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Related Concept Videos

Fast Fourier Transform01:10

Fast Fourier Transform

851
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...
851
Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

805
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...
805
Discrete Fourier Transform01:15

Discrete Fourier Transform

825
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...
825
Basic signals of Fourier Transform01:07

Basic signals of Fourier Transform

860
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.
The sinc function, defined as sinc(x) = sin(πx)/(πx), is particularly notable for its symmetry and behavior at...
860
Discrete-time Fourier transform01:26

Discrete-time Fourier transform

992
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...
992
Convergence of Fourier Series01:21

Convergence of Fourier Series

357
The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
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Deciphering High-Resolution 3D Chromatin Organization via Capture Hi-C
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Fast Fourier transform is a training-free, ultrafast, highly efficient, and fully interpretable approach for

Max Ward1, Bac Dao2, Amitava Datta1

  • 1School of Physics, Mathematics, and Computer Sciences, University of Western Australia, Perth, Australia.

Scientific Reports
|December 10, 2025
PubMed
Summary

A new Fast Fourier Transform (FFT) method offers efficient, interpretable epigenomic data compression. This training-free approach significantly reduces file size while maintaining high accuracy for data modeling.

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Area of Science:

  • Bioinformatics
  • Genomic Data Analysis
  • Signal Processing

Background:

  • Data compression is crucial for feature selection and modeling in genomics.
  • Current autoencoder methods for epigenomic data are computationally intensive and lack interpretability.

Purpose of the Study:

  • To develop a training-free, efficient, and interpretable data compression method for epigenomic data.
  • To overcome the limitations of autoencoder-based compression techniques.

Main Methods:

  • A novel Fast Fourier Transform (FFT)-based approach was developed for data compression.
  • The method was applied to compress epigenomic data, specifically histone modification data.

Main Results:

  • The FFT method achieved up to 1,000-fold compression of epigenomic data.
  • High reconstruction fidelity was maintained (cosine similarity of 99.7%).
  • Compression was ultrafast (70 ms on GPU, 20 s on CPU) and required no training.

Conclusions:

  • The FFT method provides a significant improvement over autoencoders for epigenomic data compression.
  • The approach offers full interpretability of compressed features, unlike black-box autoencoders.
  • This method enables high accuracy in classification models (AUC 0.960), representing a paradigm shift in data compression.