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19. Approximately dual pairs of wavelet frames

Author

Benavente, Ana, Christensen, Ole, Hasannasab, Marzieh, Kim, Hong Oh, Kim, Rae Young, and Kovac, Federico D.

Subjects
Mathematics - Functional Analysis, 42C40, 42C15
Abstract

This paper deals with structural issues concerning wavelet frames and their dual frames. It is known that there exist wavelet frames $\{a^{j/2}\psi( a^j\cdot -kb)\}_{j,k\in \mathbb Z}$ in $L^2(\mathbb R)$ for which no dual frame has wavelet structure. We first generalize this result by proving that there exist wavelet frames for which no approximately dual frame has wavelet structure. Motivated by this we show that by imposing a very mild decay condition on the Fourier transform of the generator $\psi\in L^2(\mathbb R),$ a certain oversampling $\{a^{j/2}\psi( a^j\cdot -kb/N)\}_{j,k\in \mathbb Z}$ indeed has an approximately dual wavelet frame; most importantly, by choosing the parameter $N\in \mathbb N$ sufficiently large we can get as close to perfect reconstruction as desired, which makes the approximate dual frame pairs perform equally well as the classical dual frame pairs in applications.

Published
2021

28. More Than 50 Percent Reduction in LDL Cholesterol in Patients With Target LDL <70 mg/dL After a Stroke

Author

Amarenco, Pierre, Lavallée, Philippa C., Kim, Jong S., Labreuche, Julien, Charles, Hugo, Giroud, Maurice, Lee, Byung-Chul, Mahagne, Marie-Hélène, Meseguer, Elena, Nighoghossian, Norbert, Steg, Philippe Gabriel, Vicaut, Éric, Bruckert, Eric, Kim, Jong S, Touboul, Pierre-Jean, Leys, Didier, Béjot, Yannick, Pico, Fernando, Touzé, Emmanuel, Ducrocq, Gregory, Abtan, Jérémy, Varenne, Olivier, Touboul, Pierre-Jean, Kemmel, Agnes, Syana, Fausta, Ledra, Manele, Nagasara, Tharani, Ledjeroud, Mervette, Samia, Bahous, Hadia, Hafirassou, Hazare, Benyoub, Jaghouni, Ikrame El, Yelles, Nessima, Zemouri, Sofia, Ladjeroud, Mervette, Kerai, Salim, In, YunJeong, Hobeanu, Cristina, Guidoux, Celine, Cabrejo, Lucie, Lapergue, Bertrand, Sabben, Candice, Gonzalez-Valcarcel, Jaime, Rigual, Ricardo, Sirimarco, Gaia, Martin-Bechet, Anna, Viedma, Elena, Avram, Ioan, Samson, Yves, Rosso, Charlotte, Crozier, Sophie, Leder, Sara, Léger, Anne, Deltour, Sandrine, Mutlu, Gurkan, Yger, Marion, Zavanone, Chiara, Baronnet, Flore, Pires, Christine, Lapergue, Bertrand, Wang, Adrien, Evrard, Serge, Tchikviladze, Maya, Bourdain, Frédéric, Lopez, Delphine, Pico, Fernando, de la Tour, Laetitia Bayon, Chadenat, Marie-Laure, Duong, Duc Long, Genty, Solène, Hirel, Catherine, Mutlu, Gurkan, Nifle, Chantal, Servan, Jérôme, Stanciu, Daniela, Sudacevschi, Veronica, Tir, Mélissa, Troussière, Anne-Cécile, Yeung, Jennifer, Zeghoudi, Anne-Céline, Tidafi-Bayou, Ikram, Lachaud, Sylvain, Cho, Tae-Hee, Mechtouff, Laura, Ritzenthaller, Thomas, Derex, Laurent, Albanesi, Carlo, Ong, Elodie, Benoit, Amandine, Berhoune, Nadia, Felix, Sandra, Esteban-Mader, Maud, Sibon, Igor, Kazadi, Annabelle, Rouanet, François, Renou, Pauline, Debruxelles, Sabrina, Poli, Mathilde, Sagnier, Sharmila, Mas, Jean-Louis, Domigo, Valérie, Lamy, Catherine, Bodiguel, Eric, Grimaud, Jérôme, Bohotin, Valentin, Obadia, Michael, Sabben, Candice, Morvan, Erwan, Rodier, Gilles, Vadot, Wilfried, Hénon, Hilde, Cordonnier, Charlotte, Dumont, Frédéric, Bodenant, Marie, Lucas, Christian, Moulin, Solène, Dequatre, Nelly, Alamowitch, Sonia, Muresan, Jean-Paul, Drouet, Thomas, Gallea, Magalie, Dalloz, Marie-Amélie, Delorme, Stephen, Yger, Marion, Béjot, Yannick, Loisel, Philippe, Bonnin, Carine, Bernigal, Virginie, Osseby, Guy