding the largest (or smallest) eigenvalues and the corresponding
LOBPCG
Concept in applied mathematics
reduces to the DFT when the sampling points are located on the unit circle at equally spaced angles. Expressing the above as a matrix, we get X = D x
Non-uniform discrete Fourier transform
Non-uniform_discrete_Fourier_transform
Retrieved September 24, 2023. Его краснодарское Величество (in Russian), DFT.ru, April 21, 2008 Daedalic Entertainment shuts down internal game development
List_of_video_game_developers
Method of encoding digital data on multiple carrier frequencies
{\displaystyle M} -point DFT/IDFT matrix with some diagonal phase shift matrices. Then, the right hand side DFT/IDFT matrix and the k {\displaystyle k}
Orthogonal frequency-division multiplexing
Orthogonal_frequency-division_multiplexing
Chemical compounds containing only hydrogen and one other chemical element
1021/jp037942l. Wang, Xuefeng; Andrews, Lester (29 June 2002). "Neon Matrix Infrared Spectra and DFT Calculations of Tungsten Hydrides WH x (x = 1−4, 6)". The Journal
Binary_compounds_of_hydrogen
Computer that uses photons or light waves
applications, require frequent use of the 2D discrete Fourier transform (DFT) – for example in solving differential equations describing wave propagation
Optical_computing
Mechanism of spontaneous symmetry breaking
genuinely ab initio in the literature) the advent of density functional theory (DFT) opened up new avenues to treat larger systems including solids. This allowed
Jahn–Teller_effect
Type of composite material
Cemented carbides are metal matrix composites where carbide particles act as the aggregate and a metallic binder serves as the matrix (analogous to concrete
Cemented_carbide
Quantum-mechanical simulation framework
In density functional theory (DFT) the adiabatic-connection fluctuation-dissipation theorem (ACFD) is an exact formula for the Kohn–Sham correlation energy
Adiabatic connection fluctuation dissipation theorem
Adiabatic_connection_fluctuation_dissipation_theorem
Spectroscopic technique
Since some thermodynamic calculations ignored in the harmonic approximation, DFT-calculated harmonic frequencies are systematically too high. Hence, an scaling
Raman_spectroscopy
Chemical reaction
Negishi coupling of trans-[PdMeCl(PMePh2)2] with ZnMeCl: an experimental and DFT study of the transmetalation step". Chemistry: A European Journal. 16 (29):
Negishi_coupling
Signal processing technique
transform (DFT), which operates on samples of the signal, and which provides a mathematical approximation to the full integral solution. The DFT is almost
Spectral_density_estimation
values. Zhang et al. took a step further to combine the first-principle DFT calculations with MD to study the influence of stacking fault energy (SFE)
Strengthening mechanisms of materials
Strengthening_mechanisms_of_materials
Statistical model
{\tilde {X}}_{N/2+1}} be the (complex-valued) discrete Fourier transform (DFT) of the time series. Then for the Whittle likelihood one effectively assumes
Whittle_likelihood
Mexican physicist
perform the discrete Fourier transform (DFT) in these types of systems. Using this he has shown that precisely the DFT of a number operator in an s-dimensional
Héctor_Manuel_Moya_Cessa
Theory of stochastic processes
discrete Fourier transform and discrete cosine transform—are compared. The DFT and DCT are optimal only when the covariance structure has the specific symmetry
Kosambi–Karhunen–Loève theorem
Kosambi–Karhunen–Loève_theorem
Wireless signal analysis technique
c / 2 {\displaystyle \theta _{k}={{(\pi \cdot k)}^{2} \over N_{c}/2}} A DFT over K-1 (one waveform lost due to array switching) waveforms that measured
Channel_sounding
Type of electric high-speed train
Archived from the original on 18 December 2023. Retrieved 18 December 2023. The DfT accreditation process document specified 31 lengthened units, with options
British_Rail_Class_390
Digital audio synthesis technique
written in C by Camille Bassuel, implementing several DSP tools, including DFT to generate a wavetable set Hermann Seib (2011-01-07). "PPG Wave 2.2 / 2
Wavetable_synthesis
Chemical compound
Kalmykov, Stepan N. (November 2021). "Hydration of the pertechnetate anion. DFT study". Journal of Molecular Liquids. 342 117404. doi:10.1016/j.molliq.2021
Pertechnetic_acid
functional theory (DFT) and used to study the electronic structure and consequent physical properties of molecules and materials. As with any DFT calculation
Korringa–Kohn–Rostoker_method
Møller–Plesset perturbation theory. Although many density functional theory (DFT) codes simply calculate spin-contamination using the Kohn-Sham orbitals as
Spin_contamination
Chemical element with atomic number 6 (C)
Skeleton − Elucidation of Hypervalent Interaction Based on X-ray Analysis and DFT Calculation". Journal of the American Chemical Society. 127 (12): 4354–4371
