scholarly journals Improving Fourier Partial Sum Approximation for Discontinuous Functions Using a Weight Function

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Beong In Yun
Keyword(s):  
Target Function ◽  
Gibbs Phenomenon ◽  
Weighted Averaging ◽  
Jump Discontinuity ◽  
Partial Sums ◽  
Left Hand ◽  
Partial Sum ◽  
Hand Part ◽  
Approximate Function ◽  
The Right

We introduce a generalized sigmoidal transformation wm(r;x) on a given interval [a,b] with a threshold at x=r∈(a,b). Using wm(r;x), we develop a weighted averaging method in order to improve Fourier partial sum approximation for a function having a jump-discontinuity. The method is based on the decomposition of the target function into the left-hand and the right-hand part extensions. The resultant approximate function is composed of the Fourier partial sums of each part extension. The pointwise convergence of the presented method and its availability for resolving Gibbs phenomenon are proved. The efficiency of the method is shown by some numerical examples.

Failure to Sing the Left-Hand Part of the Score during Piano Performance: Loss of the Pitch and Stroop Vocalizations

1989 ◽  
Vol 6 (3) ◽  
pp. 299-314 ◽  
Author(s):  
Yves Guiard
Keyword(s):  
The Other ◽  
Vocal Response ◽  
Left Hand ◽  
Performance Loss ◽  
Clear Cut ◽  
Right Hand ◽  
Hand Part ◽  
Continuous Regime ◽  
And Performance ◽  
The Right

An experiment compared the ability of classical pianists to sing, during keyboard performance, the right- and the left-hand part of the score being played. Upon instructions requiring them to "sing" one or the other voice of the score, the subjects spontaneously chose to sing and name the notes simultaneously, in keeping with the French traditional way of reading music, thus producing a two- dimensional tonal and verbal vocal act in response to each visual stimulus. Singing the right-hand part of the music, whether in unison with or in place of the right hand, while concurrently playing the left-hand part was judged easy by all subjects, and performance, typically, was correct in all respects. The other task, consisting of singing the left-hand part of the music, was judged more difficult by all subjects, and performance, more often than not, was poor. Careful inspection of the many errors that were recorded in the latter task revealed a few clear-cut regularities. Failures were vocal, but not manual. More specifically, vocal failures took place on the tonal dimension of the vocal response, but not on its verbal dimension: The song, but not the naming of the notes, was prone to fail, with either a loss of the pitch, or a systematic trend toward singing unduly—albeit accurately—the notes of the right-hand part. A number of subjects were found to display this intriguing tonal/verbal dissociation—naming a note at a pitch corresponding to another note—in a continuous regime. It is emphasized that this phenomenon amounts to the spontaneous production of musical events that belong to the Stroop category.

A Century of Air-photography

Antiquity ◽  
1954 ◽  
Vol 28 (112) ◽  
pp. 206-210 ◽  
Author(s):  
O. G. S. Crawford
Keyword(s):  
Science Museum ◽  
Victor Hugo ◽  
Short History ◽  
Left Hand ◽  
Du Bois ◽  
Hand Part ◽  
History Of ◽  
The Right

When I wrote a short history of archaeological and other air-photography in 1928 the earliest examples quoted were those taken by Major Elsdale between 1880 and 1887 ; this information was given me by the late Colonel Sir Charles Arden-Close, himself a pioneer of the craft. Since then two earlier instances have come to light. The Science Museum, South Kensington, has exhibited an air-photograph of Boston, Mass., taken in 1877 ; but unfortunately it has no history. In a book published in 1930 there is reproduced a photograph taken above Paris from a captive balloon, taken by that photographic genius who called himself Nadar. Through the good offices of Professor Vaufrey, editor of L’AnthropoZogie, prints were obtained from the Service Photographique des Monuments Historiques, and two combined are here reproduced on PLATE III. They look towards the Arc de Triomphe, and have on the left the Avenue du Bois de Bouiogne (Avenue Foch) and on the right that of Victor Hugo : note that these splendid thoroughfares, then only a decade old, were still only half built-up (the left hand part of the photograph is defective). Photography itself was not much older, Fox Talbot’s first efforts having been made from 1842 onwards.

Tapping to Ragtime: Cues to Pulse Finding

2001 ◽  
Vol 18 (4) ◽  
pp. 455-489 ◽  
Author(s):  
Joel Snyder ◽  
Carol L. Krumhansl
Keyword(s):  
Lower Percentage ◽  
Musical Experience ◽  
Left Hand ◽  
Right Hand ◽  
Temporal Cues ◽  
Hand Part ◽  
Pitch Information ◽  
Negative Effect ◽  
The Right ◽  
Stimulus Materials

