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Related Concept Videos

State Space Representation01:27

State Space Representation

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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
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State Space to Transfer Function01:21

State Space to Transfer Function

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The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
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Tandem Mass Spectrometry01:21

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Tandem mass spectrometry is a technique that uses multiple mass analyzers in series to obtain a higher selectivity and reduce chemical noise during analyte detection. Instruments with multiple analyzers separated by an interaction cell enable secondary fragmentation and selected study of the fragment ions.Secondary fragmentations occur in the interaction cell and can be induced by various factors. Fragmentation induced by collision with inert gases, such as N2, Ar, He, etc., is called...
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Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

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The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...
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Design Example01:23

Design Example

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The innovation of touch-tone telephony revolutionized the telecommunications industry by replacing the traditional rotary dial with a dual-tone multi-frequency (DTMF) signaling system. This system uses a matrix-style keypad with buttons arranged in four rows and three columns, creating 12 distinct signals each assigned to a pair of frequencies. Each button press results in a simultaneous generation of two sinusoidal tones – one from a low-frequency group (697 to 941 Hz) and one from a...
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¹H NMR Signal Multiplicity: Splitting Patterns01:13

¹H NMR Signal Multiplicity: Splitting Patterns

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When protons A and X are coupled, their nuclear spin energy levels are slightly modified. This is because the energy required to excite proton A to a spin state parallel to proton X is slightly different from the energy required for it to become anti-parallel to spin X. Consequently, there are two possible excitation frequencies for A (A1 and A2), depending on the spin state of X, and vice versa. The mutual nature of coupling implies that the difference between frequencies A1 and A2, indicated...
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Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping
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Focus issue introduction: space-division multiplexing.

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    Single-fiber transmission capacity now exceeds 1 Pb/s due to rapid advancements in space-division multiplexing (SDM) technologies. This focus issue highlights the latest research across all SDM components and systems.

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    Area of Science:

    • Optics and Photonics
    • Telecommunications Engineering

    Background:

    • Single-fiber transmission capacity has surpassed 1 Petabit per second (Pb/s) since 2011.
    • Significant progress has been made in all facets of space-division multiplexing (SDM).

    Discussion:

    • This focus issue compiles cutting-edge research on SDM technologies.
    • It covers advancements in optical fibers, passive and active components, and transmission systems.

    Key Insights:

    • Space-division multiplexing is the key enabler for exceeding 1 Pb/s single-fiber capacity.
    • Rapid development spans components like multiplexers, amplifiers (EDFA, Raman), and ROADM/WSS.

    Outlook:

    • The collection provides a comprehensive overview of the current state-of-the-art in SDM.
    • It sets the stage for future research directions in high-capacity optical networks.