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Related Concept Videos

Properties of Fourier series II01:21

Properties of Fourier series II

Time scaling of signals is a crucial concept in signal processing that affects the Fourier series representation without altering its coefficients. The process modifies the fundamental frequency, thereby changing how the series represents the signal over time. This principle is essential in various applications, including audio and image processing, where signal manipulation is frequent. Understanding function symmetries is fundamental to simplifying the Fourier series.
A function f(t) is...
Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...
Basic signals of Fourier Transform01:07

Basic signals of Fourier Transform

The Fourier Transform is a pivotal mathematical tool in signal processing, enabling the transformation of time-domain signals into their frequency-domain representations. Among the numerous elements within this domain, certain functions like the sinc function, delta function, and exponential signals hold significant importance due to their unique properties and implications.
The sinc function, defined as sinc(x) = sin(πx)/(πx), is particularly notable for its symmetry and behavior at zero. It...
Properties of Fourier Transform I01:21

Properties of Fourier Transform I

The application of Fourier Transform properties in radio broadcasting is multifaceted, enabling significant advancements in the way signals are transmitted and received. Key areas where these properties are utilized include simultaneous multi-channel transmission, audio clip speed adjustments, live broadcast delays for different time zones, audio frequency adjustments, and signal demodulation.
In radio broadcasting, multiple audio signals often need to be transmitted simultaneously. The Fourier...
Properties of Fourier Transform II01:24

Properties of Fourier Transform II

The Fourier Transform (FT) is an essential mathematical tool in signal processing, transforming a time-domain signal into its frequency-domain representation. This transformation elucidates the relationship between time and frequency domains through several properties, each revealing unique aspects of signal behavior.
The Frequency Shifting property of Fourier Transforms highlights that a shift in the frequency domain corresponds to a phase shift in the time domain. Mathematically, if x(t) has...
Parseval's Theorem for Fourier transform01:15

Parseval's Theorem for Fourier transform

Parseval's theorem is a fundamental principle in signal processing that enables the calculation of a signal's energy in either the time domain or the frequency domain. This theorem is pivotal in demonstrating energy conservation between these two domains, ensuring that the computed energy value remains consistent regardless of the domain of analysis.
To understand Parseval's theorem, it is essential to first comprehend how signal energy is typically calculated. When considering a signal's...

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Related Experiment Video

Updated: Jul 2, 2026

Combined Invasive Subcortical and Non-invasive Surface Neurophysiological Recordings for the Assessment of Cognitive and Emotional Functions in Humans
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Published on: May 19, 2016

Fourier shell correlation threshold criteria.

Marin van Heel1, Michael Schatz

  • 1Imperial College London, Department of Biological Sciences, London SW7 2AY, UK. m.vanheel@imperial.ac.uk

Journal of Structural Biology
|August 30, 2005
PubMed
Summary
This summary is machine-generated.

Fixed Fourier shell correlation (FSC) thresholds are unreliable for determining reproducible resolution in electron microscopy. New information-based threshold curves offer a more statistically sound approach for assessing reconstruction quality.

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Area of Science:

  • Structural biology
  • Electron microscopy

Background:

  • The Fourier shell correlation (FSC) is the standard measure for electron microscopy reconstruction quality.
  • Determining a reproducible FSC threshold for resolution remains controversial.

Purpose of the Study:

  • To investigate the theoretical behavior of FSC and factors influencing it.
  • To evaluate the validity of fixed FSC thresholds for reproducible resolution criteria.

Main Methods:

  • Theoretical analysis of FSC behavior.
  • Model experiments to test FSC threshold validity.
  • Discussion of sigma-factor and information-based threshold curves.

Main Results:

  • Fixed FSC thresholds (e.g., 0.5) are not statistically sound for reproducible resolution.
  • Factors like voxel count, structural symmetry, and size affect FSC.
  • Information-based threshold curves provide a better measure for interpretation.

Conclusions:

  • Fixed FSC thresholds are based on incorrect statistical assumptions.
  • New information-based FSC threshold curves offer a more reliable criterion for assessing resolution in 3D reconstructions.