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mathematics of signal processing, the harmonic wavelet transform, introduced by David Edward Newland in 1993, is a wavelet-based linear transformation of a
Harmonic_wavelet_transform
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
Function for integral Fourier-like transform
continuous-time (analog) signals and so are related to harmonic analysis. Discrete wavelet transform (continuous in time) of a discrete-time (sampled) signal
Wavelet
Functions used by the continuous wavelet transform
wavelets Cauchy wavelet Addison wavelet Wavelet Abstract Harmonic Analysis of Continuous Wavelet Transforms. Springer Science & Business Media. 2005
Continuous_wavelet
complex wavelet transform (CWT) is a complex-valued extension to the standard discrete wavelet transform (DWT). It is a two-dimensional wavelet transform which
Complex_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
Mathematical transform that expresses a function of time as a function of frequency
signals, as in wavelet transforms and chirplet transforms, with the wavelet analog of the Fourier transform being the continuous wavelet transform. The following
Fourier_transform
Discrete sine transform Discrete wavelet transform Hadamard transform (or, Walsh–Hadamard transform) Fast wavelet transform Hankel transform, the determinant
List_of_transforms
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
Beckenstein, Fourier and Wavelet Analysis (Springer, 2004), p. 264 Morelli, E., "High accuracy evaluation of the finite Fourier transform using sampled data
Finite_Fourier_transform
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
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
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
Signal representation
Reciprocal space Short-time Fourier transform Time–frequency representation Time–frequency analysis Wavelet Wavelet transform – digital image processing, signal
Frequency_domain
Mathematical operation
area of harmonic analysis, the fractional Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform. It can be
Fractional_Fourier_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
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
Inverse of the average of the inverses of a set of numbers
In mathematics, the harmonic mean is a kind of average, one of the Pythagorean means. It is sometimes used for ratios and rates such as speeds, and is
Harmonic_mean
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
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 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
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
Branch of mathematics
computing the Fourier transform of a sampled musical note. One can then re-synthesize the same sound by mixing purely harmonic sounds with frequency components
Fourier_analysis
N-th root of the product of n numbers
arithmetic mean and the harmonic mean. For all positive data sets containing at least one pair of unequal values, the harmonic mean is always the least
Geometric_mean
case. The discrete wavelet transform is extended to the multidimensional case using the tensor product of well known 1-D wavelets. In 2-D for example
Wavelet for multidimensional signals analysis
Wavelet_for_multidimensional_signals_analysis
Type of wavelet
analysis, compactly supported wavelets derived from Legendre polynomials are termed Legendre wavelets or spherical harmonic wavelets. Legendre functions have
Legendre_wavelet
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
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
American mathematician (born 1939)
College Park and is a leading researcher in wavelet analysis and Director of the Norbert Wiener Center for Harmonic Analysis and Applications. He was named
John_Benedetto
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 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
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
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
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
Numeric quantity representing the center of a collection of numbers
Pythagorean means are the arithmetic mean (AM), the geometric mean (GM), and the harmonic mean (HM). These means were studied with proportions by Pythagoreans and
Mean
Concept in linear algebra
Gabor frames and wavelet frames, are introduced and discussed. In usual Fourier transformation, the function in time domain is transformed to the frequency
Overcompleteness
from NSF. He received patents on signal encryption methodology using wavelet transforms, and co-founded Lightkey Optical Components, LLC. He also studied
Ulf_Lennart_Österberg
t^{2}}} one gets the kernel of the Gabor transform. Gabor filter Gabor wavelet Fourier analysis Wavelet Morlet wavelet Gabor, D. (1946). "Theory of communication
Gabor_atom
Linear filter used for texture analysis
theorem), the Fourier transform of a Gabor filter's impulse response is the convolution of the Fourier transform of the harmonic function (sinusoidal function)
Gabor_filter
Probabilistic problem-solving algorithm
phenomenon in question. Pseudo-random number sampling algorithms are used to transform uniformly distributed pseudo-random numbers into numbers that are distributed
Monte_Carlo_method
Statistical property quantifying how much a collection of data is spread out
Arithmetic-Geometric Contraharmonic Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode Dispersion Average absolute deviation
Statistical_dispersion
Changing the speed or duration of an audio signal without affecting its pitch
sinusoid and transient waveforms), or use other techniques based on the wavelet transform, or artificial neural network processing[citation needed], producing
Audio time stretching and pitch scaling
Audio_time_stretching_and_pitch_scaling
Oscillatory error in Fourier series
continuous wavelet transform, the wavelet Gibbs phenomenon never exceeds the Fourier Gibbs phenomenon. Also, using the discrete wavelet transform with Haar
Gibbs_phenomenon
Probability distribution
