Pulse wave | EPFL Graph Search

A pulse wave or pulse train is a type of non-sinusoidal waveform that includes square waves (duty cycle of 50%) and similarly periodic but asymmetrical waves (duty cycles other than 50%). It is a term used in synthesizer programming, and is a typical waveform available on many synthesizers. The exact shape of the wave is determined by the duty cycle or pulse width of the oscillator output. In many synthesizers, the duty cycle can be modulated (pulse-width modulation) for a more dynamic timbre. The pulse wave is also known as the rectangular wave, the periodic version of the rectangular function. The average level of a rectangular wave is also given by the duty cycle, therefore by varying the on and off periods and then averaging these said periods, it is possible to represent any value between the two limiting levels. This is the basis of pulse-width modulation. Frequency-domain representation The Fourier series expansion for a rectangular pulse wave with period T

Sampling and Exact Reconstruction of Pulses with Variable Width

Loïc Arnaud Baboulaz, Gilles Baechler, Adam James Scholefield, Martin Vetterli

Recent sampling results enable the reconstruction of signals composed of streams of fixed-shaped pulses. These results have found applications in topics as varied as channel estimation, biomedical imaging and radio astronomy. However, in many real signals, the pulse shapes vary throughout the signal. In this paper, we show how to sample and perfectly reconstruct Lorentzian pulses with variable width. Since a stream of Lorentzian pulses has a finite number of degrees of freedom per unit time, it belongs to the class of signals with finite rate of innovation (FRI). In the noiseless case, perfect recovery is guaranteed by a set of theorems. In addition, we verify that our algorithm is robust to model-mismatch and noise. This allows us to apply the technique to two practical applications: electrocardiogram (ECG) compression and bidirectional reflectance distribution function (BRDF) sampling. ECG signals are one dimensional, but the BRDF is a higher dimensional signal, which is more naturally expressed in a spherical coordinate system; this motivated us to extend the theory to the 2D and spherical cases. Experiments on real data demonstrate the viability of the proposed model for ECG acquisition and compression, as well as the efficient representation and low-rate sampling of specular BRDFs.

Institute of Electrical and Electronics Engineers2017

An Analysis of Current and Electric Field Pulses Associated With Upward Negative Lightning Flashes Initiated from the Säntis Tower

Mohammad Azadifar, Lixia He, Davide Pavanello, Marcos Rubinstein

We present a study on the characteristics of current and electric field pulses associated with upward lightning flashes initiated from the instrumented Säntis Tower in Switzerland. The electric field was measured 15 km from the tower. Upward flashes always begin with the initial stage composed of the upward‐leader phase and the initial‐continuous‐current (ICC) phase. Four types of current pulses are identified and analyzed in the paper: (1) return‐stroke pulses, which occur after the extinction of the ICC and are preceded by essentially no‐current time intervals; (2) mixed‐mode ICC pulses, defined as fast pulses superimposed on the ICC, which have characteristics very similar to those of return strokes and are believed to be associated with the reactivation of a decayed branch or the connection of a newly created channel to the ICC‐carrying channel at relatively small junction heights; (3) “classical” M‐component pulses superimposed on the continuing current following some return strokes; and (4) M‐component‐type ICC pulses, presumably associated with the reactivation of a decayed branch or the connection of a newly created channel to the ICC‐carrying channel at relatively large junction heights. We consider a data set consisting of 9 return‐stroke pulses, 70 mixed‐mode ICC pulses, 11 classical M‐component pulses, and 19 M‐component‐type ICC pulses (a total of 109 pulses). The salient characteristics of the current and field waveforms are analyzed. A new criterion is proposed to distinguish between mixed‐mode and M‐component‐type pulses, which is based on the current waveform features. The characteristics of M‐component‐type pulses during the initial stage are found to be similar to those of classical M‐component pulses occurring during the continuing current after some return strokes. It is also found that about 41% of mixed‐mode ICC pulses were preceded by microsecond‐scale pulses occurring in electric field records some hundreds of microseconds prior to the onset of the current, very similar to microsecond‐scale electric field pulses observed for M‐component‐type ICC pulses and which can be attributed to the junction of an in‐cloud leader channel to the current‐carrying channel to ground. Classical M‐component pulses and M‐component‐type ICC pulses tend to have larger risetimes ranging from 6.3 to 430 μs. On the other hand, return‐stroke pulses and mixed‐mode ICC pulses have current risetimes ranging from 0.5 to 28 μs. Finally, our data suggest that the 8‐μs criterion for the current risetime proposed by Flache et al. is a reasonable tool to distinguish between return strokes and classical M‐components. However, mixed‐mode ICC pulses superimposed on the ICC can sometimes have considerably longer risetimes, up to about 28 μs, as observed in this study.

2018

Asymptotical Analysis of Timing Imperfections in UWB Receivers

Cyril Botteron, Pierre-André Farine, John Farserotu

Abstract—In this paper, a model is proposed to analyze the influence of timing imperfections on ultra-wide bandwidth (UWB) time-hopping spread-spectrum (TH-SS) signaling schemes, where N pulses are coherently added to increase the received signal-tonoise ratio (SNR). Based on this model, we derive asymptotical (valid for large N) expressions for the received signal after pulse summation and matched filtering. As an application example, we study the influence of timing jitter and frequency offsets on the maximum SNR, assuming a 2nd derivative Gaussian pulse shape. The analytical results we obtain are verified with numerical simulations.

2004

An Analysis of Current and Electric Field Pulses Associated With Upward Negative Lightning Flashes Initiated from the Säntis Tower

Mohammad Azadifar, Lixia He, Davide Pavanello, Marcos Rubinstein

2018