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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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Relation of DFT to z-Transform01:20

Relation of DFT to z-Transform

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The Discrete Fourier Transform (DFT) is a crucial tool for analyzing the frequency content of discrete-time signals. It converts a sequence of N samples from the time domain into its corresponding sequence in the frequency domain, where each sample represents a specific frequency component.
To understand how the DFT works, it's helpful to consider the z-transform, which is a method for representing discrete sequences in the complex frequency domain. The z-transform involves summing the...
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Transformations of Functions III01:20

Transformations of Functions III

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Transformations modify the graphical representation of a function without changing its fundamental form. One common transformation is reflection, which flips the graph across a designated axis. When the vertical coordinates of all points are multiplied by the negative one, the entire graph is mirrored over the horizontal axis. This transformation reverses the vertical orientation of peaks and troughs, akin to signal inversion in electrical systems, where a waveform is flipped, but the timing of...
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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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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

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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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Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method
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Directional dual-tree rational-dilation complex wavelet transform.

Gorkem Serbes, Halil Ozcan Gulcur, Nizamettin Aydin

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    Summary
    This summary is machine-generated.

    The dyadic discrete wavelet transform (DWT) struggles with oscillatory signals like embolic signals (ESs). A new directional dual-tree rational-dilation complex wavelet transform is introduced for direct analysis of quadrature Doppler signals.

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    Area of Science:

    • Signal Processing
    • Biomedical Engineering
    • Wavelet Analysis

    Background:

    • Dyadic discrete wavelet transform (DWT) is effective for non-oscillatory transient signals.
    • The low Q-factor of dyadic DWT atoms limits its efficacy for oscillatory signals, including embolic signals (ESs).
    • Embolic signals are derived from quadrature Doppler signals, requiring pre-processing like phase filtering before wavelet analysis.

    Purpose of the Study:

    • To introduce a novel wavelet transform for direct analysis of quadrature Doppler signals.
    • To overcome the limitations of dyadic DWT in processing oscillatory embolic signals.
    • To develop a method that extracts directional information during the analysis of quadrature signals.

    Main Methods:

    • Introduction of a directional dual-tree rational-dilation complex wavelet transform.
    • Application of the new transform directly to quadrature Doppler signals.
    • Utilizing the transform's inherent ability to extract directional information.

    Main Results:

    • The proposed directional dual-tree rational-dilation complex wavelet transform can be applied directly to quadrature signals.
    • This new transform inherently extracts directional information during analysis.
    • It offers an improved approach for processing oscillatory signals like ESs compared to dyadic DWT.

    Conclusions:

    • The directional dual-tree rational-dilation complex wavelet transform provides a more effective method for analyzing oscillatory signals, such as embolic signals.
    • This transform simplifies the processing of quadrature Doppler signals by eliminating the need for separate phase filtering.
    • It advances wavelet-based analysis for biomedical signals requiring directional information extraction.