John von Neumann (JvN) was one of the greatest scientists and minds of the 20th century. His research encompassed a large variety of topics (especially from mathematics), and the results he obtained essentially contributed to the progress of science and technology. Within this article, one function that JvN defined long time ago, namely the cardinal sinus (sinc), was employed to define transforms to be applied on 1D signals, either in continuous or discrete time. The main characteristics of JvN Transforms (JvNTs) are founded on a theory described at length in the article. Two properties are of particular interest: orthogonality and invertibility. Both are important in the context of data compression. After building the theoretical foundation of JvNTs, the corresponding numerical algorithms were designed, implemented and tested on artificial and real signals. The last part of the article is devoted to simulations with such algorithms by using 1D signals. An extensive analysis on JvNTs effectiveness is performed as well, based on simulation results. In conclusion, JvNTs prove to be useful tools in signal processing.

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This article introduces the spline approximation concept, in the context of system identification, aiming to obtain useful autoregressive models of reduced order. Models with a small number of poles are extremely useful in real time control applications, since the corresponding regulators are easier to design and implement. The main goal here is to compare the identification models complexity when using two types of experimental data: raw (affected by noises mainly produced by sensors) and smoothed. The smoothing of raw data is performed through a least squares optimal stochastic cubic spline model. The consecutive data points necessary to build each polynomial of spline model are adaptively selected, depending on the raw data behavior. In order to estimate the best identification model (of ARMAX class), two optimization strategies are considered: a two-step one (which provides first an optimal useful model and then an optimal noise model) and a global one (which builds the optimal useful and noise models at once). The criteria to optimize rely on the signal‑to‑noise ratio, estimated both for identification and validation data. Since the optimization criteria usually are irregular in nature, a metaheuristic (namely the advanced hill climbing algorithm) is employed to search for the model optimal structure. The case study described in the end of the article is concerned with a real plant with nonlinear behavior, which provides noisy acquired data. The simulation results prove that, when using smoothed data, the optimal useful models have significantly less poles than when using raw data, which justifies building cubic spline approximation models prior to autoregressive identification.