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Properties of DTFT I01:24

Properties of DTFT I

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In signal processing, Discrete-Time Fourier Transforms (DTFTs) play a critical role in analyzing discrete-time signals in the frequency domain. Various properties of the DTFTs such as linearity, time-shifting, frequency-shifting, time reversal, conjugation, and time scaling help understand and manipulate these signals for different applications.
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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.
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Properties of Fourier Transform II01:24

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The Fourier Transform (FT) is an essential mathematical tool in signal processing, transforming a time-domain signal into its frequency-domain representation. This transformation elucidates the relationship between time and frequency domains through several properties, each revealing unique aspects of signal behavior.
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The unit rectangular pulse function is mathematically represented by a rectangular function centered at the origin with a height of one unit. This function is defined by two parameters: T, which specifies the center location of the pulse along the time axis, and τ, which determines the pulse duration.
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Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method
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Directional dual-tree complex wavelet packet transforms for processing quadrature signals.

Gorkem Serbes1, Halil Ozcan Gulcur2, Nizamettin Aydin3

  • 1Biomedical Engineering Department, Bahcesehir University, Besiktas, Istanbul, Turkey.

Medical & Biological Engineering & Computing
|November 13, 2014
PubMed
Summary
This summary is machine-generated.

New directional discrete wavelet packet transforms efficiently process quadrature signals for detecting embolic signals, crucial for stroke risk assessment. These methods offer improved time-frequency analysis over traditional transforms.

Keywords:
Complex wavelet packet transformEmbolic signalsQuadrature signalUltrasound

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Area of Science:

  • Signal Processing
  • Biomedical Engineering
  • Cardiovascular Diagnostics

Background:

  • Quadrature signals are vital in science and engineering, including Doppler ultrasound for cardiovascular assessment.
  • Processing these signals is essential for directional blood flow information and detecting embolic signals, indicators of potential stroke.
  • Traditional Fourier and discrete wavelet transforms struggle with the non-stationary nature of embolic signals.

Purpose of the Study:

  • Introduce novel directional discrete wavelet packet transforms for quadrature signal processing.
  • Address the limitations of existing methods in analyzing non-stationary embolic signals.
  • Develop computationally efficient techniques for stroke risk assessment.

Main Methods:

  • Developed directional discrete wavelet packet transforms.
  • Applied asymmetrical and symmetrical phasing filter techniques for directional information extraction.
  • Evaluated performance using single-frequency, synthetic narrow-band, and embolic quadrature signals.

Main Results:

  • Proposed directional discrete wavelet packet transforms effectively process quadrature signals.
  • Demonstrated ability to map directional information with less computational complexity.
  • Validated performance on various signal types, including embolic signals.

Conclusions:

  • Directional discrete wavelet packet transforms offer a superior approach for analyzing quadrature signals in embolic detection.
  • These methods enhance the capability for non-invasive stroke risk assessment.
  • The introduced transforms provide a computationally efficient and effective tool for signal processing in cardiovascular applications.