Divertimento con wavelets

En este trabajo se presenta una pequeña introducción a las wavelets. Estas se interpretan com otra forma de mirar la inormación, formada por diferentes niveles o capas. En concreto se pone el ejemplo de una wavelet basada en la descomposición de una señal en una capa formada por el valñor medio de las muestras tomadas de dos en dos y otra capa formada por su difernecia, esto equivaldira al procedimiento que hacemos los electrópnicos cuando refiriéndonos a un amplificador difeencial preferimos havlar de la tenisón en modo común y la tensión diferencial en lugar de hablar del valor de tensión de cada entrada. En la conferencia se podrá escuchar diferentes melodías musicales descompuestas en diferentes capas mediante wavelets y se podrá apreciar el efecto que se produce debido al aliasing qe ello comporta. También se proponen las wavelets una forma de codificar un mensaje.Postprint (published version

Efficient implementation with FIR filters of operators based on B-splines to represent and classify signals of one and two dimensions

Peer ReviewedPostprint (published version

Decimator filter based on B-splines

Peer Reviewe

Decimator filter based on B-splines

The cascaded integrator-comb (CIC) filters are widely used as decimators in many applications, such as in delta sigma AD converters to decimate the sampled signal on its output. One problem with these filters is that by increasing its order to improve the signal attenuation in the stop band, worsens the passband response. In this paper we propose a so-called least-squares filters (LSF) based on B-splines to improve that response, compensating for CIC filter drop and flattening the magnitude response of the pass band. We also study the relationship between the CIC filters, otherwise called moving average, and the B-splines expanded by an integer factor. We show that the least-squares filters based on B-splines can be decomposed in CIC filters, with a higher order than the splines used, plus a compensator filter. Another important contribution of this work are the FIR approximations of anti-causal IIR filters needed to implement LSFs.Peer ReviewedPostprint (published version

Efficient cubic spline interpolation implemented with FIR filters

Classical Cubic spline interpolation needs to solve a set of equations of high dimension. In this work we show how to compute the interpolant using a FIR digital filter, with a reduced number of operations per interpolated point and high accuracy. Additionally, the computation can be made on real time as the signal samples are acquired. Following this approach, we show how to obtain easily the derivatives of the interpolant in a similar way, and also signal approximations to reduce the oscillations that appear when using high order splines. These techniques are very well suited to compute continuous representations of image contours on closed shapes and to find its curvature and singularities.Peer ReviewedPostprint (published version

MÈTODES ESTADÍSTICS A L'ENGINYERIA (2n quadrimestre, 1a avaluació)

Examen per a Mecànica i Electrònica (tarda