α−spline functions, which are a generalization of conventional B−splines, are defined with several parameters which provide more flexibility in terms of the variety of shapes that the functions can adopt. Because of this feature, the α−spline functions have shown improvements in the performance of several applications, including the design of digital filters. This article proposes a novel parametrization to generate new families of α−spline functions that allows a more efficient control of the shape of these functions. Different combinations of parameters are presented, and a detailed analysis of the properties of the new functions is carried out. In addition, the new α−spline functions are applied to the design of digital filters, providing an appropriate design procedure. The characteristics of the new filters are analysed and compared with previous design techniques, demonstrating the remarkable superiority of their performance.

The massive deployment of light-emitting diode (LED) lightning infrastructure has opened the opportunity to reuse it as visible light communication (VLC) to leverage the current RF spectrum crisis in indoor scenarios. One of the main problems in VLC is the limited dynamic range of LEDs and their nonlinear response, which may lead to a severe degradation in the communication, and more specifically in the bit error rate (BER). This is aggravated by the extensive usage of multicarrier multiplexing, based on optical orthogonal frequency division multiplexing (O-OFDM), characterized by a high peak-to-average power ratio. Here, we present a chaos-based coded modulation (CCM) setup specifically adapted to the LED nonlinearities. It replaces the usual modulation, while keeping the multicarrier O-OFDM structure unchanged. First, we obtain a semi-analytical bound for the bit error probability, taking into account the LED nonlinear response. The bound results particularly tight for the range of signal-to-noise ratio of interest. Then, we propose a method to design the modulator based on optimization techniques. The objective function is the semi-analytical bound, and the optimization is applied to a parameterization of the CCM conjugation function. This appropriately shapes the chaotic waveform and leads to BER improvements that outperform classical counterparts under ideal predistortion.

Nearly perfect reconstruction (N-PR) modified discrete Fourier Transform (MDFT) filter banks (FBs) have been widely applied to signal coding and their use for data transmission in multicarrier communications has also been addressed in the literature. However, comparison and assessment of the performance of alternative designs for uniform N-PR MDFT-based systems is hampered by the lack of explicit formulas for easily calculating their expected performance. In this sense, this work introduces a unified formulation which can be used for the three different kinds of uniform N-PR MDFT filter banks which have been described in the literature. We demonstrate that the relationship between output and input signals is identical for all of them when a filter bank (FB) configuration is considered. From this expression, amplitude distortion and aliasing errors can be measured. With respect to filter bank multicarrier (FBMC) systems, two new measures that bound the maximum level of intercarrier and intersymbol interferences are defined.