ABSTRACT
This chapter focuses on basic mathematical instruments to extract statistical information from the acquired data. It provides some concepts of statistics and probability theory. The chapter talks about the instruments for the decomposition of turbulent data with a look on the objective to determine the structure of turbulent flows. It specifically focuses on Fourier analysis, proper orthogonal decomposition (POD), dynamic mode decomposition, and conditional averaging. Experimental data are classified into two broad categories: deterministic and random. The chapter also provides some definitions and fundamentals on errors quantification. The process of data regression consists in fitting data with a model function. The Fourier Transform (FT) decomposes signals into a linear combination of orthogonal sinusoidal basis functions at different frequencies. The use of POD to perform low-order modeling of turbulent flows was firstly proposed by Lumley with the aim of identifying coherent structures in the flow.
