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Split-radix FFT algorithm
About: Split-radix FFT algorithm is a research topic. Over the lifetime, 1845 publications have been published within this topic receiving 41398 citations.
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TL;DR: A low cost real-time synthesizer design allowing processing of recorded and live sounds, synthesis of instruments and synthesis of speech and the singing voice is proposed.
Abstract: We present a new additive synthesis method based on spectral envelopes and inverse Fast Fourier Transform (FFT -1). User control is facilitated by the use of spectral envelopes to describe the characteristics of the short term spectrum of the sound in terms of sinusoidal and noise components. Such characteristics can be given by users or obtained automatically from natural sounds. Use of the inverse FFT reduces the computation cost by a factor on the order of 15 compared to oscillators. We propose a low cost real-time synthesizer design allowing processing of recorded and live sounds, synthesis of instruments and synthesis of speech and the singing voice.
93 citations
TL;DR: An extended split-radix fast Fourier transform (FFT) algorithm is proposed that has the same asymptotic arithmetic complexity as the conventional split- Radix FFT algorithm but has the advantage of fewer loads and stores.
Abstract: An extended split-radix fast Fourier transform (FFT) algorithm is proposed. The extended split-radix FFT algorithm has the same asymptotic arithmetic complexity as the conventional split-radix FFT algorithm. Moreover, this algorithm has the advantage of fewer loads and stores than either the conventional split-radix FFT algorithm or the radix-4 FFT algorithm.
90 citations
TL;DR: This paper derives explicit expressions for the mean square error in the FFT when floating-point arithmetics are used, and upper and lower bounds for the total relative meansquare error are given.
Abstract: The fast Fourier transform (FFT) is an algorithm to compute the discrete Fourier coefficients with a substantial time saving over conventional methods. The finite word length used in the computer causes an error in computing the Fourier coefficients. This paper derives explicit expressions for the mean square error in the FFT when floating-point arithmetics are used. Upper and lower bounds for the total relative mean square error are given. The theoretical results are in good agreement with the actual error observed by taking the FFT of data sequences.
89 citations
TL;DR: A fast algorithm for computing volume potentials - that is, the convolution of a translation invariant, free-space Green's function with a compactly supported source distribution defined on a uniform grid is introduced.
84 citations
TL;DR: A “prime factor” Fast Fourier Transform algorithm is described which is self-sorting and computes the transform in place and it is obtained that the required indexing is actually simpler than that for a conventional FFT.
83 citations