Fourier analysis and Fourier optics

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Difference between Fourier analysis and Fourier optics

Fourier analysis vs. Fourier optics

In mathematics, Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier optics is the study of classical optics using Fourier transforms (FTs), in which the wave is regarded as a superposition of plane waves that are not related to any identifiable sources; instead they are the natural modes of the propagation medium itself.

Convolution

In mathematics (and, in particular, functional analysis) convolution is a mathematical operation on two functions (f and g) to produce a third function, that is typically viewed as a modified version of one of the original functions, giving the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated.

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Convolution theorem

In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution is the pointwise product of Fourier transforms.

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Cross-correlation

In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other.

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Digital image processing

In computer science, Digital image processing is the use of computer algorithms to perform image processing on digital images.

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Dirac delta function

In mathematics, the Dirac delta function (function) is a generalized function or distribution introduced by the physicist Paul Dirac.

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Eigenfunction

In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function f in that space that, when acted upon by D, is only multiplied by some scaling factor called an eigenvalue.

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Fourier transform

The Fourier transform (FT) decomposes a function of time (a signal) into the frequencies that make it up, in a way similar to how a musical chord can be expressed as the frequencies (or pitches) of its constituent notes.

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Frequency

Frequency is the number of occurrences of a repeating event per unit of time.

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Harmonic

A harmonic is any member of the harmonic series, a divergent infinite series.

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Nyquist–Shannon sampling theorem

In the field of digital signal processing, the sampling theorem is a fundamental bridge between continuous-time signals (often called "analog signals") and discrete-time signals (often called "digital signals").

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Optics

Optics is the branch of physics which involves the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it.

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Orthogonal functions

In mathematics, orthogonal functions belong to a function space which is a vector space that has a bilinear form.

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Partial differential equation

In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.

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Phase (waves)

Phase is the position of a point in time (an instant) on a waveform cycle.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Signal processing

Signal processing concerns the analysis, synthesis, and modification of signals, which are broadly defined as functions conveying "information about the behavior or attributes of some phenomenon", such as sound, images, and biological measurements.

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Wavelet

A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases, and then decreases back to zero.

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Whittaker–Shannon interpolation formula

The Whittaker–Shannon interpolation formula or sinc interpolation is a method to construct a continuous-time bandlimited function from a sequence of real numbers.

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Window function

In signal processing, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen interval.

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