This equation is the exponential form of the integral that can be used to compute the coefficients of a Fourier Series (Exponential Form). These coefficients can be used to represent a periodic function ,\( \htmlClass{sdt-0000000096}{f} \)(\( \htmlClass{sdt-0000000118}{t} \)), with period, \( \htmlClass{sdt-0000000112}{T} \) as a Fourier series.
| \( k \) | This symbol represents any given integer, \( k \in \htmlClass{sdt-0000000122}{\mathbb{Z}}\). |
| \( e \) | This symbol represents Euler's constant. It is approximately \(2.718\). |
| \( x \) | This symbol represents a function that represents a signal. |
| \( \int \) | This is the symbol for an integral, sometimes referred to as an antiderivative. Graphically, it can be understood as the area between a curve and the axis the integral is taken with respect to. |
| \( T_{0} \) | This is the symbol for the fundamental period of a signal is the minimum duration after which the signal repeats its pattern, defining its most basic cycle. This period is crucial for analyzing the signal's frequency and understanding its repetitive behavior. |
| \( t \) | This symbol represents time. It is often measured by its SI unit seconds (\( \htmlClass{udt-0000000002}{s} \)). |
| \( a \) | This is a symbol for any generic constant. It can hold any numerical value |
| \( \pi \) | This is the symbol for pi, mathematical constant representing the ratio of a circle's circumference(\( \htmlClass{sdt-0000000128}{c} \)) to its diameter(\( \htmlClass{sdt-0000000034}{d} \)). |
| \( j \) | This symbol represents the imaginary unit, which is defined as the square root of \(-1\). \( j = \sqrt{-1}\). It is the most fundamental unit in the field of complex numbers, allowing for the expression of numbers that cannot be represented on the real number line. |