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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.

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....

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.
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Sampling Methods: Overview

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A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling.
In analytical chemistry, the choice of...

Small-Signal Analysis of MOSFET Amplifiers

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In small-signal analysis, a MOSFET transistor amplifier acts as a linear amplifier when operating in its saturation region. The gate-to-source voltage (VGS) of the MOSFET is the sum of the DC biasing voltage and the small time-varying input signal. This combination sets up the operating point and modulates the drain current (ID) that flows from the drain to the source. When a small AC signal is superimposed on the DC bias voltage at the gate, the instantaneous drain current comprises three...

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Updated: Oct 12, 2025

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

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Edge-based modulation transfer function measurement method using a variable oversampling ratio.

Kenichiro Masaoka

|November 23, 2021

Summary

This study introduces OMNI-sine, an improved edge-based method for estimating modulation transfer function (MTF). It enhances diagonal MTF accuracy by using a variable oversampling ratio to correct for misalignment issues.

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Area of Science:

Image quality assessment
Optical metrology
Digital imaging standards

Background:

The ISO 12233 standard provides an edge-based method for Modulation Transfer Function (MTF) estimation.
Current methods struggle with accuracy for diagonal measurements due to fixed oversampling ratios and misalignment.
Accurate MTF is crucial for evaluating imaging system performance.

Purpose of the Study:

To develop an improved edge-based method for accurate diagonal MTF estimation.
To address the limitations of fixed oversampling ratios in the ISO 12233 standard.
To enhance the precision and reliability of MTF measurements for imaging systems.

Main Methods:

A novel edge-based method, OMNI-sine, is proposed.
It utilizes a variable oversampling ratio tailored to the edge's slant angle.
This approach corrects for periodic misalignment between pixel projection and bin arrays.

Main Results:

OMNI-sine demonstrates improved accuracy and precision in diagonal MTF estimation compared to standard methods.
The variable oversampling ratio effectively mitigates errors caused by misalignment.
Enhanced MTF estimates are achieved across various diagonal orientations.

Conclusions:

The OMNI-sine method offers a significant advancement for diagonal MTF measurements.
It provides more reliable image quality assessment for imaging devices.
This technique is vital for maintaining and improving digital imaging standards.