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Lecture

Fourier Transform: Basics and Applications

In course

MICRO-561: Fundamentals of biomicroscopy

Introduction to the basic operational principles of the most commonly used optical microscopes such as widefield and fluorescence.
Introduction to essential microscopy components such as lenses, objectives, filters, cameras and light sources. ...

Description

This lecture covers the basics of Fourier transform, including spatial and temporal functions, Fourier transform pairs, and examples of Fourier transforms of various functions such as impulse, Gaussian, rectangular, and harmonic functions. The instructor explains the concept of spatial frequency and temporal frequency, and demonstrates the application of Fourier transform in analyzing different types of functions.

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Instructors (2)

Arne Seitz

04/1996-06/2000 Scientific co-worker at Philipps-University of Marburg, Dep. of Physical Chemistry 07/2000-10/2002 Post Doc at Max-Planck Unit for Structural Molecular Biology in Hamburg 11/2002-11/2005 Post Doc at European Molecular Biolohy Laboratory (EMBL), Cell Biology and Cell Biophysics Programme 11/2005-03/2009 Staff Scientist at Advanced Light Microscopy Facility, EMBL 04/2009- Head of Bioimaging and Optics platforme (BIOP), Ecole Polytechnique Fédérale de Lausanne (EPFL)

Hatice Altug

2020-current Full Professor at the Institute of Bioengineering, EPFL, Switzerland2013-2020 Associate Professor (with tenure) at the Institute of Bioengineering, EPFL, Switzerland 2013 Associate Professor (with tenure) at Electrical and Computer Engineering Department of Boston University, USA 2007-2013 Assistant Professor (tenure-track) at Electrical and Computer Engineering Department of Boston University, USA 2007 Post-doctoral Fellow at Center for Engineering in Medicine of Harvard Medical School, USA 2000-2007 PhD. in Applied Physics at Stanford University, USA 1996-2000 B.S. in Physics at Bilkent University, Turkey

Official source

Ontological neighbourhood

Information engineering

Signal processing: Fourier analysis

Related concepts (24)

Fourier transform

In physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made the Fourier transform is sometimes called the frequency domain representation of the original function.

Discrete Fourier transform

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT (IDFT) is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies.

Discrete-time Fourier transform

In mathematics, the discrete-time Fourier transform (DTFT), also called the finite Fourier transform, is a form of Fourier analysis that is applicable to a sequence of values. The DTFT is often used to analyze samples of a continuous function. The term discrete-time refers to the fact that the transform operates on discrete data, often samples whose interval has units of time. From uniformly spaced samples it produces a function of frequency that is a periodic summation of the continuous Fourier transform of the original continuous function.

Fractional Fourier transform

In mathematics, in the area of harmonic analysis, the fractional Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform. It can be thought of as the Fourier transform to the n-th power, where n need not be an integer — thus, it can transform a function to any intermediate domain between time and frequency. Its applications range from filter design and signal analysis to phase retrieval and pattern recognition.

Spatial frequency

In mathematics, physics, and engineering, spatial frequency is a characteristic of any structure that is periodic across position in space. The spatial frequency is a measure of how often sinusoidal components (as determined by the Fourier transform) of the structure repeat per unit of distance. The SI unit of spatial frequency is cycles per meter (m). In applications, spatial frequency is often expressed in units of cycles per millimeter (mm) or equivalently per mm. In wave propagation, the spatial frequency is also known as wavenumber.

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