Victor, Hervieu-BègueMarsac, Marie, Garnier, Pierre, Accassat, Sandrine, Epinat, Magali, Varvat, Jérôme, Marinescu, Doïna, Triquenot-Bagan, Aude, Ozkul- Wermester, Ozlem, Philippeau, Frédéric, Olaru, Angel, Vieillart, Anne, Lannuzel, Annie, Demoly, Alice, Wolff, Valérie, Diaconu, Mihaela, Bataillard, Marc, Montoro, Francisco Macian, Faugeras, Frédéric, Gimenez, Laeticia, Abdallah-Lebeau, Françoise, Timsit, Serge, Viakhireva-Dovganyuk, Irina, Tirel-Badets, Anne, Merrien, François-Mathias, Goas, Philippe, Rouhart, François, Jourdain, Aurore, Guillon, Benoit, Hérissson, Fanny, Sevin-Allouet, Mathieu, Nasr, Nathalie, Olivot, Jean-Marc, Lecluse, Alderic, Marc, Guillaume, Touzé, Emmanuel, de la Sayette, Vincent, Apoil, Marion, Lin, Li, Cogez, Julien, Guettier, Sophie, Godefroy, Olivier, Lamy, Chantal, Bugnicourt, Jean-Marc, Taurin, Grégory, Mérienne, Marc, Gere, Julien, Chessak, Anne-Marie, Habet, Tarik, Ferrier, Anna, Bourgois, Nathalie, Minier, Dominique, Caillier-Minier, Marie, Contégal- Callier, Fabienne, Vion, Philippe, Vaschalde, Yvan, Amrani, Mohammed El, Emilie, Zuber, Mathieu, Bruandet, Marie, Join- Lambert, Claire, Garcia, Pierre-Yves, Serre, Isabelle, Faucheux, Jean-Marc, Radji, Fatia, Leca-Radu, Elena, Debroucker, Thomas, Cumurcuc, Rodica, Cakmak, Serkan, Peysson, Stéphane, Ellie, Emmanuel, Bernady, Patricia, Moulin, Thierry, Montiel, Paola, Revenco, Eugeniu, Decavel, Pierre, Medeiros, Elisabeth, Bouveret, Myriam, Louchart, Pierre, Vaduva, Claudia, Couvreur, Grégory, Sartori, Eric, Carpentier, Alnajar, Levasseur, Michèle, Louchart, Pierre, Faucheux, Jean-Marc, Neau, Philippe, Vandamme, Xavier, Meresse, Isabelle, Stantescu, Bataillard, Marc, Ozsancak, Canan, Beauvais, Katell, Auzou, Pascal, Amevigbe, Joséphine, Vuillemet, Francis, Dugay-Arentz, Marie-Hélène, Carelli, Gabriela, Martinez, Mikel, Maillet-Vioud, Marcel, Escaillas, Jean-Pierre, Chapuis, Stéphane, Tardy, Jean, Manchon, Eric, Varnet, Olivier, Kim, Yong-Jae, Chang, Yoonkyung, Song, Tae-Jin, Kim, Jong Sung, Han, Jung-Hoon, Noh, Kyung Chul, Lee, Eun-Jae, Kang, Dong-Wha, Kwon, Sun Uck, Kwon, Boseoung, Park, Seongho, Lee, Dongwhane, Kwon, Hyuk Sung, Jeong, Daeun, Lee, MinHwan, Kim, Joonggoo, Lee, Hanbin, Nam, Hyo Jung, Lee, Sang Hun, Kim, Bum Joon, Cha, Jae-kwan, Kim, DaeHyun, Kim, Rae Young, Sohn, Sang Wuk, Shim, Dong-Hyun, Lee, Hyungjin, Nah, Hyun-Wook, Sung, Sang Min, Lee, Kyung Bok, Yoon Lee, Jeong, Yoon, Jee Eun, Kim, Eung-Gyu, Seo, Jung Hwa, Kim, Yong-Won, Hwang, Yangha, Park, Man Seok, Kim, Joon-Tae, Choi, Kang-Ho, Nam, Hyo Suk, Heo, Ji Hoe, Kim, Young Dae, Hwang, In Gun, Park, Hyung Jong, Kim, Kyoung Sub, Baek, Jang Hyun, Song, Dong Beom, Yoo, Joon Sang, Park, Jong-Moo, Kwon, Ohyun, Lee, Woong-Woo, Lee, Jung-Ju, Kang, Kyusik, Kim, Byung Kun, Lim, Jae-Sung, Oh, Mi Sun, Yu, Kyung-Ho, Hong, Bora, Jang, Mihoon, Jang, Seyoung, Jin, Jung Eun, Kim, Jei, Jeong, Hye Seon, Hong, Keun Sik, Park, Hong Kyun, Cho, Yong Jin, Bang, Oh Young, Seo, Woo-Keun, and Chung, Jongwon

