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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.
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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...

Downsampling

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When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
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Discrete Fourier Transform

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The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...

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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

Using an aliasing operator and a single discrete Fourier transform to down-sample the Fresnel transform.

Modesto Medina-Melendrez¹, Albertina Castro, Miguel Arias-Estrada

¹Instituto Tecnológico de Culiacán, Juan de Dios Bátiz 310 Pte, Col. Guadalupe, Culiacán SIN 80220, Mexico. modestogmm@itculiacan.edu.mx

|April 20, 2012

Summary

This study introduces an efficient method for down-sampling wavefields in Digital Holography using an aliasing operator and a single discrete Fourier transform, reducing computational load for image retrieval.

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Area of Science:

Optics and Photonics
Computational Imaging
Digital Holography

Background:

Digital Holography (DH) applications often require only a few wavefield samples for image reconstruction.
Current methods like direct and spectral discrete Fresnel transforms can lead to excessive sampling rates.
Existing wavefield computation methods necessitate multiple 2D discrete Fourier transforms (2D-DFT), increasing computational cost.

Purpose of the Study:

To develop a more efficient numerical method for computing down-sampled wavefields in DH.
To reduce the computational load associated with wavefield propagation and sampling in DH.
To enable precise control over down-sampling rates without compromising image quality.

Main Methods:

Introduction of an aliasing operator for controlled wavefield down-sampling.
Utilization of a single 2D discrete Fourier transform (2D-DFT) instead of multiple transforms.
Integration of the aliasing operator with the Fresnel transform for efficient wavefield computation.

Main Results:

The proposed method significantly reduces computational complexity compared to existing techniques.
Achieves efficient down-sampling of wavefields obtained through Fresnel transform.
Demonstrates the feasibility of using a single 2D-DFT for down-sampled wavefield calculation.

Conclusions:

The novel approach offers an efficient solution for down-sampling wavefields in Digital Holography.
This method lowers the computational burden, making DH applications more accessible.
The use of an aliasing operator and a single 2D-DFT is a promising advancement in holographic imaging.