Section outline

  • The Week consists of the following lessons: 

    • Introduction to stochastic processes. We show what a stochastic process is, when it is stationary, and how it can be modelled and characterized by first and higher order statistics, and we discuss the role of moments like mean and cross-correlation. 

    • Stationarity, ergodicity, and memory. The concept of ergodicity allows us to link temporal and ensemble statistics and estimate statistics by a time-limited observation. We also show how to derive statistics of discrete processes from continuous ones. 

    • Power Spectrum Density is introduced, illustrating its link with autocorrelation, uses, and estimation: the periodogram (benefits and limitations) and the spectrum analyzer. White processes are defined in continuous and discrete cases. 

    • Processes and LTI systems. The lesson shows how Linear Time Invariant interacts with processes: how input and output statistics like cross-spectra or auto-correlation are related to the LTI impulse response, and how these properties can be used in practical applications. 

    • Examples and applications. Three examples from real-world applications are introduced and discussed within two talks.  

    • The first is estimating delay at the base of positioning and navigation in GNSS or RADAR. It is carried out as a complete analysis, showing how to assess and qualify the delay in a simple but instructive case.  

    • The second example illustrates the base of the numerical transmissions, and one application to transmission over huge (astronomic) distances.  

    • The third and last example refers to the principle of operation of a linear antenna array, and how the data collected by the elementary antennas can be processed to digitally ‘point’ the array.