Published
2023
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35. B-spline approximations of the Gaussian, their Gabor frame properties, and approximately dual frames

Author

Christensen, Ole, Kim, Hong Oh, and Kim, Rae Young

Subjects
Mathematics - Functional Analysis, 42C40, 42C15
Abstract

We prove that Gabor systems generated by certain scaled B-splines can be considered as perturbations of the Gabor systems generated by the Gaussian, with a deviation within an arbitrary small tolerance whenever the order $N$ of the B-spline is sufficiently large. As a consequence we show that for any choice of translation/modulation parameters $a,b>0$ with $ab<1,$ the scaled version of $B_N$ generates Gabor frames for $N$ sufficiently large. Considering the Gabor frame decomposition generated by the Gaussian and a dual window, the results lead to estimates of the deviation from perfect reconstruction that arise when the Gaussian is replaced by a scaled B-spline, or when the dual window of the Gaussian is replaced by certain explicitly given and compactly supported linear combinations of the B-splines. In particular, this leads to a family of approximate dual windows of a very simple form, leading to "almost perfect reconstruction" within any desired error tolerance whenever the product $ab$ is sufficiently small. In contrast, the known (exact) dual windows have a very complicated form. A similar analysis is sketched with the scaled B-splines replaced by certain truncations of the Gaussian. As a consequence of the approach we prove (mostly known) convergence results for the considered scaled B-splines to the Gaussian in the $L^p$-spaces, as well in the time-domain as in the frequency domain., Comment: Accepted for publication in J. Fourier Anal. Appl

Published
2017

43. Two-Level Excitation Current Driver to Reduce the Driving Power of an Electromagnetic Contactor.

Author

Park, Tae-Hwan, Kim, Rae-Young, and Lim, Sang-Kil

Subjects
ACTINIC flux
Abstract

As the capacity of the electrical system increases, so does the capacity of the electromagnetic contactor (MC). This increases the burden on the MC drive, which consumes unnecessary power in the system. MC is characterized by different initial starting-operating currents and holding currents to maintain contact. However, the operating voltage is constant regardless of the operating state. The initial starting current is considerably larger than that required to maintain contact. However, once the electromagnetic contactor is in the closed state, the current to maintain the contact is relatively small compared to the initial starting operating currents. Therefore, this study proposes two types of two-level excitation-current type MC drives that can reduce the drive power by employing features that have different conditions depending on the operating state of the MC. The overall drive power is reduced by applying different excitation currents based on the operating state. The controller and system proposed in this study were simulated using Powersim 9.1 (PSIM), and the feasibility was verified by manufacturing an analog-type driver using LM2576 and a digital-type driver using an MCU. The simulation and experimental results provide significant data for verifying the high performance and reliability of the proposed controller and system. [ABSTRACT FROM AUTHOR]

Published
2024
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