A describing function study of saturated quantization and its application to the stability analysis of multi-bit sigma delta modulators

Just as their single-bit counterparts, multi-bit sigma delta modulators exhibit nonlinear behavior due to the presence of the quantizer in the loop. In the multi-bit case this is caused by the fact that any quantizer has a limited output range and hence gives an implicit saturation effect. Due to this, any multi-bit modulator is prone to modulator overloading. Unfortunately, until now, designers had to rely on extensive time-domain simulations to predict the overloading level, because there is no adequate analytical theory to model this effect. In this work, we have developed such an analytical theory based on multiple input describing function analysis. This way, we obtained expressions for the signal gain, the noise gain and the variance of the quantization noise. Here, both the case of DC as well as sinusoidal signals was considered. These results were used for the stability analysis of multi-bit Sigma Delta modulators, which allows to predict the overloading level. Code implementing the proposed expressions is available for download at http://cas1.elis.ugent. be/cas/en/download

Nonlinear Stability Prediction of Multibit Delta-Sigma Modulators for Sinusoidal Inputs

This paper proposes a novel algorithm that can be integrated with various design and evaluation tools, to more accurately and rapidly predict stability in multi-bit delta-sigma (Δ-Σ) modulators. Analytical expressions using the nonlinear gains from the concept of modified nonlinearity in control theory are incorporated into the mathematical model of multi-bit Δ-Σ modulators to predict the stable amplitude limits for sinusoidal input signals. The nonlinear gains lead to a set of equations which can numerically estimate the quantizer gain as a function of the input sinusoidal signal amplitude. This method is shown to accurately predict the stable amplitude limits of sinusoids for 2nd-, 3rd-, 4th-, 5th- and 6th-order 3- and 5-level mid-tread quantizer based Δ-Σ modulators. The algorithm is simple to apply and can be extended to midrise quantizers or to any number of quantizer levels. The only required input parameters for this algorithm are the number of quantizer levels and the coefficients of the noise transfer function

Tutorial web de técnicas de digitalización de audio para la asignatura Tratamiento digital de audio

El objetivo del presente proyecto fin de carrera es el desarrollo de un Tutorial Web para la asignatura de Tratamiento Digital de Audio, impartida en el tercer curso de Ingeniería Técnica de Telecomunicación, especialidad Sonido e Imagen. Este tutorial aborda las técnicas de digitalización más comunes aplicadas en audio digital para mejorar la relación señal – ruido de la secuencia digitalizada, que son, concretamente: sobremuestreo, dither y Noise-Shaping. Se expondrán, por tanto, los conceptos teóricos de la materia en combinación con aplicaciones interactivas que faciliten la experimentación práctica de las técnicas estudiadas._________________________________________El Tutorial de Técnicas de Digitalización de Audio está disponible on-line en la url: http://www.tsc.uc3m.es/~sescalona/TutorialTecnicasDigitalizacionAudio.html Si el servidor no está disponible o existe algún problema de acceso, se adjunta el mismo en el fichero comprimido adjunto para ejecutarlo off-line.Ingeniería Técnica en Sonido e Image