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Related Concept Videos

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.
The linearity property of DTFTs is fundamental. If two discrete-time signals are multiplied by constants a and b respectively, and then combined to...
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Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

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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.
For a discrete-time periodic signal x[n]...
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Discrete Fourier Transform01:15

Discrete Fourier Transform

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The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
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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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Properties of Fourier Transform I01:21

Properties of Fourier Transform I

402
The application of Fourier Transform properties in radio broadcasting is multifaceted, enabling significant advancements in the way signals are transmitted and received. Key areas where these properties are utilized include simultaneous multi-channel transmission, audio clip speed adjustments, live broadcast delays for different time zones, audio frequency adjustments, and signal demodulation.
In radio broadcasting, multiple audio signals often need to be transmitted simultaneously. The Fourier...
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Properties of DTFT II01:24

Properties of DTFT II

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In the study of discrete-time signal processing, understanding the properties of the Discrete-Time Fourier Transform (DTFT) is crucial for analyzing and manipulating signals in the frequency domain. Several properties, including frequency differentiation, convolution, accumulation, and Parseval's relation, offer powerful tools for signal analysis.
The frequency differentiation property is illustrated by considering a DTFT pair and differentiating both sides with respect to ω.
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Phase Function Effects on Identification of Terahertz Spectral Signatures Using the Discrete Wavelet Transform.

Mahmoud E Khani1, Dale P Winebrenner2, M Hassan Arbab1

  • 1Department of Biomedical Engineering, Stony Brook University, Stony Brook, NY, 11794 USA.

IEEE Transactions on Terahertz Science and Technology
|March 19, 2021
PubMed
Summary
This summary is machine-generated.

Discrete Wavelet Transform (DWT) effectively extracts material absorption signatures from terahertz spectra. This signal processing technique, with phase correction, enables robust material identification in non-destructive evaluation.

Keywords:
Discrete wavelet transformsphase functionrough surface scatteringspectral analysisterahertz (THz)zero-phase transform

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Area of Science:

  • Spectroscopy and Spectrometry
  • Signal Processing
  • Materials Science

Background:

  • Terahertz (THz) spectroscopy is valuable for material identification.
  • Extracting characteristic absorption signatures from THz spectra can be challenging due to scattering.
  • Wavelet transforms offer potential for signal analysis in complex spectral data.

Purpose of the Study:

  • To apply the Discrete Wavelet Transform (DWT) for extracting material absorption signatures from THz reflection spectra.
  • To evaluate the performance of different mother wavelets (Daubechies, LA, Coiflet) in this application.
  • To develop a phase correction method for accurate spectral analysis using DWT.

Main Methods:

  • Application of Discrete Wavelet Transform (DWT) to terahertz reflection spectra.
  • Comparison of Daubechies, Least Asymmetric (LA), and Coiflet mother wavelets.
  • Calculation of advancement coefficients for zero-phase DWT.
  • Testing with alpha-lactose monohydrate/polyethylene samples with varying surface roughness.

Main Results:

  • Wavelet and scaling filter phase functions cause spectral shifts in the wavelet domain.
  • A method for achieving zero-phase DWT using advancement coefficients was developed.
  • The DWT-based algorithm successfully extracted 0.53 and 1.38 THz resonant signatures.
  • Extraction was effective even with significant surface scattering effects.

Conclusions:

  • DWT is a powerful tool for analyzing terahertz spectra.
  • Phase correction is crucial for accurate spectral signature extraction using DWT.
  • The DWT analysis provides a robust method for material identification in terahertz non-destructive evaluation (NDE).