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Relating observability and compressed sensing of time-varying signals in recurrent linear networks

MohammadMehdi Kafashan1, Anirban Nandi1, ShiNung Ching2

  • 1Department of Electrical and Systems Engineering, Washington University in St. Louis, One Brookings Drive, Campus Box 1042, MO 63130, United States.

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Linear time-invariant Systems01:23

Linear time-invariant Systems

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Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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Basic Continuous Time Signals01:22

Basic Continuous Time Signals

Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
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Classification of Systems-II01:31

Classification of Systems-II

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Classification of Signals01:30

Classification of Signals

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Sampling Continuous Time Signal

In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
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