Fourier transform is only localized in frequency. Therefore, standard Fourier Transforms are only applicable to stationary processes, while wavelets are applicable
Beta_distribution
Data visualization
Arithmetic-Geometric Contraharmonic Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode Dispersion Average absolute deviation
Box_plot
Design of tasks
Spectral density estimation Fourier analysis Least-squares spectral analysis Wavelet Whittle likelihood Survival Survival function Kaplan–Meier estimator (product
Design_of_experiments
Non-destructive material testing using ultrasonic waves
Chi, Sheng-Wei; Ozevin, Didem; Indacochea, J. Ernesto (2017). "Wavelet Based Harmonics Decomposition of Ultrasonic Signal in Assessment of Plastic Strain
Ultrasonic_testing
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
Generates a forecast of future values of a time series
Arithmetic-Geometric Contraharmonic Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode Dispersion Average absolute deviation
Exponential_smoothing
Statistical transformation
as |ρ| is not too large and N is not too small. The behavior of this transform has been extensively studied since Fisher introduced it in 1915. Fisher
Fisher_transformation
Interpretation of probability
Arithmetic-Geometric Contraharmonic Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode Dispersion Average absolute deviation
Bayesian_probability
Number of values in the final calculation of a statistic that are free to vary
Arithmetic-Geometric Contraharmonic Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode Dispersion Average absolute deviation
Degrees of freedom (statistics)
Degrees_of_freedom_(statistics)
Experiment in which information about the test is masked to reduce bias
Arithmetic-Geometric Contraharmonic Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode Dispersion Average absolute deviation
Blinded_experiment
Statistical phenomenon
Arithmetic-Geometric Contraharmonic Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode Dispersion Average absolute deviation
Regression_toward_the_mean
Type of average of a collection of numbers
helps to distinguish it from other types of means, such as geometric and harmonic. Arithmetic means are also frequently used in economics, anthropology,
Arithmetic_mean
Graphical representation of the distribution of numerical data
transformation Power transform Box–Cox transformation Yeo–Johnson transformation Variance-stabilizing transformation Anscombe transform Fisher transformation
Histogram
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
related to harmonic analysis. Almost all practically useful discrete wavelet transforms use discrete-time filter banks. Similarly, Beta wavelet and its derivative
Beta_wavelet
Tool for digital signal processing
Olivier; Laligant, Olivier; Truchetet, Frederic (2002). "Discrete wavelet transform implementation in Fourier domain for multidimensional signal". Journal
Filter_bank
Single measure of some attribute of a sample
Arithmetic-Geometric Contraharmonic Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode Dispersion Average absolute deviation
Statistic
Statistical property
Arithmetic-Geometric Contraharmonic Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode Dispersion Average absolute deviation
Standard_error
Statistical indicators in signal processing
which textures are irregular or non-uniform. Short time Fourier transform or Wavelet might be the most appropriate techniques to analyse non-stationary
Hjorth_parameters
Mathematical function
function on the unit sphere Ω {\displaystyle \Omega } and its spherical harmonic transform coefficient g l m {\displaystyle g_{lm}} at the degree l {\displaystyle
Slepian_function
Table that displays the frequency of variables
transformation Power transform Box–Cox transformation Yeo–Johnson transformation Variance-stabilizing transformation Anscombe transform Fisher transformation
Contingency_table
Covariance and correlation
affine transform. Specifically, T i ( ⋅ ) {\displaystyle T_{i}(\cdot )} can be circular translation transform, rotation transform, or scale transform, etc
Cross-correlation
Selection of data points in statistics
Arithmetic-Geometric Contraharmonic Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode Dispersion Average absolute deviation
Sampling_(statistics)
Statistical test
transformation Power transform Box–Cox transformation Yeo–Johnson transformation Variance-stabilizing transformation Anscombe transform Fisher transformation
Z-test
Statistical hypothesis test
Arithmetic-Geometric Contraharmonic Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode Dispersion Average absolute deviation
Chi-squared_test
Statistical test that compares goodness of fit
requires that the models be nested – i.e. the more complex model can be transformed into the simpler model by imposing constraints on the former's parameters
Likelihood-ratio_test
Statistic measuring inter-rater agreement for categorical items
Spectral density estimation Fourier analysis Least-squares spectral analysis Wavelet Whittle likelihood Survival Survival function Kaplan–Meier estimator (product
Cohen's_kappa
Statistical interpretation with many tests
multiple comparisons Boole–Bonferroni bound Closed testing procedure E-values Harmonic mean p-value procedure Related concepts Testing hypotheses suggested by
Multiple_comparisons_problem
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
Arithmetic-Geometric Contraharmonic Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode Dispersion Average absolute deviation
Coefficient_of_variation
definitions to the dyadic derivatives. Walsh function Haar wavelet Harmonic analysis Walsh transform Engels, W. (1985). "On the characterization of the dyadic
Dyadic_derivative
Statistical hypothesis test
Arithmetic-Geometric Contraharmonic Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode Dispersion Average absolute deviation
F-test
Variable representing a random phenomenon
Probability. CRC Press. ISBN 9781466575592. Mackey, George (July 1980). "Harmonic analysis as the exploitation of symmetry – a historical survey" (PDF).
