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A Fourier series is a way to represent a function as the sum of simple sine and cosine waves.

The Fourier Transform is a mathematical transform that decomposes functions depending on space or time into functions depending on spatial or temporal frequency.

The Inverse Fourier Transform is the process of recovering the original function from its frequency domain representation.

The Convolution Theorem states that the Fourier transform of a convolution of two signals is the pointwise product of their Fourier transforms.

The Discrete Fourier Transform is a type of Fourier transform used for discrete signals, often for signal and image processing.

The Fast Fourier Transform is an algorithm that computes the Discrete Fourier Transform (DFT) much faster than a direct computation.

A harmonic in the context of Fourier analysis is a component frequency of the signal that is an integer multiple of the fundamental frequency.

In Fourier analysis, $e^{ix}$ represents complex exponentials and is crucial for Euler's formula, expressing sinusoids in terms of exponentials.

The frequency spectrum is a representation of a signal in the frequency domain, showing how much of the signal lies within each given frequency band.

In Fourier series, orthogonality refers to the condition of sine and cosine functions that allows them to be independent components of the signal representation.

CTFS represents periodic, continuous-time signals as a sum of continuous-time sinusoids weighted by complex coefficients.

Gibbs Phenomenon refers to the overshoots and ripples that occur near jump discontinuities when approximating functions using their Fourier series.

Parseval's theorem states that the sum (or integral) of the square of a function is equal to the sum (or integral) of the square of its transform, used in energy and power analysis of signals.

Aliasing in Fourier analysis is the effect that occurs when a signal is sampled at a rate that is insufficient to capture the changes in the signal, resulting in a distortion called an alias.