Positive B-splines used as Mappings in the Probabilistic Quantizer

A Dithered quantizer consists of an external signal called Dither added to the input signal prior to quantization to control the statistical properties of the quantization error. In the framework known as Quantum Signal Processing (QSP) an equivalent quantizer was developed, called probabilistic qua...

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Fecha de publicación:: 2024

Institución:: Universidad Pedagógica y Tecnológica de Colombia

Repositorio:: RiUPTC: Repositorio Institucional UPTC

Idioma:: eng

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spelling	2024-06-052024-07-05T19:12:12Z2024-07-05T19:12:12Zhttps://revistas.uptc.edu.co/index.php/ingenieria/article/view/1738710.19053/uptc.01211129.v33.n68.2024.17387https://repositorio.uptc.edu.co/handle/001/14391A Dithered quantizer consists of an external signal called Dither added to the input signal prior to quantization to control the statistical properties of the quantization error. In the framework known as Quantum Signal Processing (QSP) an equivalent quantizer was developed, called probabilistic quantizer, which is able to generate a Dither signal with an arbitrary joint probability distribution. This paper demonstrates how positive B-spline functions can be used as a mapping in the probabilistic quantizer and the mathematical advantages to perform their analysis. In addition, we established a relation between the order of the B-spline and the rendering of conditional moments of the error. Experimental results show that the proposed approach performs on par with Dither quantizer, and its implementation is easier.Un Cuantificador Dither consiste en una señal externa denominada Dither que se añade a la señal de entrada antes de la cuantización para controlar las propiedades estadísticas del error de cuantización. En el marco conocido como Procesamiento Cuántico de Señales (QSP por sus siglas en inglés), se desarrolló un cuantificador equivalente denominado cuantificador probabilístico, el cual es capaz de generar una señal Dither con una distribución de probabilidad conjunta arbitraria. Este trabajo demuestra cómo las funciones B-spline positivas pueden utilizarse como mapeo en el cuantificador probabilístico y las ventajas matemáticas para realizar su análisis. Además, establecemos una relación entre el orden de la B-spline y la representación de los momentos condicionales del error. Los resultados experimentales muestran que el enfoque propuesto ofrece un rendimiento a la par que el cuantificador Dither y su implementación es más fácil.application/pdfengengUniversidad Pedagógica y Tecnológica de Colombiahttps://revistas.uptc.edu.co/index.php/ingenieria/article/view/17387/14134Copyright (c) 2024 Juan-Pablo Hoyos-Sánchez, Pablo-Emilio Jojoahttp://creativecommons.org/licenses/by/4.0http://purl.org/coar/access_right/c_abf394http://purl.org/coar/access_right/c_abf2Revista Facultad de Ingeniería; Vol. 33 No. 68 (2024): April-June 2024 (Continuous Publication); e17387Revista Facultad de Ingeniería; Vol. 33 Núm. 68 (2024): Abril-Junio 2024 (Publicación Continua); e173872357-53280121-1129B-splineconditional momentsDither quantizerprobabilistic quantizerquantum signal processingB-splinecuantificador Dithercuantificador probabilísticomomentos condicionalesprocesamiento cuántico de señalesPositive B-splines used as Mappings in the Probabilistic QuantizerB-Splines positivas usadas como mapeos en el cuantificador probabilísticoinfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_2df8fbb1info:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a477http://purl.org/coar/version/c_970fb48d4fbd8a85Hoyos-Sánchez, Juan-PabloJojoa, Pablo-Emilio001/14391oai:repositorio.uptc.edu.co:001/143912025-07-18 11:53:51.455metadata.onlyhttps://repositorio.uptc.edu.coRepositorio Institucional UPTCrepositorio.uptc@uptc.edu.co
dc.title.en-US.fl_str_mv	Positive B-splines used as Mappings in the Probabilistic Quantizer
dc.title.es-ES.fl_str_mv	B-Splines positivas usadas como mapeos en el cuantificador probabilístico
title	Positive B-splines used as Mappings in the Probabilistic Quantizer
