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Signals and Systems

Group Velocity: Mathematical Proof

The term group velocity defines the rate at which the envelope of a signal propagates in a transmission medium. This signal transmitted over the medium is obtained when a modulating signal modulates a central frequency, typically called the carrier [1]. As a result, the modulating signal and the envelope are equivalent. While the envelope propagates […]

Categories
Signals and Systems

Frequency Constant Phase Shift and Distortion

Transmission media and electronic components can have multiple effects on the signals propagating through them [1] [2]. To avoid phase distortion, it is necessary that the phase of the system, the phase shift introduced by the medium, is linear with frequency. This case, whose effect consists of a time delay of the signal, is often […]

Categories
Signals and Systems

The Mathematics of Linear Distortion

The mathematics of linear distortion only applies to linear and time invariant systems [1] [2]. Therefore, these systems and their translation to the frequency domain, where the mathematical analysis is simplified, are briefly summarized. Then it is discussed how the presented theory can be applied to real transmission media and/or electronic components. Finally, the mathematics […]