Abstract
The discrete Fourier transform (DFT) is the only Fourier transform candidate suitable for digital computer implementation, while all the other must be related to the DFT. The direct computation of an N-point DFT has a complexity of the order of N 2 operations, while the fast algorithm for DFT calculation, the Fast Fourier Transform (FFT), drastically reduces the complexity to Nlog 2 N operations. For large N, the computational complexity is reduced by several orders of magnitude. The reduction technique is a fundamental topic of digital signal processing and is based on two equivalent techniques, known as decimation in time and decimation in frequency. In this chapter this technique will be formulated in the framework of the parallel architecture seen in Chap. 7, with a unified approach that is valid for the 1D case, as well as for the general mD case.
In the second part of the chapter, the use of the FFT is developed in several applications of digital signal processing.
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- 1.
For an alternative introduction, we suggest the tutorial paper [4].
- 2.
To the author’s knowledge, the largest FFT implemented is found in the NASA SETI (Search for Extra-terrestrial intelligence) project with N equal to 230≃109.
- 3.
In FFT packages where real and imaginary parts are introduced separately, it is important to fill the imaginary part with N zeros.
References
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© 2011 Springer-Verlag London Limited
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Cariolaro, G. (2011). Signal Analysis via Digital Signal Processing. In: Unified Signal Theory. Springer, London. https://doi.org/10.1007/978-0-85729-464-7_13
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DOI: https://doi.org/10.1007/978-0-85729-464-7_13
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