where w(n) is an analysis window. At each time instant, the STFT is a discrete-time Fourier transform or discrete Fourier transform (DFT). Many DFT computing algorithms and architectures have been proposed. However, the direct use of the DFI' without considering the special sliding window effect of STFT is not an efficient approach. There are two major approaches for STFT. One is based on the f...

The discrete Fourier transform of the greatest common divisor � id[a](m) = m � k=1 gcd(k,m)α m , with αm a primitive m-th root of unity, is a multiplicative function that generalizes both the gcd-sum function and Euler’s totient function. On the one hand it is the Dirichlet convolution of the identity with Ramanujan’s sum, � id[a] = id ∗ c•(a), and on the other hand it can be written as a gener...

We present the Nahm transform of the doubly-periodic instantons previously introduced by the author, converting them into certain meromorphic solutions of Hitchin’s equations over an elliptic curve.

The p-adic q-integral (= Iq-integral) was defined by author in the previous paper [1, 3]. In this paper, we consider Iq-Fourier transform and investigate some properties which are related to this transform. §

[08.3] Compute e−πx 2 ∗ e−πx2 and sinx x ∗ sinx x . (Be careful what you assert: sin x x is not in L (R).) Discussion: The idea is to invoke f ∗ g = (f̂ · ĝ)̂ for even functions f, g ∈ L, since for even functions the inverse Fourier transform is the same as the forward Fourier transform. Conveniently, Gaussians are in L ∩ L, and have Fourier transforms which are again Gaussians: ̂ e−πax(ξ) = 1 √ a...

In several problems in Harmonic Analysis, .and in Number Theory as well, lemmas on small values of holomorphic functions play an important role. Let us give first an example from Harmonic Analysis. distributions with compact support in 17% " whose Fourier transforms satisfy, in C " , a lower estimate of the form (0.2) with v, ,..., v, also distributions with compact support 131, 33). In many ex...

The magnetohydrodynamic MHD and rotating flow of second-grade fluid over a suddenly moved flat plate is investigated, where the second-grade fluid saturates the porous medium. The new exact solution is derived by using the Fourier sine and Laplace transforms. Many interesting available results in the literature are obtained as limiting cases of our solution. Finally, some graphical results are ...

In this paper, for positive integers m, M , and a prime p such that M |pm − 1, we derive linear complexity over the prime field Fp of M -ary Sidel’nikov sequences of period pm−1 using discrete Fourier transform. As a special case, the linear complexity of the ternary Sidel’nikov sequence is presented. It turns out that the linear complexity of a ternary Sidel’nikov sequence with the symbol k0 =...

In this paper, we apply a new method of evaluating the Discrete Fourier Transform that requires significantly less computational effort. In this evaluation, the Discrete Fourier Transform is defined over the support of the sequence of interest. The method can be applied to search for sequences with zero periodic autocorrelation function. As an example we apply the procedure and we were able to ...