In the field of mathematics, aside from elementary and algebraic functions, there is a large group of special functions. In this chapter, a few of special functions that are more often used in signal processing are introduced. Namely, complex exponential, sinus cardinal, Heaviside step (a.k.a. unit step), sign, ramp, rectangular, and triangular functions are briefly studied. A bit more space is devoted to Dirac delta function (distribution) \(\delta (t)\) and its properties. For the sake of transition to mathematics for signal processing, the traditional “x” variable is replaced with “t” implying time domain progression.

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Elementary Special Functions

  • Robert Sobot

摘要

In the field of mathematics, aside from elementary and algebraic functions, there is a large group of special functions. In this chapter, a few of special functions that are more often used in signal processing are introduced. Namely, complex exponential, sinus cardinal, Heaviside step (a.k.a. unit step), sign, ramp, rectangular, and triangular functions are briefly studied. A bit more space is devoted to Dirac delta function (distribution) \(\delta (t)\) and its properties. For the sake of transition to mathematics for signal processing, the traditional “x” variable is replaced with “t” implying time domain progression.