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Discrete-time Fourier transform01:26

Discrete-time Fourier transform

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The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
One of the notable...
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Basic Discrete Time Signals01:16

Basic Discrete Time Signals

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The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is the...
741
Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

719
The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...
719
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

946
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
946
The Integrated Rate Law: The Dependence of Concentration on Time02:39

The Integrated Rate Law: The Dependence of Concentration on Time

43.8K
While the differential rate law relates the rate and concentrations of reactants, a second form of rate law called the integrated rate law relates concentrations of reactants and time. Integrated rate laws can be used to determine the amount of reactant or product present after a period of time or to estimate the time required for a reaction to proceed to a certain extent. For example, an integrated rate law helps determine the length of time a radioactive material must be stored for its...
43.8K
Time and frequency -Domain Interpretation of PI Control01:27

Time and frequency -Domain Interpretation of PI Control

439
Proportional-Integral (PI) controllers are essential in many control systems to improve stability and performance. They are commonly used in everyday devices like thermostats to enhance system damping and reduce steady-state error. When the zero in the controller's transfer function is optimally placed, the system benefits significantly in terms of stability and accuracy.
Acting as a low-pass filter, the PI controller slows the system's response and extends settling times. This requires...
439

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Related Experiment Video

Updated: Feb 13, 2026

High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques
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High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques

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Mitigating fringing in discrete frequency infrared imaging using time-delayed integration.

Shihao Ran1, Sebastian Berisha1, Rupali Mankar1

  • 1Department of Electrical and Computer Engineering, University of Houston, 4726 Calhoun Rd., Houston, TX 77204, USA.

Biomedical Optics Express
|March 20, 2018
PubMed
Summary
This summary is machine-generated.

Time-delayed integration reduces fringing artifacts in infrared spectroscopic microscopy. This advancement improves molecular imaging speed and potentially lowers costs for biomedical applications.

Keywords:
(140.5965) Semiconductor lasers, quantum cascade(180.0180) Microscopy(300.0300) Spectroscopy

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Area of Science:

  • Spectroscopic microscopy
  • Molecular imaging
  • Biomedical optics

Background:

  • Infrared (IR) spectroscopic microscopes offer label-free molecular imaging for histology, forensics, and pharma.
  • Current IR imaging is too slow for clinical diagnosis due to source and detector limitations.
  • Coherent light sources increase IR imaging speed but introduce fringing artifacts.

Purpose of the Study:

  • To develop a method for reducing fringing artifacts in IR spectroscopic microscopy.
  • To enhance the speed and applicability of IR imaging for biomedical applications.
  • To explore cost-effective detector options for IR imaging.

Main Methods:

  • Application of time-delayed integration in one dimension.
  • Utilizing coherent light sources (e.g., synchrotron, quantum cascade lasers).
  • Minimal alterations to standard infrared imaging pipelines.

Main Results:

  • Dramatic reduction in fringing artifacts was achieved.
  • The technique integrates seamlessly with existing IR imaging pipelines.
  • Potential for using less expensive linear focal plane array detectors.

Conclusions:

  • Time-delayed integration is an effective method to mitigate coherence artifacts in IR microscopy.
  • This technique significantly improves the feasibility of IR spectroscopic microscopy for high-throughput biomedical applications.
  • The method opens possibilities for more affordable and faster molecular imaging systems.