Related Experiment Video

Updated: Aug 7, 2026

A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors
11:15

A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors

Published on: May 30, 2016

A Fourier characteristic of coding sequences: origins and a non-Fourier approximation

Changchuan Yin1, Stephen S-T Yau

  • 1Department of Mathematics, Statistics and Computer Science, The University of Illinois at Chicago, Chicago, IL 60607-7045, USA.

Journal of Computational Biology : a Journal of Computational Molecular Cell Biology
|November 25, 2005
PubMed

More Related Videos

High-throughput Identification of Gene Regulatory Sequences Using Next-generation Sequencing of Circular Chromosome Conformation Capture (4C-seq)09:06

High-throughput Identification of Gene Regulatory Sequences Using Next-generation Sequencing of Circular Chromosome Conformation Capture (4C-seq)

Published on: October 5, 2018

De novo Identification of Actively Translated Open Reading Frames with Ribosome Profiling Data08:23

De novo Identification of Actively Translated Open Reading Frames with Ribosome Profiling Data

Published on: February 18, 2022

Related Concept Videos

Trigonometric Fourier series01:17

Trigonometric Fourier series

Fourier series is a foundational mathematical technique that decomposes periodic functions into an infinite series of sinusoidal harmonics. This method enables the representation of complex periodic signals as sums of simple sine and cosine functions, facilitating their analysis and interpretation in various fields, including signal processing, acoustics, and electrical engineering.
The trigonometric Fourier series specifically expresses a periodic function with a defined period T using sine...
Exponential Fourier series01:24

Exponential Fourier series

In audio signal processing, the exponential Fourier series plays a crucial role in sound synthesis, allowing complex sounds to be broken down into simpler sinusoidal components. This decomposition process is fundamental in analyzing and reconstructing musical notes and other audio signals. The exponential Fourier series expresses periodic signals as the sum of complex exponentials at both positive and negative harmonic frequencies, providing a powerful tool for signal analysis.
Euler's identity...
Properties of Fourier series I01:20

Properties of Fourier series I

The Fourier series is a powerful tool in signal processing and communications, allowing periodic signals to be expressed as sums of sine and cosine functions. A foundational property of the Fourier series is linearity. If we consider two periodic signals, their linear combination results in a new signal whose Fourier coefficients are simply the corresponding linear combinations of the original signals' coefficients. This property is crucial in applications like frequency modulation (FM) radio,...
Convergence of Fourier Series01:21

Convergence of Fourier Series

The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
Fast Fourier Transform01:10

Fast Fourier Transform

The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.