What Is the Fast Fourier Transform?
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The Fast Fourier Transform (FFT) is a computational tool that efficiently computes the Discrete Fourier Transform (DFT) of a series of data samples. It is used for signal analysis, such as power spectrum analysis and filter simulation, on digital computers. The FFT simplifies the complexity of the DFT, making it faster and more practical for long data sets. It converts a signal from its original domain (time or space) into the frequency domain and vice versa. The FFT algorithm is based on complex number arithmetic and has various implementations, including recursive and non-recursive methods. It is accurate and widely used due to its speed and efficiency.
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| Papers (4) | Insight |
|---|---|
| The paper is about the Fast Fourier Transform (FFT), which is a family of algorithms used to compute the Discrete Fourier Transform (DFT). The paper does not explicitly define what the FFT is, but it discusses its applications and properties. | |
471 Citations | The fast Fourier transform (FFT) is a computational tool for efficiently computing the discrete Fourier transform (DFT) of a time series. It is used for signal analysis and filter simulation on digital computers. |
| The paper provides a definition and derivation of the fast Fourier transform (FFT), a computational tool used for signal analysis and filter simulation on digital computers. | |
| The Fast Fourier Transform (FFT) is an algorithm that speeds up the computation of the Discrete Fourier Transform (DFT) by simplifying its complexity. |
Related Questions
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What can you say about fast Fourier transform?3 answersThe fast Fourier Transform (FFT) is an algorithm that simplifies the computation of the discrete Fourier transform (DFT) by reducing its complexity. It converts a signal from its original domain into the frequency domain and vice versa, allowing for the decomposition of a sequence into components of different frequencies. FFT algorithms are more accurate and much faster than evaluating the DFT directly, especially for long data sets. There are various FFT algorithms based on complex number arithmetic, number theory, and group theory. The FFT is widely used in engineering, science, and mathematics, and its implementation in parallel computing has become essential for solving large-scale problems. It is an efficient method for computing the DFT, requiring a relatively low number of arithmetic operations. Additionally, the FFT provides an approximate method for evaluating the distribution of aggregate losses in insurance and finance, with proven efficiency in univariate, bivariate, and multivariate settings.
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