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Parseval's Theorem

Parseval's Theorem

Parseval's theorem is a fundamental concept in signal processing and harmonic analysis. It asserts that for a periodic function, the average power of the signal over one period equals the sum of the squared magnitudes of all its complex Fourier coefficients. This theorem, named after Marc-Antoine Parseval, provides a powerful tool for analyzing the energy distribution in signals.
Interestingly, Parseval's theorem also holds for the trigonometric form of the Fourier series, which expresses a...

Parseval's Theorem for Fourier transform

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...

Quartile

Quartile

Quartiles are numbers that separate the data into quarters. Quartiles may or may not be part of the data. To find the quartiles, first, find the median or second quartile. The first quartile, Q1, is the middle value of the lower half of the data, and the third quartile, Q3, is the middle value, or median, of the upper half of the data. To get the idea, consider the same data set:
1; 1; 2; 2; 4; 6; 6.8; 7.2; 8; 8.3; 9; 10; 10; 11.5
The median or second quartile is seven. The lower half of the...

Diffusion

Diffusion

Diffusion is the passive movement of substances down their concentration gradients—requiring no expenditure of cellular energy. Substances, such as molecules or ions, diffuse from an area of high concentration to an area of low concentration in the cytosol or across membranes. Eventually, the concentration will even out, with the substance moving randomly but causing no net change in concentration. Such a state is called dynamic equilibrium, which is essential for maintaining overall...

Diffusion

Diffusion

Diffusion is a type of passive transport. In passive transport, a substance tends to move from an area of high concentration to an area of low concentration until the concentration is equal across the space. For example, take the diffusion of substances through the air. When someone opens a perfume bottle in a room filled with people, the perfume is at its highest concentration in the bottle and is at its lowest at the edges of the room. The perfume vapor will diffuse, or spread away, from the...

Olfaction

Olfaction

The sense of smell is achieved through the activities of the olfactory system. It starts when an airborne odorant enters the nasal cavity and reaches olfactory epithelium (OE). The OE is protected by a thin layer of mucus, which also serves the purpose of dissolving more complex compounds into simpler chemical odorants. The size of the OE and the density of sensory neurons varies among species; in humans, the OE is only about 9-10 cm2.
The olfactory receptors are embedded in the cilia of the...

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Related Experiment Video

Updated: Jun 17, 2026

Imaging Odor-Evoked Activities in the Mouse Olfactory Bulb using Optical Reflectance and Autofluorescence Signals

Imaging Odor-Evoked Activities in the Mouse Olfactory Bulb using Optical Reflectance and Autofluorescence Signals

Published on: October 31, 2011

An interview with Olivier Pourquie.

James Briscoe¹

¹National Institute of Medical Research, The Ridgeway, Mill Hill, London NW7 1AA, UK. jbrisco@nimr.mrc.ac.uk

Development (Cambridge, England)

|January 19, 2010

Summary

Olivier Pourquié is the new Editor in Chief of Development, bringing his expertise in genetics and molecular biology to guide the journal. His research interests will shape the future content and direction of this key publication in developmental biology.

Area of Science:

Developmental Biology
Genetics
Molecular and Cellular Biology

Background:

Olivier Pourquié appointed as the new Director of the Institute of Genetics and Molecular and Cellular Biology (IGBMC).
Pourquié assumes the role of Editor in Chief for the journal Development.
This transition marks a significant leadership change within the developmental biology community.

Discussion:

The interview with James Briscoe explores Olivier Pourquié's extensive research career.
Focus on Pourquié's research interests in genetics and molecular and cellular biology.
Discussion on how these interests will influence the journal's future content.

Key Insights:

Pourquié's leadership signifies a new era for the journal Development.

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Published on: October 31, 2011

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His background in genetics and molecular biology will enrich the journal's scope.

The appointment is expected to foster advancements in developmental biology research.

Outlook:

Future content of Development will likely reflect Pourquié's research focus.
Potential for new directions and expanded coverage in developmental biology.
Strengthening the journal's position as a leading publication in the field.