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...
| Main Authors: | , |
|---|---|
| Format: | Online |
| Language: | eng |
| Published: |
Universidad Pedagógica y Tecnológica de Colombia
2024
|
| Subjects: | |
| Online Access: | https://revistas.uptc.edu.co/index.php/ingenieria/article/view/17387 |
| _version_ | 1801706105596805120 |
|---|---|
| author | Hoyos-Sánchez, Juan-Pablo Jojoa, Pablo-Emilio |
| author_facet | Hoyos-Sánchez, Juan-Pablo Jojoa, Pablo-Emilio |
| author_sort | Hoyos-Sánchez, Juan-Pablo |
| collection | OJS |
| 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. |
| format | Online |
| id | oai:oai.revistas.uptc.edu.co:article-17387 |
| institution | Revista Facultad de Ingeniería |
| language | eng |
| publishDate | 2024 |
| publisher | Universidad Pedagógica y Tecnológica de Colombia |
| record_format | ojs |
| spelling | oai:oai.revistas.uptc.edu.co:article-173872024-06-06T01:05:54Z Positive B-splines used as Mappings in the Probabilistic Quantizer B-Splines positivas usadas como mapeos en el cuantificador probabilístico Hoyos-Sánchez, Juan-Pablo Jojoa, Pablo-Emilio B-spline conditional moments Dither quantizer probabilistic quantizer quantum signal processing B-spline cuantificador Dither cuantificador probabilístico momentos condicionales procesamiento cuántico de señales 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. 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. Universidad Pedagógica y Tecnológica de Colombia 2024-06-05 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion application/pdf https://revistas.uptc.edu.co/index.php/ingenieria/article/view/17387 10.19053/uptc.01211129.v33.n68.2024.17387 Revista Facultad de Ingeniería; Vol. 33 No. 68 (2024): April-June 2024 (Continuous Publication); e17387 Revista Facultad de Ingeniería; Vol. 33 Núm. 68 (2024): Abril-Junio 2024 (Publicación Continua); e17387 2357-5328 0121-1129 eng https://revistas.uptc.edu.co/index.php/ingenieria/article/view/17387/14134 Copyright (c) 2024 Juan-Pablo Hoyos-Sánchez, Pablo-Emilio Jojoa http://creativecommons.org/licenses/by/4.0 |
| spellingShingle | B-spline conditional moments Dither quantizer probabilistic quantizer quantum signal processing B-spline cuantificador Dither cuantificador probabilístico momentos condicionales procesamiento cuántico de señales Hoyos-Sánchez, Juan-Pablo Jojoa, Pablo-Emilio Positive B-splines used as Mappings in the Probabilistic Quantizer |
| title | Positive B-splines used as Mappings in the Probabilistic Quantizer |
| title_alt | B-Splines positivas usadas como mapeos en el cuantificador probabilístico |
| 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_short | Positive B-splines used as Mappings in the Probabilistic Quantizer |
| title_sort | positive b splines used as mappings in the probabilistic quantizer |
| topic | B-spline conditional moments Dither quantizer probabilistic quantizer quantum signal processing B-spline cuantificador Dither cuantificador probabilístico momentos condicionales procesamiento cuántico de señales |
| topic_facet | B-spline conditional moments Dither quantizer probabilistic quantizer quantum signal processing B-spline cuantificador Dither cuantificador probabilístico momentos condicionales procesamiento cuántico de señales |
| url | https://revistas.uptc.edu.co/index.php/ingenieria/article/view/17387 |
| work_keys_str_mv | AT hoyossanchezjuanpablo positivebsplinesusedasmappingsintheprobabilisticquantizer AT jojoapabloemilio positivebsplinesusedasmappingsintheprobabilisticquantizer AT hoyossanchezjuanpablo bsplinespositivasusadascomomapeosenelcuantificadorprobabilistico AT jojoapabloemilio bsplinespositivasusadascomomapeosenelcuantificadorprobabilistico |
