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Related Concept Videos

Inverse z-Transform by Partial Fraction Expansion01:20

Inverse z-Transform by Partial Fraction Expansion

The inverse z-transform is a crucial technique for converting a function from its z-domain representation back to the time domain. One effective method for finding the inverse z-transform is the Partial Fraction Method, which involves decomposing a function into simpler fractions with distinct coefficients. These fractions correspond to known z-transform pairs, facilitating the inverse transformation process.
To begin the process, the poles of the function are identified and the function is...
Difference Equation Solution using z-Transform01:24

Difference Equation Solution using z-Transform

The z-transform is a powerful tool for analyzing practical discrete-time systems, often represented by linear difference equations. Solving a higher-order difference equation requires knowledge of the input signal and the initial conditions up to one term less than the order of the equation.
The z-transform facilitates handling delayed signals by shifting the signal in the z-domain, which corresponds to delaying the signal in the time domain, and advancing signals by similarly shifting in the...
Properties of the z-Transform II01:16

Properties of the z-Transform II

The property of Accumulation in signal processing is derived by analyzing the accumulated sum of a discrete-time signal and using the time-shifting property to determine its z-transform. This principle reveals that the z-transform of the summed signal is related to the z-transform of the original signal by a multiplicative factor.
Moreover, the convolution property indicates that the convolution of two signals in the time domain corresponds to the product of their z-transforms in the frequency...
Deconvolution01:20

Deconvolution

Deconvolution, also known as inverse filtering, is the process of extracting the impulse response from known input and output signals. This technique is vital in scenarios where the system's characteristics are unknown, and they must be inferred from the observable signals.
Deconvolution involves several mathematical techniques to derive the impulse response. One common approach is polynomial division. In this method, the input and output sequences are treated as coefficients of...
Basic Operations on Signals01:22

Basic Operations on Signals

Basic signal operations include time reversal, time scaling, time shifting, and amplitude transformations. These operations are fundamental in signal processing and analysis.
Time Reversal mirrors a continuous-time signal about the vertical axis at t=0. This is achieved by substituting t with −t. For example, if a signal x(t) is considered, the time-reversed signal is x(−t). This operation can be graphically represented, showing the mirrored signal.
Definition of z-Transform01:26

Definition of z-Transform

The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is an essential analytical tool, analogous to the Laplace transform used in continuous-time systems. It plays a crucial role in the analysis of signals and systems, complementing the discrete-time Fourier transform. Both the z-transform and the Laplace transform convert differential or difference equations into algebraic equations, simplifying the process of solving complex problems.

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Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
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Published on: February 23, 2018

A versatile analytical expression for the inverse Abel transform applied to experimental data with noise.

Shuiliang Ma1, Hongming Gao, Guangjun Zhang

  • 1State Key Laboratory of Advanced Welding Production Technology, Harbin Institute of Technology, Harbin 150001, China. shlgma@126.com

Applied Spectroscopy
|June 19, 2008
PubMed
Summary

This study introduces a new method for reconstructing plasma emission coefficients from noisy projection data. The technique offers superior accuracy, especially with sparse data and varying noise levels.

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Area of Science:

  • Plasma physics
  • Applied mathematics
  • Image reconstruction

Background:

  • Accurate reconstruction of plasma emission coefficients is crucial for understanding plasma behavior.
  • Existing methods often struggle with noisy or sparse projection data.

Purpose of the Study:

  • To develop and validate a novel method for reconstructing radially distributed plasma emission coefficients.
  • To analyze parameters influencing inversion accuracy and compare performance against existing techniques.

Main Methods:

  • Utilizing overlapping piecewise polynomial least squares fitting for projection representation and inversion.
  • Analyzing parameters affecting inversion accuracy.

Main Results:

  • The proposed method demonstrates higher accuracy compared to other techniques, particularly for sparse data and varying noise levels.
  • Excellent results were achieved with experimental arc plasma intensity data, even without noise filtering.

Conclusions:

  • The developed method provides a robust and accurate approach for plasma emission coefficient reconstruction.
  • It shows significant advantages in handling noisy and sparse datasets, outperforming conventional methods.