Random_variable
Time series model
Arithmetic-Geometric Contraharmonic Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode Dispersion Average absolute deviation
Autoregressive conditional heteroskedasticity
Autoregressive_conditional_heteroskedasticity
Signal processing technique
ISBN 978-0-13-113956-5. Thomson, D. J. (1982). "Spectrum estimation and harmonic analysis". Proceedings of the IEEE. 70 (9): 1055–1096. Bibcode:1982IEEEP
Spectral_density_estimation
Discrete Fourier transform algorithm
Computational Harmonic Analysis. 41 (3): 713–748. doi:10.1016/j.acha.2015.05.002. Price, Eric; Song, Zhao (2015). "A Robust Sparse Fourier Transform in the Continuous
Sparse_Fourier_transform
Specialized form of regression analysis, in statistics
Arithmetic-Geometric Contraharmonic Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode Dispersion Average absolute deviation
Robust_regression
Measure of statistical dispersion
Arithmetic-Geometric Contraharmonic Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode Dispersion Average absolute deviation
Interquartile_range
Statistic which divides a data set into 100 parts and analyzes it as a percentage
transformation Power transform Box–Cox transformation Yeo–Johnson transformation Variance-stabilizing transformation Anscombe transform Fisher transformation
Percentile
Nonparametric test of the null hypothesis
ISBN 0-471-16068-7.) suggest transforming the data to ranks (if they are not already ranks) and then performing the t-test on the transformed data, the version of
Mann–Whitney_U_test
Function related to statistics and probability theory
transformation Power transform Box–Cox transformation Yeo–Johnson transformation Variance-stabilizing transformation Anscombe transform Fisher transformation
Likelihood_function
Statistical considerations on how many observations to make
Arithmetic-Geometric Contraharmonic Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode Dispersion Average absolute deviation
Sample_size_determination
Class of statistical models
transformation Power transform Box–Cox transformation Yeo–Johnson transformation Variance-stabilizing transformation Anscombe transform Fisher transformation
Generalized_linear_model
Austrian mathematician (born 1951)
"Gabor Wavelets and the Heisenberg Group: Gabor Expansions and Short Time Fourier Transform from the Group Theoretical Point of View". Wavelets. Elsevier
Hans_Georg_Feichtinger
case behavior for the Haar wavelet packet analysis. In other words, noiselets are totally incompressible by the Haar wavelet packet analysis. Like the
Noiselet
Study of collection and analysis of data
century, was led by the work of Francis Galton and Karl Pearson, who transformed statistics into a rigorous mathematical discipline used for analysis
Statistics
Spectral density estimation Fourier analysis Least-squares spectral analysis Wavelet Whittle likelihood Survival Survival function Kaplan–Meier estimator (product
List of probability distributions
List_of_probability_distributions
Similar to the basis of a vector space, but not necessarily linearly independent
theory has roots in harmonic and functional analysis, operator theory, linear algebra, and matrix theory. The Fourier transform has been used for over
Frame_(linear_algebra)
Statistics concept
with new basis functions, such as splines, radial basis functions, and wavelets. These families of basis functions offer a more parsimonious fit for many
Polynomial_regression
Family of statistical methods based on sampling of available data
Arithmetic-Geometric Contraharmonic Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode Dispersion Average absolute deviation
Resampling_(statistics)
Statistical method
transformation Power transform Box–Cox transformation Yeo–Johnson transformation Variance-stabilizing transformation Anscombe transform Fisher transformation
Factor_analysis
Form of scientific experiment
transformation Power transform Box–Cox transformation Yeo–Johnson transformation Variance-stabilizing transformation Anscombe transform Fisher transformation
Randomized_controlled_trial
Scientific procedure performed to validate a hypothesis
Spectral density estimation Fourier analysis Least-squares spectral analysis Wavelet Whittle likelihood Survival Survival function Kaplan–Meier estimator (product
Experiment
Method used in statistics, pattern recognition, and other fields
example, to define phage types of Salmonella enteritidis based on Fourier transform infrared spectra, to detect animal source of Escherichia coli studying
Linear_discriminant_analysis
Position that there is no relationship between two phenomena
Arithmetic-Geometric Contraharmonic Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode Dispersion Average absolute deviation
Null_hypothesis
Statistical method
intervals from bootstrapping transformed data (e.g., by taking the logarithm) would ideally be the same as transforming the confidence intervals from
Bootstrapping_(statistics)
Multidimensional data algorithm
multiple positions and scales, by augmenting the dictionary to be that of a wavelet basis. This can be done efficiently using the convolution operator without
Matching_pursuit
HARMONIC WAVELET-TRANSFORM
HARMONIC WAVELET-TRANSFORM
Boy/Male
British, English
From the Damp Meadow
Girl/Female
Latin American
Concord.
