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Concept# Pulse shaping

Summary

In electronics and telecommunications, pulse shaping is the process of changing a transmitted pulses' waveform to optimize the signal for its intended purpose or the communication channel. This is often done by limiting the bandwidth of the transmission and filtering the pulses to control intersymbol interference. Pulse shaping is particularly important in RF communication for fitting the signal within a certain frequency band and is typically applied after line coding and modulation.
Need for pulse shaping
Transmitting a signal at high modulation rate through a band-limited channel can create intersymbol interference. The reason for this are Fourier correspondences (see Fourier transform). A bandlimited signal corresponds to an infinite time signal, that causes neighbouring pulses to overlap. As the modulation rate increases, the signal's bandwidth increases. As soon as the spectrum of the signal is a sharp rectangular, this leads to a sinc shape in the time domain. This ha

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Related publications (9)

Jayakrishnan Unnikrishnan, Martin Vetterli

We study the design of sampling trajectories for stable sampling and the reconstruction of bandlimited spatial fields using mobile sensors. The spectrum is assumed to be a symmetric convex set. As a performance metric we use the path density of the set of sampling trajectories that is defined as the total distance traveled by the moving sensors per unit spatial volume of the spatial region being monitored. Focusing first on parallel lines, we identify the set of parallel lines with minimal path density that contains a set of stable sampling for fields bandlimited to a known set. We then show that the problem becomes ill posed when the optimization is performed over all trajectories by demonstrating a feasible trajectory set with arbitrarily low path density. However, the problem becomes well-posed if we explicitly specify the stability margins. We demonstrate this by obtaining a non-trivial lower bound on the path density of an arbitrary set of trajectories that contain a sampling set with explicitly specified stability bounds.

Jayakrishnan Unnikrishnan, Martin Vetterli

We study the design of sampling trajectories for stable sampling and reconstruction of bandlimited spatial fields using mobile sensors. As a performance metric we use the path density of a set of sampling trajectories, defined as the total distance traveled by the moving sensors per unit spatial volume of the spatial region being monitored. We obtain new results for the problem of designing stable sampling trajectories with minimal path density, that admit perfect reconstruction of bandlimited fields. In particular, we identify the set of parallel lines with minimal path density that contains a set of stable sampling for isotropic fields.

2013Certain aspects of the present disclosure relate to a method for equalizing a pulse signal corrupted by a noise and by various channel effects for obtaining a signal based on the periodic-sinc pulse, which is suitable for Finite Rate of Innovation (FRI) processing applied at a receiver of a pulse-based communication system (e.g., an Ultra-Wideband receiver).

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