In the next two lectures, we will continue to expand our toolbox for computing in frequency domain, by adding two important computational tools. The first, the Fast Fourier Transform (FFT) is a family of algorithms for efficiently computing the Discrete Fourier Transform. These algorithms are of great practical importance, as theymake it possible to perform frequency domain analysis of very lar...

The DFT can be reduced from exponential time with the Fast Fourier Transform algorithm. Fast Fourier Transform (FFT) One wonders if the DFT can be computed faster: Does another computational procedure an algorithm exist that can compute the same quantity, but more e ciently. We could seek methods that reduce the constant of proportionality, but do not change the DFT's complexity O ( N ) . Here,...

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A fast Fourier transform (FFT) is an efficient algorithm to compute the discrete Fourier transform (DFT) of an input vector. Efficient means that the FFT computes the DFT of an n-element vector in O(n logn) operations in contrast to the O(n2) operations required for computing the DFT by definition. FFTs exist for any vector length n and for real and higher-dimensional data. Parallel FFTs have b...

Fast Fourier Transform is one of the most important numerical algorithms in history. It has wide range of applications: audio signal processing, medical imaging, image processing, pattern recognition, computational chemistry, error correcting codes and spectral methods for PDE’s. The goal of this project is to implement an OpenCL based FFT algorithm that has comparable performance with existing...

Discussion of the considerations involved in high-performance FFT implementations, which center largely on memory access and other non-arithmetic concerns, as illustrated by a case study of the FFTW

FFT-based filters find wide use in both live and ‘tape’ electronic music. Here an attempt is made to develop straightforward guidelines for choosing parameters such as window size and overlap in order to obtain desired time and frequency resolution and minimize artifacts. As an application, filters derived from other sound sources (“FFT vocoders” or “timbre stamps”) are discussed in detail.