Two experiments investigated cues to pulse finding using a relatively unconstrained, naturalistic paradigm. Participants tapped what they felt was a comfortable pulse on a keyboard playing a percussive sound. The stimulus materials were based on ragtime excerpts, played metronomically (i.e., without expressive timing or tempo variation). The first experiment, with 8 musically experienced and 8 musically inexperienced subjects, played each excerpt in two versions: a pitch-varied version (the original excerpt) and a monotonic version (with all tones changed to middle C) that was designed to remove all melodic and harmonic cues to pulse. Neither the absence of pitch information nor musical experience significantly affected performance. The second experiment tested 12 musically experienced subjects on shorter excerpts from the same ragtime pieces. Full (right-hand and left-hand parts together) and right-hand-only versions of the excerpts were each played in pitch-varied and monotonic versions. Removing the left-hand part significantly affected tapping performance on a number of measures, causing a lower percentage of tapping on the downbeat, more off-beat taps, more aperiodic taps, more switches between tapping modes, a higher variability of the intertap interval, and larger deviations from the beat. As a whole, these indicate a negative effect of removing the left-hand part. Again, differences between pitch-varied and monotonic versions were generally small. Analysis of the music revealed the following cues to pulse finding: a predictable alternating bass pattern in the left-hand part and a majority of notes on metrically strong positions in both the right-hand and left-hand parts. These results suggest that, for piano ragtime music, temporal cues are prominently available for finding and following the pulse and that pulse finding is largely independent of pitch information. Implications of the experimental measures and music-analytic techniques for models of pulse perception are considered.

Tactile comfort characterization of knitted fabrics based on the ring-shaped style tester

2020 ◽  
pp. 004051752095739
Author(s):  
Yawen Shao ◽  
Yi Sun ◽  
Dongming Zheng ◽  
Gui Liu ◽  
Zhaoqun Du ◽  
...  
Keyword(s):  
Structural Parameters ◽  
Subjective Evaluation ◽  
Structural Parameter ◽  
Knitted Fabrics ◽  
Left Hand ◽  
Right Hand ◽  
Hand Part ◽  
And Cluster Analysis ◽  
The Right ◽  
Hand Area

The main content of this paper is to objectively characterize the tactile comfort of fabric through the ring-shaped style tester. It mainly explains the objective tactile comfort of knitted fabric through the curve parameters measured by the ring-shaped style tester and structural parameter thickness. In this paper, by adopting the methods of correlation analysis and cluster analysis, the curve parameters, including slope in the linear segments of the left-hand part of the curve ( K1), the right-hand area of the curve ( A2), the distance between the abrupt point and the peak point ( X), the linearity of the left-hand curve ( L) and the ratio of the left-hand area to the right-hand area of the curve ( C), are used. In order to verify its effectiveness, the results of subjective evaluation are compared and analyzed with the objective clustering. The experimental results show that the subjective judgment has good correlation with the objective clustering. This indicates that the curve parameters obtained through the ring-shaped style tester and structural parameters can be used to effectively represent the tactile comfort performance of fabrics.

The Gibbs Phenomenon and Lebesgue Constants for Regular Sonnenschein Matrices

1962 ◽  
Vol 14 ◽  
pp. 723-728 ◽  
Author(s):  
W. T. Sledd
Keyword(s):  
Fourier Series ◽  
Gibbs Phenomenon ◽  
Summability Method ◽  
Jump Discontinuity ◽  
Partial Sums ◽  
Lebesgue Constants ◽  
Dirichlet Conditions ◽  
Image Position

Ifψ(x)is a real-valued function which has a jump discontinuity atx= ε and otherwise satisfies the Dirichlet conditions in a neighbourhood ofx= ε then{sn(x)}the sequence of partial sums of the Fourier series forψ(x)cannot converge uniformly atx =ε. Moreover, it can be shown that given τ in [ — π, π] then there is a sequence {tn} such thattn→ ε andThis behaviour of{sn(x)}is called the Gibbs phenomenon. If {σn(x)} is the transform of{sn(x)}by a summability methodT, and if {σn(x)} also has the property described then we say thatTpreserves the Gibbs phenomenon.

The Gibbs Phenomenon for Generalized Taylor and Euler Transforms

1975 ◽  
Vol 27 (2) ◽  
pp. 384-395
Author(s):  
Robert E. Powell ◽  
Richard A. Shoop
Keyword(s):  
Fourier Series ◽  
Gibbs Phenomenon ◽  
Jump Discontinuity ◽  
Partial Sums ◽  
Dirichlet Conditions

Let f be a real-valued function satisfying the Dirichlet conditions in a neighborhood of x = x0, at which point f has a jump discontinuity. If {Sn(x)} is the sequence of partial sums of the Fourier series of f at x, then ﹛Sn(x)﹜ cannot converge uniformly at x — x0. Moreover, for any number , there exists a sequence ﹛tn﹜, where tn → x0 and

Planar Vibrations of Rigid Structure Resting on Kinematical Supports of Yu. D. Cherepinsky

2020 ◽  
pp. 5-18
Author(s):  
Alexander Tyapin
Keyword(s):  
Dynamic Instability ◽  
Vertical Component ◽  
Equation Of Motion ◽  
Free Vibrations ◽  
Inertia Moment ◽  
Left Hand ◽  
Hand Part ◽  
The Right ◽  
Gravity Acceleration ◽  
Planar Vibrations

