Topic
Prime-factor FFT algorithm
About: Prime-factor FFT algorithm is a research topic. Over the lifetime, 2346 publications have been published within this topic receiving 65147 citations. The topic is also known as: Prime Factor Algorithm.
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TL;DR: It is shown that for the fine-frequency estimator a good method is to fit a Gaussian function to the fast-Fourier-transform (FFT) peak and its two neighbors, which achieves a frequency standard deviation and a bias in the order of only a few percent of a bin.
Abstract: In the case of a single sinusoid or multiple well-separated sinusoids, a coarse estimator consisting of a windowed Fourier transform followed by a fine estimator which is an interpolator is a good approximation to an optimal frequency acquisition and measurement algorithm. The design tradeoffs are described. It is shown that for the fine-frequency estimator a good method is to fit a Gaussian function to the fast-Fourier-transform (FFT) peak and its two neighbors. This method achieves a frequency standard deviation and a bias in the order of only a few percent of a bin. In the case of short-time stationarity, for a moderate number of averages and for an adaptive threshold detector, only between 0.5 and 1 dB is lost when averaging is traded off for FFT length, in contrast to the asymptotic result of 1.5 dB. The COSPAS-SARSAT satellite system for emergency detection and localization is used to illustrate the concepts. The algorithm is analyzed theoretically, and good agreement is found with test results. >
29 citations
TL;DR: A novel algorithm to perform cooperative wideband spectrum sensing (CWSS) for cognitive radios (CRs) based on a sub-Nyquist version of the sparse fast Fourier transform (sFFT) algorithm is presented, and it is executed cooperatively by using M identical nodes.
Abstract: This brief presents a novel algorithm to perform cooperative wideband spectrum sensing (CWSS) for cognitive radios (CRs). The proposed algorithm is based on a sub-Nyquist version of the sparse fast Fourier transform (sFFT) algorithm, and it is executed cooperatively by using $\boldsymbol{M}$ identical nodes. In this case, we designed a CWSS circuit based on the proposed algorithm that implements the main functional procedures of the sub-Nyquist sFFT algorithm by using multi-coset sampling and relatively prime sampling rates. According to the verification results, the proposed circuit based on the designed CWSS algorithm is suitable for implementing CWSS in CRs for sparse spectra composed of highly noisy multiband signals, and it improves the performance of previous sub-Nyquist sFFT algorithm and previous sFFT hardware implementation.
29 citations
TL;DR: In this paper, a fast Fourier transform (FFT) based method for time-varying power system harmonic measurement is proposed, where the harmonic signal is preprocessed by infinite impulse response filter bank and Teager-Kaiser energy operator for fast detection of instability onset time.
Abstract: As the rapid development in power electronic devices, the harmonic pollution becomes one of principle power quality problems in power system. The fast Fourier transform (FFT) is widely used for analysing and measuring power system harmonics. However, the limitation of the FFT such as an aliasing effect, spectrum leakage picket-fence effect, would contribute to inaccuracy results. Furthermore, the real power system harmonic is actually a non-stationary signal while FFT is a tool for stable signal. This study focuses on a novel FFT based method for time-varying power system harmonic measurement. The harmonic signal is preprocessed by infinite impulse response filter bank and Teager–Kaiser energy operator for fast detection of instability onset time. Then an adaptive Kaiser self-convolution window-based interpolated FFT algorithm is used to estimate each harmonic component. The results of both simulation and practical implementation show that the proposed method is suitable to deal with time-varying harmonic and achieves a higher accuracy compared with the traditional FFT-based techniques.
29 citations
06 Apr 2003
TL;DR: A theorem is presented that decomposes a polynomial transform into smallerPolynomial transforms, and it is shown that the FFT is obtained as a special case, which is used to derive a new class of recursive algorithms for the discrete cosine transforms of type II and type III.
Abstract: The Cooley-Tukey FFT algorithm decomposes a discrete Fourier transform (DFT) of size n = km into smaller DFT of size k and m. In this paper we present a theorem that decomposes a polynomial transform into smaller polynomial transforms, and show that the FFT is obtained as a special case. Then we use this theorem to derive a new class of recursive algorithms for the discrete cosine transforms (DCT) of type II and type III. In contrast to other approaches, we manipulate polynomial algebras instead of transform matrix entries, which makes the derivation transparent, concise, and gives insight into the algorithms' structure. The derived algorithms have a regular structure and, for 2-power size, minimal arithmetic cost (among known DCT algorithms).
29 citations
TL;DR: In this article, a 2-D systolic array algorithm for the discrete cosine transform (DCT) is presented, which is based on the inverse discrete Fourier transform (DFT) version of the Goertzel algorithm via Horner's rule.
Abstract: A 2-D systolic array algorithm for the discrete cosine transform (DCT) is presented. It is based on the inverse discrete Fourier transform (DFT) version of the Goertzel algorithm via Horner's rule. This array requires N cells and multipliers, takes square root N+2 clock cycles to produce a complete N-point DCT, and is able to process a continuous stream of data sequences. >
29 citations