Behavior of quantization noise for sinusoidal signals. A revision.

 

P. R. Pérez–Alcázar¹*, A. Santos²

 

¹ Departamento de Ingeniería Electrónica Facultad de Ingeniería, UNAM, Mexico. *pperezalcazar@fi–b.unam.mx

² Departamento de Ingeniería Electrónica Universidad Politécnica de Madrid, Spain.

 

ABSTRACT

This paper presents a brief revision of several studies presented in the literature about the behavior of quantization noise for sinusoidal signals and for uniform quantizers. From this revision, the conclusion is that quantization noise has been assumed to be additive and has a white spectrum, although some published studies, considering the problem either from a deterministic point of view or from a stochastic one, have shown a different noise behavior for some specific cases. Some of these cases are related with the parameters that characterize the sinusoidal signal and other with the conditions under which the process of conversion is realized. There are some cases that have not very been well considered in the previous literature and about which it is convenient to call attention. By this reason and using computer simulations with sinusoidal input signals, it is illustrated here that the quantization noise spectrum can show a discrete or complex structure depending on the relation between the sampling rate used and the frequency of the signal. Moreover, some points to consider in order to get a better description of the quantization noise are presented.

Palabras clave: Analog–digital conversion, quantization noise, noise spectrum.

 

RESUMEN

Este artículo presenta una breve revisión de varios estudios presentados en la literatura sobre el comportamiento del ruido de cuantización señales sinusoidales y cuantificadores uniformes. A partir de esta revisión, la conclusión es que generalmente se ha asumido que el ruido de cuantización es aditivo y tiene un espectro blanco; aunque algunos estudios publicados, considerando el problema desde un punto de vista determinístico o desde un punto de vista estocástico, han mostrado un comportamiento diferente del ruido para algunos casos específicos. Algunos de estos casos están relacionados con los parámetros que caracterizan la señal sinusoidal y otros con las condiciones bajo las cuales se realiza el proceso de conversión. Hay algunos casos que no han sido muy bien considerados en la literatura previa y sobre los cuales conviene llamar la atención. Por esta razón, utilizando simulaciones mediante computadora, con señales de entrada sinusoidales, se muestra aquí que el espectro del ruido de cuantización puede mostrar una estructura discreta o compleja dependiendo de la relación entre la velocidad de muestreo utilizada y la frecuencia de la señal. Además, algunos puntos a considerar para obtener una mejor descripción del ruido de cuantización son presentados.

Keywords: Analog–digital conversion, quantization noise, noise spectrum.

 

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