Girl/Female
Greek Latin
Daughter of Ares.
Girl/Female
Christian & English(British/American/Australian)
Harmony
Male
French
Pet form of Norman French Ace, ACELET means "noble at birth."
Female
Greek
(ΑÏμονία) Greek name HARMONIA means "concord, harmony." In mythology, this is the name of the daughter of Ares and Aphrodite. Her Latin name is Concordia.
Girl/Female
American, British, English, Greek, Latin
A State of Order or Agreement; Unity; Concord; Musically in Tune; A Tuneful Sound
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’.
Female
English
English name derived from the vocabulary word harmony, from Greek Harmonia, HARMONY means "concord, harmony."
Girl/Female
English
Unity; concord; musically in tune. Harmonia was the mythological daughter of Aphrodite.
Boy/Male
Anglo, Australian, British, English
Meadow of Quivering Aspens
Girl/Female
American, Australian, British, Chinese, Christian, English, French, Greek, Latin
A State of Order or Agreement; A Beautiful Blending; Agreement; Concord; Musical Combination of Chords; Harmony; Joining
Male
English
English surname transferred to forename use, from the German personal name Harman, HARMON means "bold/hardy man."
Girl/Female
English
Unity; concord; musically in tune. Harmonia was the mythological daughter of Aphrodite.
Boy/Male
Anglo, British, English
From the Damp Meadow
Girl/Female
American, Australian, British, Christian, English, French, Greek, Latin
A State of Order or Agreement; Unity; Concord; Harmony; Agreement
Boy/Male
British, English
Meadow of Quivering Aspens
Boy/Male
English
From Wake's meadow.
Female
Hebrew
(×ַיֶּלֶת) Hebrew name derived from a name for the morning star, AYELET means "deer; gazelle."
Female
English
Variant spelling of English Harmony, HARMONIE means "concord, harmony."
HARMONIC WAVELET-TRANSFORM
HARMONIC WAVELET-TRANSFORM
Boy/Male
Arabic, Muslim
Leader
Boy/Male
Indian
Arbitrator, Judge
Girl/Female
Arabic, Muslim
She Narrated Hadith
Boy/Male
British, English
From the Island Near the Clearing
Boy/Male
American, British, English
From the North Cross Roads
Male
Finnish
Finnish form of Hebrew Yechezqel, HESEKIEL means "God will strengthen."
Boy/Male
Australian, Vietnamese
Virtuous
Girl/Female
Hebrew
Protected.
Female
English
Variant spelling of Welsh Gwyneth, GWENETH means "luck, happiness."Â
Male
English
Anglicized form of Hebrew Tsidqiyah, ZIDKIJAH means "righteousness of the Lord." In the bible, this is the name of many characters, including the name which Mattaniah adopted after becoming (the last) king of Judah.
HARMONIC WAVELET-TRANSFORM
HARMONIC WAVELET-TRANSFORM
HARMONIC WAVELET-TRANSFORM
HARMONIC WAVELET-TRANSFORM
HARMONIC WAVELET-TRANSFORM
v. i.
To agree in vocal or musical effect; to form a concord; as, the tones harmonize perfectly.
a.
Not harmonic.
n.
Concord or agreement in facts, opinions, manners, interests, etc.; good correspondence; peace and friendship; as, good citizens live in harmony.
n.
Alt. of Harmonite
a.
Of, pertaining to, or obtained from, carbon; as, carbonic oxide.
n.
One who shows the agreement or harmony of corresponding passages of different authors, as of the four evangelists.
a.
Alt. of Harmonical
n.
One who understands the principles of harmony or is skillful in applying them in composition; a musical composer.
n.
A musical note produced by a number of vibrations which is a multiple of the number producing some other; an overtone. See Harmonics.
a.
Concordant; musical; consonant; as, harmonic sounds.
v. t.
To accompany with harmony; to provide with parts, as an air, or melody.
a.
Free from waves; undisturbed; not agitated; as, the waveless sea.
v. i.
To agree in action, adaptation, or effect on the mind; to agree in sense or purport; as, the parts of a mechanism harmonize.
pl.
of Harmony
n.
See Harmonic suture, under Harmonic.
n.
A literary work which brings together or arranges systematically parallel passages of historians respecting the same events, and shows their agreement or consistency; as, a harmony of the Gospels.
n.
A little wave; a ripple.
a.
Producing mathematically perfect harmony or concord; sweetly or perfectly harmonious.
a.
Relating to harmony, -- as melodic relates to melody; harmonious; esp., relating to the accessory sounds or overtones which accompany the predominant and apparent single tone of any string or sonorous body.
n.
See Camelet.