The author derives the equation of motion for a structure resting on kinematical pendulum supports of Yu.D.Cherepinsky. Both structure and supports are assumed to be rigid; no sliding is assumed during rolling. Two components of seismic excitation are considered (horizontal one and vertical one). Equation of motion for free vibrations looks like that of the free vibrations for massive pendulum support standing alone (it was studied earlier). It is fact the equation of motion for pendulum, but center of rotation, inertia moment and stiffness are varying with time. This equation may be simplified to the linear one by skipping the second order terms. The equation of motion for seismic response after linearization is the extension of the Mathieu-Hill’s equation, where horizontal component is responsible for the right-hand part (in the conventional Mathieu-Hill’s equation it is zero), and vertical component creates parametric excitation in the left-hand part. In fact, vertical seismic acceleration modifies gravity acceleration g, which controls the effective natural frequency for pendulum. Thus, there might appear dynamic instability (though without infinite response due to the finite duration of excitation). The author presents numerical example.

scholarly journals On a class of splines free of Gibbs phenomenon

2020 ◽  
Author(s):  
Sergio Amat ◽  
Juan Ruiz ◽  
Chi-Wang Shu ◽  
Juan Carlos Trillo
Keyword(s):  
Spline Interpolation ◽  
Gibbs Phenomenon ◽  
Jump Discontinuity ◽  
Regularity Conditions ◽  
Weighted Mean ◽  
Piecewise Polynomials ◽  
Jump Discontinuities ◽  
Nonlinear Technique ◽  
The Right ◽  
Theoretical Accuracy

When interpolating data with certain regularity, spline functions are useful. They are defined as piecewise polynomials that satisfy certain regularity conditions at the joints. In the literature about splines it is possible to find several references that study the apparition of Gibbs phenomenon close to jump discontinuities in the results obtained by spline interpolation. This work is devoted to the construction and analysis of a new nonlinear technique that allows to improve the accuracy of splines near jump discontinuities eliminating the Gibbs phenomenon. The adaption is easily attained through a nonlinear modification of the right hand side of the system of equations of the spline, that contains divided differences. The modification is based on the use of a new limiter specifically designed to attain adaption close to jumps in the function. The new limiter can be seen as a nonlinear weighted mean that has better adaption properties than the linear weighted mean. We will prove that the nonlinear modification introduced in the spline keeps the maximum theoretical accuracy in all the domain except at the intervals that contain a jump discontinuity, where Gibbs oscillations are eliminated. Diffusion is introduced, but this is fine if the discontinuity appears due to a discretization of a high gradient with not enough accuracy. The new technique is introduced for cubic splines, but the theory presented allows to generalize the results very easily to splines of any order. The experiments presented satisfy the theoretical aspects analyzed in the paper.

Editorial Note

1946 ◽  
Vol 11 (1) ◽  
pp. 2-2
Keyword(s):  
Editorial Note ◽  
Speech Sounds ◽  
Left Hand ◽  
Hand Column ◽  
Right Hand ◽  
Infant Speech ◽  
The Right

In the article “Infant Speech Sounds and Intelligence” by Orvis C. Irwin and Han Piao Chen, in the December 1945 issue of the Journal, the paragraph which begins at the bottom of the left hand column on page 295 should have been placed immediately below the first paragraph at the top of the right hand column on page 296. To the authors we express our sincere apologies.

Is the Future the Right Time?

2010 ◽  
Vol 57 (4) ◽  
pp. 308-314 ◽  
Author(s):  
Marc Ouellet ◽  
Julio Santiago ◽  
Ziv Israeli ◽  
Shai Gabay
Keyword(s):  
Auditory Task ◽  
English Speakers ◽  
Visual Modality ◽  
Opposite Pattern ◽  
Time Line ◽  
Temporal Reference ◽  
Left Hand ◽  
Reading Direction ◽  
Mental Time Line ◽  
The Right

Spanish and English speakers tend to conceptualize time as running from left to right along a mental line. Previous research suggests that this representational strategy arises from the participants’ exposure to a left-to-right writing system. However, direct evidence supporting this assertion suffers from several limitations and relies only on the visual modality. This study subjected to a direct test the reading hypothesis using an auditory task. Participants from two groups (Spanish and Hebrew) differing in the directionality of their orthographic system had to discriminate temporal reference (past or future) of verbs and adverbs (referring to either past or future) auditorily presented to either the left or right ear by pressing a left or a right key. Spanish participants were faster responding to past words with the left hand and to future words with the right hand, whereas Hebrew participants showed the opposite pattern. Our results demonstrate that the left-right mapping of time is not restricted to the visual modality and that the direction of reading accounts for the preferred directionality of the mental time line. These results are discussed in the context of a possible mechanism underlying the effects of reading direction on highly abstract conceptual representations.

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