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Related Concept Videos

Fast Fourier Transform01:10

Fast Fourier Transform

258
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...
258
Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

277
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...
277
Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

213
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]...
213
Discrete Fourier Transform01:15

Discrete Fourier Transform

209
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...
209
Discrete-time Fourier transform01:26

Discrete-time Fourier transform

256
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...
256
Trigonometric Fourier series01:17

Trigonometric Fourier series

176
Fourier series is a foundational mathematical technique that decomposes periodic functions into an infinite series of sinusoidal harmonics. This method enables the representation of complex periodic signals as sums of simple sine and cosine functions, facilitating their analysis and interpretation in various fields, including signal processing, acoustics, and electrical engineering.
The trigonometric Fourier series specifically expresses a periodic function with a defined period T using sine...
176

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Time Series Forecasting Model Based on the Adapted Transformer Neural Network and FFT-Based Features Extraction.

Kyrylo Yemets1, Ivan Izonin1,2, Ivanna Dronyuk3

  • 1Department of Artificial Intelligence, Lviv Polytechnic National University, 79905 Lviv, Ukraine.

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|February 13, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces an enhanced transformer model for time series forecasting, improving accuracy by using fast Fourier transform (FFT) to add frequency-domain features. The novel approach significantly boosts predictive performance for sensor data.

Keywords:
ANNBig DataDeepARLSTMattention mechanismdeep learningfast Fourier transformfeature extractionforecastingperformance evaluationsensorstime seriestransformer

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Area of Science:

  • Data Science
  • Machine Learning
  • Signal Processing

Background:

  • Accurate time series forecasting is vital across finance, climatology, and engineering.
  • Neural networks struggle with sensor data due to volume, noise, and long-term dependencies.
  • Existing models face challenges with diverse sensor data characteristics.

Purpose of the Study:

  • To enhance time series forecasting accuracy for sensor-collected data.
  • To address limitations of current neural network models in handling complex time series.
  • To improve predictive performance by incorporating frequency-domain information.

Main Methods:

  • Proposed an adapted transformer architecture for time series prediction.
  • Introduced a data preprocessing method using fast Fourier transform (FFT) to convert time-domain to frequency-domain.
  • Enriched data with complex-valued frequency-domain features to boost informational content.

Main Results:

  • The proposed model demonstrated superior performance across three diverse sensor datasets.
  • Achieved higher accuracy compared to state-of-the-art models like LSTM, DeepAR, and Transformer.
  • Consistently outperformed existing methods across five distinct performance metrics.

Conclusions:

  • The adapted transformer model with FFT preprocessing significantly improves time series forecasting accuracy.
  • The method effectively handles challenges posed by large volumes, noise, and long-term dependencies in sensor data.
  • This approach offers a robust solution for accurate forecasting in data-driven applications.