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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...

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 signal...

Sampling Theorem

Sampling Theorem

In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.

Downsampling

Downsampling

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.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...

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...

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. The spectrum...

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Related Experiment Video

Updated: Jul 19, 2026

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

General solution of undersampling frequency conversion and its optimization for parallel photodisplacement imaging.

Toshihiko Nakata¹, Takanori Ninomiya

¹Production Engineering Research Laboratory, Hitachi Ltd., Totsuka-ku, Yokohama, Japan. toshihiko.nakata.ac@hitachi.com

|October 28, 2006

Summary

This study presents an optimized undersampling frequency conversion method for parallel photodisplacement imaging. The technique enables simultaneous, high-speed imaging of reflectivity, topography, and photodisplacement, crucial for defect detection.

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Digital Inline Holographic Microscopy (DIHM) of Weakly-scattering Subjects

Digital Inline Holographic Microscopy (DIHM) of Weakly-scattering Subjects

Published on: February 8, 2014

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Last Updated: Jul 19, 2026

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

Digital Inline Holographic Microscopy (DIHM) of Weakly-scattering Subjects

Digital Inline Holographic Microscopy (DIHM) of Weakly-scattering Subjects

Published on: February 8, 2014

Area of Science:

Optics and Photonics
Image Processing
Materials Science

Background:

Undersampling frequency conversion in parallel photodisplacement imaging poses challenges for data acquisition.
Phase-modulated heterodyne interference requires precise sampling for accurate information retrieval.

Purpose of the Study:

To develop a general solution for undersampling frequency conversion and its optimization in parallel photodisplacement imaging.
To enable simultaneous imaging of photodisplacement, topography, and reflectivity for subsurface defect detection.

Main Methods:

Utilized Fourier analysis of the sampling procedure to derive a general solution for frequency and amplitude downconversion.
Determined optimal frequency conditions for heterodyne beat signal, modulation signal, and sensor gate pulse to eliminate undesirable components.
Optimized frequency parameters to maximize the sideband-to-carrier amplitude ratio, achieving high selectivity (>80 dB).

Main Results:

Successfully derived a general solution for frequency and amplitude downconversion in undersampled photodisplacement imaging.
Identified optimal frequency parameters for orthogonal conversion and discrete reproduction of information components.
Achieved high selectivity (>80 dB) for signal components.

Conclusions:

The developed technique allows for simultaneous imaging of reflectivity, topography, and photodisplacement.
Demonstrated high-speed subsurface lattice defect detection with an acquisition time of 0.26 s per 256x256 pixel area.
This method offers a significant advancement in parallel photodisplacement imaging for material analysis.