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.

Radar processing gain improvement over frequency using the discrete wavelet transform

Abstract: The range-gated fast Fourier transform (FFT) is the most common implementation of the optimum receiver for radar signals having random phase, frequency, and arrival time. In practice, the receiver is only optimum for input signals with frequency equal to an FFT bin frequency. Here the discrete wavelet transform (DWT) is applied to the FFT output to recover processing gain (PG) lost for nonoptimum input signals. Since the FFT and FFT-DWT have optimum performance for different input frequencies, these algorithms can be combined by binary integration (BI) to result in a dramatically improved worst case PG over frequency.

High capacity FFT-based audio watermarking

Abstract: This paper proposes a novel high capacity audio watermarking algorithm to embed data and extract it in a bit-exact manner based on changing the magnitudes of the FFT spectrum. The key idea is to divide the FFT spectrum into short frames and change the magnitude value of the FFT samples based on the average of the samples of each frame. Using the average of FFT magnitudes makes it possible to improve the robustness, since the average is more stable against changes compared with single samples. In addition to good capacity, transparency and robustness, this scheme has three parameters which facilitate the regulation of these properties. Considering the embedding domain, audio watermarking techniques can be classified into time domain and frequency domain methods. In frequency domain watermarking [1-7], after taking one of the usual transforms such as the Discrete/Fast Fourier Transform (DFT/FFT) [4-6], the Modified Discrete Cosine Transform (MDCT) or the Wavelet Transform (WT) from the signal [7], the hidden bits are embedded into the resulting transform coefficients. In [4-6], which were proposed by the authors of this paper, the FFT domain is selected to embed watermarks for making use of the translation-invariant property of the FFT coefficients to resist small distortions in the time domain. In fact, using methods based on transforms provides better perceptual quality and robustness against common attacks at the price of increasing the computational complexity.

Fixed structure FFT algorithm and application in fault diagnoses

Abstract: A Fixed Structure FFT Algorithm(FS-FFT) was introduced.Changing the butterfly shape into a fixed structure,the same structure on each level can be formed.Address manipulation times to data registers can be reduced obviously,consequently,improve FFT speed.Experiments on numerical control grinder fault diagnoses have been applied,and experiment results show its practicability and validity.The efficiency of this algorithm can be improved about 7.23% than classical FFT.

An Innovative Fast Algorithm and Structure Design for Analysis and Synthesis Quadrature Mirror Filterbanks on the SBR in DRM

Abstract: This brief presents a novel fast algorithm derivation and structure design of analysis and synthesis quadrature mirror filterbanks (SQMFs) on the spectral band replication in Digital Radio Mondiale (DRM). After the preprocedure and postprocedure, a Fourier-transform-based computational kernel was required to construct two types of fast algorithms that offered certain advantages. The Proposed-I method employs a modified split-radix fast Fourier transform (FFT) for analysis quadrature mirror filterbank (AQMF) to reduce the number of additions at the last stage of the butterfly and adopts a split-radix FFT to calculate the SQMF coefficients. The Proposed-II method used the compact structure of the variable-length recursive DFT to realize the kernel procedure for the proposed fast AQMF and SQMF algorithms. In addition, a well-known lifting scheme was applied to reduce numerous multiplication and addition calculations. Compared with the original calculations for the long transform length, all multiplication, addition, and coefficient operations for the Proposed-I method (i.e., AQMF + SQMF) had 91.65%, 79.81%, and 97.22% reductions, respectively. However, for the Proposed-II method, the total reductions of multiplication, addition, and coefficient operations were 64.16%, 21.53%, and 97.12%, respectively. Compared with the fast SQMF algorithm by Huang , the Proposed-I method for SQMF reduces 58.33% of the multiplication, 65% of the addition, and 67.19% of the coefficients. Therefore, the proposed fast quadrature mirror filterbank algorithm is a better solution than other approaches for future DRM applications.

Terabit/s FFT processing – optics can do it on-the-fly

Abstract: The discrete Fourier Transform (DFT) or its more popular efficient algorithm, the Fast Fourier Transform (FFT) is one of the important mathematical functions in the toolbox of signal processing. To this date its processing speed is limited by the underlying electronic processors. We show that FFT signal processing limitations can be overcome by performing the FFT in the optical domain and demonstrate the power of the technique by performing the FFT on a single source 10 Tbit/s OFDM signal.