Signal Analysis via Digital Signal Processing
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.
KeywordsFast Fourier Transform Discrete Fourier Transform Separable Lattice Fast Fourier Transform Algorithm Secondary Lobe
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