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Reconstruction of Signal using Interpolation

Reconstruction of Signal using Interpolation

Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next sampling...

NMR Spectrometers: Radiofrequency Pulses and Pulse Sequences

NMR Spectrometers: Radiofrequency Pulses and Pulse Sequences

A pulse is a short burst of radio waves distributed over a range of frequencies that simultaneously excites all the nuclei in the sample. Upon passing a radio frequency pulse along the x-axis, the nuclei absorb energy corresponding to their Larmor frequencies and achieve resonance. This shifts the net magnetization vector from the z-axis toward the transverse plane. This angle of rotation of the magnetization vector, or the flip angle, is proportional to the duration and intensity of the pulse.

Double Resonance Techniques: Overview

Double Resonance Techniques: Overview

Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
Spin decoupling is usually achieved by...

Sampling Continuous Time Signal

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.
In the...

Rectangular and Triangular Pulse Function

Rectangular and Triangular Pulse Function

The unit rectangular pulse function is mathematically represented by a rectangular function centered at the origin with a height of one unit. This function is defined by two parameters: T, which specifies the center location of the pulse along the time axis, and τ, which determines the pulse duration.
For example, consider a rectangular pulse with a 5V amplitude, a 3-second duration, and centered at t=2 seconds. This pulse can be expressed using the rectangular function, written as,

Basic Operations on Signals

Basic Operations on Signals

Basic signal operations include time reversal, time scaling, time shifting, and amplitude transformations. These operations are fundamental in signal processing and analysis.
Time Reversal mirrors a continuous-time signal about the vertical axis at t=0. This is achieved by substituting t with −t. For example, if a signal x(t) is considered, the time-reversed signal is x(−t). This operation can be graphically represented, showing the mirrored signal.

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Related Experiment Video

Updated: Jul 9, 2026

Direct Imaging of Laser-driven Ultrafast Molecular Rotation

Direct Imaging of Laser-driven Ultrafast Molecular Rotation

Published on: February 4, 2017

Time reversal and object reconstruction with single-cycle pulses.

A B Ruffin, J Decker, L Sanchez-Palencia

|November 28, 2007

Summary

Researchers reconstructed 1D and 2D objects using backpropagated terahertz transients. The Sparrow criterion determined spatial resolution, achieving ~30% of peak and 85% of mean wavelength.

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Last Updated: Jul 9, 2026

Direct Imaging of Laser-driven Ultrafast Molecular Rotation

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Published on: February 4, 2017

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

Published on: February 12, 2014

Investigation of Early Plasma Evolution Induced by Ultrashort Laser Pulses

Investigation of Early Plasma Evolution Induced by Ultrashort Laser Pulses

Published on: July 2, 2012

Area of Science:

Optics and Photonics
Terahertz Spectroscopy
Image Reconstruction

Background:

Terahertz (THz) imaging offers non-ionizing, label-free characterization capabilities.
Reconstructing images from scattered THz signals is crucial for material analysis and object imaging.
Numerical backpropagation is a key technique for retrieving object information from wavefield measurements.

Purpose of the Study:

To demonstrate the reconstruction of one- and two-dimensional objects using scattered terahertz transients.
To evaluate the spatial resolution achieved by numerical backpropagation in the terahertz regime.

Main Methods:

Numerical backpropagation of measured scattered terahertz transients.
Analysis of spatial resolution using the Sparrow criterion.
Characterization of single-cycle terahertz waveforms and their power spectra.

Main Results:

Successful reconstruction of both one- and two-dimensional objects was achieved.
The Sparrow criterion indicated a spatial resolution of approximately 30% of the peak wavelength.
A spatial resolution of approximately 85% of the mean wavelength was also determined.

Conclusions:

Numerical backpropagation of terahertz transients is an effective method for object reconstruction.
The achieved spatial resolution is directly related to the spectral characteristics of the terahertz waveform.
This technique holds promise for high-resolution terahertz imaging applications.