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Aliasing

Aliasing

Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original...

NMR Spectroscopy: Chemical Shift Overview

NMR Spectroscopy: Chemical Shift Overview

The position of the absorption signal of a sample is reported relative to the position of the signal of tetramethylsilane (TMS), which is added as an internal reference while recording spectra. The difference between the absorption frequencies of the sample and TMS (in Hz) is divided by the spectrometer operating frequency (in MHz) to obtain a dimensionless quantity called the chemical shift. It is reported on the δ (delta) scale and expressed in parts per million.
For instance, the proton...

¹H NMR: Interpreting Distorted and Overlapping Signals

¹H NMR: Interpreting Distorted and Overlapping Signals

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...

Upsampling

Upsampling

Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...

Bandpass Sampling

Bandpass Sampling

In signal processing, bandpass sampling is an effective technique for sampling signals that have most of their energy concentrated within a narrow frequency band. This type of signal is known as a bandpass signal. The key principle of bandpass sampling involves sampling the signal at a rate that is greater than twice the signal's bandwidth to prevent aliasing.
A bandpass signal has a spectrum with a lower frequency limit, denoted as ω1, and an upper frequency limit, denoted as ω2....

NMR Spectrometers: Resolution and Error Correction

NMR Spectrometers: Resolution and Error Correction

When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...

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Related Experiment Video

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Spectral and Angle-Resolved Magneto-Optical Characterization of Photonic Nanostructures

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Modified shifted angular spectrum method for numerical propagation at reduced spatial sampling rates.

|November 18, 2014

Summary

A modified shifted angular spectrum method reduces spatial sampling for wave field propagation. This technique enhances computational efficiency for simulating scalar wave fields, particularly spherical waves.

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Area of Science:

Computational physics
Wave optics
Numerical methods

Background:

Numerical propagation of scalar wave fields is essential in optics.
The shifted angular spectrum method (SASM) reduces sampling requirements.
Further optimization of SASM is needed for specific wave types.

Purpose of the Study:

To present a modification of the shifted angular spectrum method.
To achieve a further reduction in the spatial sampling rate for wave fields.
To quantify the benefits for spherical wave propagation.

Main Methods:

Modification of the shifted angular spectrum method.
Calculation of sampling rate reduction for spherical waves.
Implementation and demonstration using a spherical wave through a circular aperture.

Main Results:

The modified SASM allows for a greater reduction in spatial sampling rate.
The method's benefit was quantified for spherical waves.
A practical implementation demonstrated the method's efficacy.

Conclusions:

The modified SASM offers improved computational efficiency for wave propagation.
This method is particularly beneficial for simulating spherical waves.
The presented implementation validates the practical application of the technique.