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Related Concept Videos

Region of Convergence of Laplace Tarnsform01:20

Region of Convergence of Laplace Tarnsform

The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This substitution...
Properties of Laplace Transform-I01:15

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The Laplace transform is a powerful mathematical tool used to convert functions from the time domain into the frequency domain, greatly simplifying the analysis and solution of linear time-invariant systems. This transformation is facilitated by several universal properties: Linearity, Time-Scaling, Time-Shifting, and Frequency Shifting.
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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.
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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...
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The Laplace transform is an indispensable mathematical technique for simplifying the resolution of differential equations by converting them into more manageable algebraic expressions. The Laplace transform of a function is denoted by L[x(t)], where x(t) is the time-domain function. The laplace transform is mathematically expressed as
Convolution Properties II01:17

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The important convolution properties include width, area, differentiation, and integration properties.
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...

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Data Acquisition and Analysis In Brainstem Evoked Response Audiometry In Mice
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Published on: May 10, 2019

Multiresolution monogenic signal analysis using the Riesz-Laplace wavelet transform.

Michael Unser1, Daniel Sage, Dimitri Van De Ville

  • 1Biomedical Imaging Group (BIG), Ecole PolytechniqueFédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland. michael.unser@epfl.ch

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|July 17, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces a novel wavelet-domain monogenic signal analysis using a complex Riesz transform. This method enables advanced feature extraction and processing for directional image patterns and signal analysis.

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Area of Science:

  • Signal Processing
  • Image Analysis
  • Wavelet Theory

Background:

  • The 1-D analytic signal is extended to 2-D as the monogenic signal.
  • Existing methods lack steerability and robust directional analysis.

Purpose of the Study:

  • To develop a steerable wavelet-domain monogenic signal analysis.
  • To enable robust feature extraction and signal processing in 2-D.

Main Methods:

  • Complexified Riesz transform for wavelet basis complexification.
  • Polyharmonic spline wavelets derived from fractional Laplace operators.
  • Multiresolution analysis with steerable, quasi-isotropic wavelets.

Main Results:

  • A representation associating wavelet indices with local orientation, amplitude, and phase.
  • Wavelet-domain instantaneous frequency estimation.
  • Improved shift and rotation invariance in wavelet decomposition.

Conclusions:

  • The proposed method offers powerful tools for directional image pattern analysis, interferogram demodulation, and hologram reconstruction.
  • Efficient implementation via perfect-reconstruction filterbanks is demonstrated.