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3 Sentences With "convolves"

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To prove Weyl's lemma, one convolves the function u with an appropriate mollifier \varphi_\varepsilon and shows that the mollification u_\varepsilon = \varphi_\varepsilon\ast u satisfies Laplace's equation, which implies that u_\varepsilon has the mean value property. Taking the limit as \varepsilon\to 0 and using the properties of mollifiers, one finds that u also has the mean value property, which implies that it is a smooth solution of Laplace's equation.Bernard Dacorogna, Introduction to the Calculus of Variations, 2nd ed., Imperial College Press (2009), p. 148.
3D sound system with Reverberation Reconstruction flowchartThe reverberation reconstruction involves measuring the sound by a four-point microphone to measure its real delivery delays in different locations. Each microphone measures an impulse response from a time-stretched pulse signal for various time frames with various sound sources. The obtained data is applied to the 5-speaker three- dimensional sound system, as in the listening room technique. The system also convolves the head-related transfer function with the impulse response from the signal recorded by the microphones and the energy is adjusted per the original time frame of the sound signal, and an additional delay is added to the sound to match the time frame of the impulse response.
For example, in his opera-in-progress, Weaveworld, Pape "employs sudden and unpredictable patterns in streams of sound in a plasma that draws from chaos models" . The tape part for Makbénach I and III convolves "timbre paths", made from chains of sampled saxophone sounds, together with a dense series of grains following particular trajectories (produced by a computer program called Cloud Generator), in order to produce timbral transformations (; ) Pape's 1995 chamber opera Monologue uses as text the Samuel Beckett play A Piece of Monologue . His most important work is Feu toujours vivant for large orchestra and 4 sampler keyboards (1997), which was commissioned by Art Zoyd and the National Orchestra of Lille, conducted by Jean-Claude Casadesus . In 2007, Gerard Pape created the CLSI ensemble (Circle for the Liberation of Sounds & Images) with various musicians and composers like Olga Krashenko, Paul Méfano, Jacqueline Méfano, Lissa Meridan, Michael Kinney, Martin Phelps, Rodolphe Bourotte, Stefan Tiedje, Jean-Baptiste Favory.

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