spellingShingle	Positive B-splines used as Mappings in the Probabilistic Quantizer B-spline conditional moments Dither quantizer probabilistic quantizer quantum signal processing B-spline cuantificador Dither cuantificador probabilístico momentos condicionales procesamiento cuántico de señales
title_short	Positive B-splines used as Mappings in the Probabilistic Quantizer
title_full	Positive B-splines used as Mappings in the Probabilistic Quantizer
title_fullStr	Positive B-splines used as Mappings in the Probabilistic Quantizer
title_full_unstemmed	Positive B-splines used as Mappings in the Probabilistic Quantizer
title_sort	Positive B-splines used as Mappings in the Probabilistic Quantizer
dc.subject.en-US.fl_str_mv	B-spline conditional moments Dither quantizer probabilistic quantizer quantum signal processing
topic	B-spline conditional moments Dither quantizer probabilistic quantizer quantum signal processing B-spline cuantificador Dither cuantificador probabilístico momentos condicionales procesamiento cuántico de señales
dc.subject.es-ES.fl_str_mv	B-spline cuantificador Dither cuantificador probabilístico momentos condicionales procesamiento cuántico de señales
description	A Dithered quantizer consists of an external signal called Dither added to the input signal prior to quantization to control the statistical properties of the quantization error. In the framework known as Quantum Signal Processing (QSP) an equivalent quantizer was developed, called probabilistic quantizer, which is able to generate a Dither signal with an arbitrary joint probability distribution. This paper demonstrates how positive B-spline functions can be used as a mapping in the probabilistic quantizer and the mathematical advantages to perform their analysis. In addition, we established a relation between the order of the B-spline and the rendering of conditional moments of the error. Experimental results show that the proposed approach performs on par with Dither quantizer, and its implementation is easier.
publishDate	2024
dc.date.accessioned.none.fl_str_mv	2024-07-05T19:12:12Z
dc.date.available.none.fl_str_mv	2024-07-05T19:12:12Z
dc.date.none.fl_str_mv	2024-06-05
dc.type.none.fl_str_mv	info:eu-repo/semantics/article
dc.type.coar.fl_str_mv	http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.coarversion.fl_str_mv	http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.version.spa.fl_str_mv	info:eu-repo/semantics/publishedVersion
dc.type.coarversion.spa.fl_str_mv	http://purl.org/coar/version/c_970fb48d4fbd8a477
status_str	publishedVersion
dc.identifier.none.fl_str_mv	https://revistas.uptc.edu.co/index.php/ingenieria/article/view/17387 10.19053/uptc.01211129.v33.n68.2024.17387
dc.identifier.uri.none.fl_str_mv	https://repositorio.uptc.edu.co/handle/001/14391
url	https://revistas.uptc.edu.co/index.php/ingenieria/article/view/17387 https://repositorio.uptc.edu.co/handle/001/14391
identifier_str_mv	10.19053/uptc.01211129.v33.n68.2024.17387
dc.language.none.fl_str_mv	eng
dc.language.iso.spa.fl_str_mv	eng
language	eng
dc.relation.none.fl_str_mv	https://revistas.uptc.edu.co/index.php/ingenieria/article/view/17387/14134
dc.rights.en-US.fl_str_mv	Copyright (c) 2024 Juan-Pablo Hoyos-Sánchez, Pablo-Emilio Jojoa http://creativecommons.org/licenses/by/4.0
dc.rights.coar.fl_str_mv	http://purl.org/coar/access_right/c_abf2
dc.rights.coar.spa.fl_str_mv	http://purl.org/coar/access_right/c_abf394
rights_invalid_str_mv	Copyright (c) 2024 Juan-Pablo Hoyos-Sánchez, Pablo-Emilio Jojoa http://creativecommons.org/licenses/by/4.0 http://purl.org/coar/access_right/c_abf394 http://purl.org/coar/access_right/c_abf2
dc.format.none.fl_str_mv	application/pdf
dc.publisher.en-US.fl_str_mv	Universidad Pedagógica y Tecnológica de Colombia
dc.source.en-US.fl_str_mv	Revista Facultad de Ingeniería; Vol. 33 No. 68 (2024): April-June 2024 (Continuous Publication); e17387
dc.source.es-ES.fl_str_mv	Revista Facultad de Ingeniería; Vol. 33 Núm. 68 (2024): Abril-Junio 2024 (Publicación Continua); e17387
dc.source.none.fl_str_mv	2357-5328 0121-1129
institution	Universidad Pedagógica y Tecnológica de Colombia
repository.name.fl_str_mv	Repositorio Institucional UPTC
repository.mail.fl_str_mv	repositorio.uptc@uptc.edu.co
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Positive B-splines used as Mappings in the Probabilistic Quantizer

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