Discrete-time Fourier Series Research Articles

Discrete-Time Fourier Series to simulate transient over voltages in power systems

This paper presents a methodology based on the Discrete-Time Fourier Series (DTFS) to calculate transient over-voltages in power systems. The proposed algorithm determines the time window with sufficient width to allow the time constants of the transients to decay to a small value. This method is simpler than the traditional numerical Laplace transform (NLT) and does not require parameters adjustment to obtain accurate results. The test case is based on a study to calculate Transient Over-Voltages (TOV) for 138 kV transmission lines in British Columbia, Canada. To assess the accuracy of the results, the DTFS solution is compared with the traditional NLT solution with optimized parameters and with the frequency-dependent time-domain models: fdLINE (JMARTI Model) and Universal Line Model (ULM).

Time-Window-Based Discrete-Time Fourier Series for Electromagnetic Transients in Power Systems

This paper approaches the solution of electromagnetic transients in the frequency domain from the point of view of choosing a time window with sufficient width to allow the time constants of the transients to decay to a small value. This criterion, and the required maximum frequency content of the simulation, fully determine the simulation parameters. Satisfying this criterion, a very simple methodology, like the discrete time Fourier series (DTFS), can provide very accurate results without the inherent difficulties of time-warping solutions based on the numerical Laplace transform (NLT). Even though the NLT can give very accurate results, it requires expert knowledge to correctly specify the damping factors, sampling schemes, and windowing functions. The DTFS solution is compared with the NLT and with analytical solution for a circuit with lumped elements, and with the most-accepted frequency-dependent transmission line models in the Electromagnetic Transients Program: the JMARTI (fdLINE) model and the Universal Line Model for a double-circuit transmission line.

Flexible Piezoelectric Sensor-Based Gait Recognition.

Most motion recognition research has required tight-fitting suits for precise sensing. However, tight-suit systems have difficulty adapting to real applications, because people normally wear loose clothes. In this paper, we propose a gait recognition system with flexible piezoelectric sensors in loose clothing. The gait recognition system does not directly sense lower-body angles. It does, however, detect the transition between standing and walking. Specifically, we use the signals from the flexible sensors attached to the knee and hip parts on loose pants. We detect the periodic motion component using the discrete time Fourier series from the signal during walking. We adapt the gait detection method to a real-time patient motion and posture monitoring system. In the monitoring system, the gait recognition operates well. Finally, we test the gait recognition system with 10 subjects, for which the proposed system successfully detects walking with a success rate over .

Periodic disturbance rejection to the Nyquist frequency and beyond

In this paper, we address periodic disturbance rejection for sampled-data control systems, where the frequency of the disturbance can be beyond the Nyquist frequency of the limited measured plant output sampling rate. The disturbance effect on steady-state response of the fictitious fast-rate plant output including intersample information is obtained using discrete-time Fourier series. A sufficient condition for disturbance rejection together with a sufficient and necessary condition for perfect disturbance elimination are provided by employing the steady-state response. A simple but effective controller design procedure combining H∞ loop shaping, Youla–Kucera parameterization, and gradient methods is provided to achieve the two conditions. The proposed approach is applied on vibration control beyond the Nyquist frequency in a commercial hard disk drive. The effectiveness of the proposed approach is verified by our simulation results showing disturbance rejection of 62% and perfect disturbance elimination, as well as by our experimental results showing disturbance rejection of 54%.

Disturbance observer-based multirate control for rejecting periodic disturbances to the Nyquist frequency and beyond

Intersample behavior cannot be ignored when a sampled-data control system is subject to periodic disturbances beyond the Nyquist frequency. In this paper, a disturbance observer-based multirate control scheme is proposed to deal with such a periodic disturbance problem. First, using discrete-time Fourier series, the effect of the periodic disturbance on steady-state response of the plant output including intersample information is derived. Next, based on the steady-state output response, a sufficient condition is provided for minimization of the disturbance effect on the output. It turns out that solving the sufficient condition is a problem of quadratic optimization with several equality constraints. The proposed approach is applied on vibration control of mechanical resonant modes beyond the Nyquist frequency in a commercial hard disk drive. Perfect disturbance elimination and disturbance deduction of 72% in fast-rate discrete-time response are observed in the simulation and experiment, respectively.

FPGA-Based Test-Bench for Resonant Inverter Load Characterization

Resonant converters often require accurate load characterization in order to ensure appropriate and safe control. Besides, for systems with a highly variable load, as the induction heating systems, a real-time load estimation is mandatory. This paper presents the development of an FPGA-based test-bench aimed to extract the electrical equivalent of the induction heating loads. The proposed test-bench comprises a resonant power converter, sigma-delta ADCs, and an embedded system implemented in an FPGA. The characterization algorithm is based on the discrete-time Fourier series computed directly from the ΔΣ ADC bit-streams, and the FPGA implementation has been partitioned into hardware and software platforms to optimize the performance and resources utilization. Analytical and simulation results are verified through experimental measurements with the proposed test-bench. As a result, the proposed platform can be used as a load identification tool either for stand-alone or PC-hosted operation.

On Speedy Recognition of Non-Aliased Realization after Multifold Downsampling of an Oversampled Bandlimited Signal

The aim of the given paper is the development of the criterion and some expressions for recognizing a nonaliased realization in the set of realizations obtained by multifold decimation (filtering and downsampling) of any oversampled bandlimited signal that has been obtained at the beginning by periodic sampling of a continuous-time signal. For each nondecimated as well as decimated realization discrete-time Fourier series coefficient values, located at Nyquist frequency are calculated, using speedy recursive expressions based on reverse order processing of the given realizations. In such a case, the summing calculation amount has been significantly reduced by applying the expressions that use, in each iteration, the respective values obtained by processing samples of a previously downsampled realization and some samples of the currently downsampled one. We formulate definitions and prove the corollaries that refer to the recursive Fourier coefficient calculation and present here an example. Finally, the simulation results for the bandlimited signal with a triangularshaped spectrum are presented.DOI: http://dx.doi.org/10.5755/j01.itc.41.3.851

On recursive stopping of decimation of discrete-time bandlimited signals

For each non-decimated as well as decimated realization discrete-time Fourier series coefficient values, located at Nyquist frequency are calculated, using original speedy recursive expressions based on reverse order processing of the given realizations. The criterion for stopping of multifold decimation of discrete-time bandlimited signals has been developed. The simulation results for the bandlimited signal with a triangularshaped spectrum are presented.

Harmonic Distortion in Switched Current Cells Due to Settling Error

An analysis of the harmonic distortion in switched-current cells produced by the non-linear settling error is presented. Two approaches for computing the harmonic components are addressed: discrete-time Fourier series and power series expansion. They are based on the large signal behavior of the SI cell. A compact and flexible expression is obtained with series expansion. An alternative expression is presented for cases where only the settling error magnitude is required. The effect of charge redistribution between the input and the sampling nodes is analyzed. It is shown that including that effect, the harmonic distortion is increased, and the DC gain of the SI integrator is reduced. An analysis of the total harmonic distortion when clock-feed-through and non-linear settling error are both taken into account is presented. It is demonstrated that minimum distortion is reached for a given capacitive value. For a SI cell designed with 0.8 μm standard CMOS technology working at a sampling frequency of 8 MHz, a minimum THD of −72 dB can be obtained with a Cgs a 2.4 pF.