We give a detailed study of the discrete Fourier transform (DFT) of r-even arithmetic functions, which form a subspace of the space of r-periodic arithmetic functions. We consider the DFT of sequences of r-even functions, their mean values and Dirichlet series. Our results generalize properties of the Ramanujan sum. We show that some known properties of r-even functions and of the Ramanujan sum...

A. Table of contents by sections: 1. Abstract (you’re reading this now) 2. Summary of the DFT (How do I do the homework?) 3. Review of continuous-time Fourier series 4. Bandlimited signals and finite Fourier series 5. Sampling theorem for periodic signals 6. Review of quirks of discrete-time frequency 7. Orthogonality and its significance 8. Discrete Fourier Transform (DFT) 9. Use of DFT to com...

Practical mixed-signal DFT solutions are presented with an emphasis on performance, cost, and test coverage. Special consideration is given to the possible DFT techniques for Phase-Locked Loops (PLLs) with associated implications on test coverage, performance, cost, and time to market. An introduction to practical DFT techniques for data converters (A/D and D/A) follow. An overview of IEEE P114...

Dynamic Fault Trees (DFT) are a generalization of Fault Trees which allows the evaluation of the reliability of complex and redundant systems. We propose to analyze DFT by a new version of time parallel simulation method we have recently introduced. This method takes into account the monotonicity of the sample-paths to derive upper and lower bounds of the paths which become tighter when we incr...

Density functional theory (DFT) is an incredible success story. The low computational cost, combined with useful (but not yet chemical) accuracy, has made DFT a standard technique in most branches of chemistry and materials science. Electronic structure problems in a dazzling variety of fields are currently being tackled. However, DFT has many limitations in its present form: too many approxima...

This brief paper describes design-for-testability (DFT) circuitry that reduces testing time and thus cost of testing DC linearity of SAR ADCs. We present here the basic concepts, an actual SAR ADC chip design employing the proposed DFT, as well as measurements that verify its effectiveness. Since the DFT circuit overhead is small, it is practicable. key words: SAR ADC, testing, DC linearity, de...

Coinage metal cyanides (MCN) form photoluminescent 1D coordination polymers. The decoration of these chains with amine and phosphine ligands shifts the wavelength for photoluminescence into the visible region. Density-functional theory (DFT) and time-dependent DFT (TD-DFT) calculations of zigzag and helical models of decorated chains are used to show that the transitions that contribute to the ...

| Based on the least mean squares (LMS) algorithm , the LMS spectrum analyzer can be used to re-cursively calculate the discrete Fourier transform (DFT) of a sliding window of data. In this paper, we compare the LMS spectrum analyzer with the straightforward non-adaptive implementation of the recursive DFT. In particular , we demonstrate the robustness of the LMS spectrum analyzer to the propag...

Adequate polarization functions reduce the error of density functional theory (DFT) for the heat of reaction for CF(4) + SiCl(4) from ∼9-12 kcal mol(-1) to ∼2-4 kcal mol(-1), and using an improved density functional further reduces it to ∼1 kcal mol(-1). This reaction was previously identified as a stumbling block for DFT, but we show that the problem with the previous calculations was not DFT ...

Sensor data have become very huge and single measures are produced at high rates, resulting in streaming sensor data. In this paper, we present a new mining tool called Online DFT, which is particularly powerful for estimating the spectrum of a data stream. Unique features of our new method include low update complexity with high-accuracy estimations for very long periods, and the ability of lo...