Carbon
British Electric passenger trains
across London and south east" (Press release). Department for Transport (DfT). 23 May 2014. Retrieved 9 June 2014. "Late-February debut for Gatwick Express
British_Rail_Class_442
"Reactions of Laser-Ablated Iridium Atoms with O2. Infrared Spectra and DFT Calculations for Iridium Dioxide and Peroxoiridium(VI) Dioxide in Solid Argon"
Iridium_compounds
Branch of physics
density functional theory (DFT), uses functionals of the spatially dependent electron density instead of full interactions. DFT is widely used in ab initio
Heat_transfer_physics
American electrical engineer
PhD (1982) from Rice University. His dissertation was titled The design of DFT algorithms. Johnson has significantly raised awareness of analog effects
Howard Johnson (electrical engineer)
Howard_Johnson_(electrical_engineer)
Class of chemical compounds
Manceron, L; Alikhani, M.E; Joly, H.A (March 1998). "Infrared matrix isolation and DFT study of NiN2". Chemical Physics. 228 (1–3): 73–80. Bibcode:1998CP
Neon_compounds
DFT MATRIX
DFT MATRIX
Boy/Male
Australian, Farsi, Vietnamese
Accomplished; To Attain; To Achieve; Period of Time; Age; Life
Girl/Female
Tamil
A dot on the forehead. the one which indian women who put down the same in between two eyebrows, Drop, Point
Girl/Female
Tamil
Bindhiya | பிநà¯à®¤à®¿à®¯à®¾
A dot on the forehead. the one which indian women who put down the same in between two eyebrows, Drop, Point
Bindhiya | பிநà¯à®¤à®¿à®¯à®¾
Girl/Female
Indian
A dot on the forehead. the one which indian women who put down the same in between two eyebrows, Drop, Point
Girl/Female
Indian
A dot on the forehead. the one which indian women who put down the same in between two eyebrows, Drop, Point
Girl/Female
Indian
A dot on the forehead. the one which indian women who put down the same in between two eyebrows, Drop, Point
Boy/Male
Indian, Sanskrit
Point; Drop; Dot
Girl/Female
American, British, Christian, Danish, English, Greek, Irish
Gift of God; Form of Dorothy
Girl/Female
English
Gift of God. Aand the most common form of the name in English- speaking countries. Famous bearer:...
Boy/Male
Hindu, Indian
Nice
Girl/Female
Hindu, Indian, Kannada, Telugu
Drop of Water; Dot on the Forehead
Female
English
Pet form of English Dorothy, DOT means "gift of God."
Surname or Lastname
English
English : nickname for a meek person, from Middle English daffte ‘mild’, ‘gentle’, ‘meek’ (Old English gedæfte). It was not until the 15th century, toward the end of the main period of surname formation in England, that the word came to mean ‘stupid’, ‘silly’.
Girl/Female
Hindu, Indian
Small Red Dot; Bindi that Married Women Wear on Their Foreheads
Boy/Male
Indian
Dot; A Dark Point
Girl/Female
Hindu
One who is deft in all theories
Girl/Female
Tamil
Bindiya | பிஂதியா
A dot on the forehead. the one which indian women who put down the same in between two eyebrows, Drop, Point
Bindiya | பிஂதியா
Girl/Female
Tamil
Sarvashaastramayi | ஸரà¯à®µà®·à®¾à®¸à¯à®¤à¯à®°à®®à®¯à¯€
One who is deft in all theories
Sarvashaastramayi | ஸரà¯à®µà®·à®¾à®¸à¯à®¤à¯à®°à®®à®¯à¯€
Girl/Female
Australian
Accomplished
Surname or Lastname
English
English : nickname from Middle English dut ‘joy’, ‘delight’.Indian : variant of Datta.German : from the Germanic personal name Dudo (see Due).
DFT MATRIX
DFT MATRIX
Girl/Female
Tamil
Boy/Male
Italian Teutonic
Wise power.
Male
Hawaiian
Short form of Hawaiian Anakoni, possibly AKONI means "invaluable."Â
Girl/Female
Hindu, Indian, Marathi
Goddess Lakshmi
Girl/Female
Arabic, Muslim
Full Moon
Girl/Female
Hindu, Indian
Protector of Rays
Boy/Male
Indian, Punjabi, Sikh
God of Sky
Girl/Female
Muslim/Islamic
Under tree/umberalla
Boy/Male
Hindu, Indian, Marathi
Always Victorious; Unopposed
Boy/Male
Bengali, Hindu, Indian, Kannada, Kashmiri, Malayalam, Marathi, Mythological, Sanskrit, Telugu, Traditional
Lord Shiva
DFT MATRIX
DFT MATRIX
DFT MATRIX
DFT MATRIX
DFT MATRIX
n.
A flying report; rumor; as, it is a mere on dit.
v. t.
To mark with dots or small spots; as, to dot a line.
adv.
Compar. of Oft.
a.
Apt; fit; dexterous; clever; handy; spruce; neat.
n.
A salamander, esp. the European smooth newt (Triton punctatus).
n.
The quality of being deft.
a.
Gay; playful; frolicsome.
n.
The quality of being daft.
a. superl.
Nearest the stern; most aft.
n.
A European lizard of the genus Seps.
p. pr. & vb. n.
of Dot
a.
Frequent; often; repeated.
adv.
Again; afterwards; soon; quickly.
a.
Stupid; foolish; idiotic; also, delirious; insane; as, he has gone daft.
v. t.
To mark or diversify with small detached objects; as, a landscape dotted with cottages.
adv.
Often; frequently; not rarely; many times.
n.
Anything small and like a speck comparatively; a small portion or specimen; as, a dot of a child.
v. i.
To make dots or specks.
imp. & p. p.
of Dot
n.
See Dit, n., 2.