The fractional Fourier transform is a time–frequency distribution and an extension of the classical Fourier transform. There are several known applications of the fractional Fourier transform in the areas of signal processing, especially in signal restoration and noise removal. This paper provides an introduction to the fractional Fourier transform and its applications. These applications deman...

We estimate discrete Fourier transform, ambiguity, and Hamming-autocorrelation of m-ary sequences in terms of their (periodic) correlation measure of order 4. Roughly speaking, we show that every pseudorandom sequence, that is, any sequence with small correlation measure up to a sufficiently large order, cannot have a large discrete Fourier transform, ambiguity, or Hamming-autocorrelation. Conv...

s is a time-frequency transform based on the concept of short-time fourier transform and wavelet transform. the main property of this transform that separate it from the discrete short-time fourier transform is variable frequency resolution. but in this transform the change of resolution of high frequencies to low frequencies is very high. so another transform as a modified s transform is intro...

All algorithms for impedance calculation use an analog-to-digital converter. The high accuracy of the impedance seen by a distance relay is an important factor in the correct isolation of the faulty part of power systems. To achieve this, a novel&#10technique based on third order interpolation is used in this paper. According to this technique, the times and the values of the obtained samples a...

Abstract Even though generalized frequency division multiplexing is an alternative waveform method expected to replace the orthogonal in future, its implementation must alleviate channel effects. Least‐squares (LS), a low‐complexity estimation technique, could be improved by using discrete Fourier transform (DFT) without increasing complexity. Unlike usage of LS method, DFT‐based requires recei...

We compare several algorithms for computing the discrete Fourier transform of n numbers. The number of “operations” of the original Cooley-Tukey algorithm is approximately 2n A(n), where A(n) is the sum of the prime divisors of n. We show that the average number of operations satisfies (l/x)Z,,,2n A(n) (n2/9)(x2/log x). The average is not a good indication of the number of operations. For examp...

This paper presents an interpolation/extrapolation technique for sequence partitions. It consists of four steps: region parametrization, region interpolation, region ordering and partition creation. The evolution of each region is divided into two types: regular motion and random deformations. Both types of evolution are parametrized by means of the Fourier descriptors of the regions and they a...

An efficient method for implementing closed form discrete fractional Fourier transform for the purpose of signal compression is presented. Implementation method is compared with that of existing closed form discrete fractional Fourier transform, with respect to computational complexity, variance of quantization error, signal to noise ratio and number of bits for the representation of coefficien...