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Related Concept Videos

Fast Fourier Transform01:10

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The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...
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The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...
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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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Magnetic resonance imaging (MRI) is a noninvasive medical imaging technique based on a phenomenon of nuclear physics discovered in the 1930s, in which matter exposed to magnetic fields and radio waves was found to emit radio signals. In 1970, a physician and researcher named Raymond Damadian noticed that malignant (cancerous) tissue gave off different signals than normal body tissue. He applied for a patent for the first MRI scanning device in clinical use by the early 1980s. The early MRI...
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The Fourier Transform is a pivotal mathematical tool in signal processing, enabling the transformation of time-domain signals into their frequency-domain representations. Among the numerous elements within this domain, certain functions like the sinc function, delta function, and exponential signals hold significant importance due to their unique properties and implications.
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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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Morphology-Based Distinction Between Healthy and Pathological Cells Utilizing Fourier Transforms and Self-Organizing Maps
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Graph Fourier transform for spatial omics representation and analyses of complex organs.

Yuzhou Chang1,2, Jixin Liu3, Yi Jiang1

  • 1Department of Biomedical Informatics, College of Medicine, Ohio State University, Columbus, OH 43210, USA.

Research Square
|February 27, 2024
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Summary

We developed SpaGFT, a novel method for analyzing spatial omics data. This tool enhances understanding of tissue organization and biological functions by accurately identifying molecular signatures and improving machine learning model performance.

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Area of Science:

  • Spatial omics
  • Graph signal processing
  • Computational biology

Background:

  • Spatial omics technologies offer high-resolution insights into tissue and cellular organization.
  • Existing methods lack robust, interpretable, and unbiased representations for spatial omics data, hindering biological discovery.
  • A theoretical framework is needed to fully leverage spatial omics data for understanding biological functions.

Conclusions:

  • SpaGFT provides a powerful and interpretable method for spatial omics data analysis.
  • The approach enhances machine learning applications in spatial biology, improving accuracy and biological insights.
  • SpaGFT advances the theoretical understanding of tissue organization and function through explainable AI.