Raised Cosine Function Research Articles

Adaptive neural dynamic surface control for uniform energy exploitation of floating wind turbine

To avoid the harmful effects of global warming on the earth planet and its atmosphere, the expansion of wind energy consumption based on new control techniques leads to improved energy capacity. The development of wind power plants on the sea is more efficient owing to the stronger wind flows in comparison with the onshore structure. Furthermore, stable installation of the offshore wind energy base meets the energy management requirements of today's consumers. As a result, dependency on fossil fuels as the main source of global warming decreases. The feedback control system and on-line sensor signals provide the stability and increased efficiency of the floating wind turbine. The aggressive environment and large size structure of the turbine lead to entering uncertainty in the turbine model and exogenous noises that should not be effectively compensated by conventional control methods. Therefore, a radial based functional neural network (RBFNN) controller is proposed to estimate and compensate the effect of uncertainty on feedback control of the wind turbine. For comparison purposes, a linear quadratic regulator (LQR) state feedback is also developed for optimal control of the floating wind turbines. The neural network adaptively determines the upper bound of uncertainty/noise. Therefore, conservative high-gain control actions to achieve robustness of the classical feedback controllers against structural deviations of the turbine body are decreased. In our newly proposed adaptive control algorithm, using a basic raised cosine function guides to restore the computational efficiency of RBFNN. With the Lyapunov-based stability analysis, the final limits of the closed-loop system and the convergence caused by the terminal sliding mode (TSM) tracking error are determined. Detailed software simulations of both the LQR and the designed RBFNN control systems indicate the superiority of the neural network-based approach.

A fast bilateral filtering algorithm based on rising cosine function

In order to speed up the bilateral filtering algorithm, a fast bilateral filtering algorithm based on raised cosine with compressibility factor (BRCF) is proposed. The BRCF uses a raised cosine function with a compression coefficient to replace Gaussian function as the range kernel function, and uses a limited number of linear convolution calculations to achieve bilateral filtering. Then, the improved BRCF (IBRCF) with a compression factor is proposed to accelerate the convergence rate of the raised cosine function. Compared to the published raised cosine algorithm, Taylor polynomial algorithm, and Gaussian polynomial algorithm, the computer simulation results show that the proposed IBRCF has a faster convergence rate with almost the same peak signal-to-noise ratio. After filtered seven images by various algorithms, the running time of the new IBRCF algorithm was confirmed to be less than 1/5 of Gaussian polynomial algorithm, while Gaussian polynomial algorithm was faster than the published raised cosine algorithm and Taylor polynomial algorithm. The mathematical proofs and algorithm flowcharts of the IBRCF algorithm are described in this paper in detail.

Performance evaluation of different precoding matrices for PAPR reduction in OFDM systems

Orthogonal frequency division multiplexing (OFDM) is an attractive technique for wireless communication systems due to its ability to mitigate frequency selectivity. However, OFDM suffers from high peak‐to‐average power ratio (PAPR) problem, which reduces the power amplifier (PA) efficiency or worse it degrades bit error rate (BER) performance and increases out‐of‐band radiation. In literature, there are different PAPR reduction techniques. Among them PAPR reduction by precoding matrices has small computational complexity along with high PAPR reduction gain. In this paper the six precoding matrices found in the literature are compared. Results showed that, all precoding matrices, except the one that based on square‐root raised cosine function (SRC), are not effective in terms of BER performance in presence of nonlinear PA, especially in high modulation order schemes (eg, 16‐QAM and 64‐QAM). However, precoding technique based on SRC matrix requires high data rate loss, to enhance the BER performance in presence of nonlinear PA. So, it can be said that, precoding technique worsens the problem especially in high modulation order schemes, except the SRC matrix‐based precoding technique, which cannot be used without high data rate loss.

A high-speed phosphorescent LED-based visible light communication system utilizing SQGNRC precoding technique

Peak-over-average power ratio (PAPR) control utilizing precoding technique based on square root-generalized raised cosine function is proposed and verified experimentally through a visible light communication system employing phosphor-based white light-emitting diodes for the first time. The simulation results show that the improved precoding matrix can further reduce PAPR by nearly 1 dB compared with existing precoding matrix based on square root raised cosine function and significantly achieve 3.5 dB improvement in contrast to original signals without precoding. The experimental result also proves that the bit error rate performance can be effectively improved by 1.62 dB at the same bandwidth and 0.76 dB at the same raw data rate in terms of quality factor when proposed precoding technique is applied, which clearly demonstrates its benefit and feasibility.

Constructed Polynomial Windows with High Attenuation of Sidelobes

In the paper the idea of the constructed polynomial windows is presented together with the obtained results of their optimization towards low level of the sidelobes. The main advantages of the polynomial windows are their low computational complexity and ability to change their frequency properties by some modifications of the polynomial coefficients in the time domain. Both of these merits are preserved in the constructed polynomial windows family discussed in the paper and the additional profit is the possibility of using two lower order polynomials with additional switching operation with similar sidelobes' attenuation as for higher order standard polynomial windows. Typical applications of the window functions in digital signal processing are related to spectral analysis based on Fourier transform and design of Finite Impulse Response (FIR) filters for the reduction of Gibbs phenomenon. Considering the Fourier analysis, the main advantage of using windows is the reduction of the spectral leakage caused by the finite number of processed samples in the time domain, due to the prevention of the rapid cutting of the series of collected data samples. Window functions can be characterised by several parameters, which influence their characteristics in frequency domain. A perfect window in the frequency domain should have a narrow mainlobe, low level of sidelobes and high sidelobes decay ratio. Nevertheless, these requirements are contradictory so many window functions partially fulfilling them have been proposed by various researchers. Classical well-known windows, used instead of the rectangular or simple Bartlett window, are Hann, Hamming and Blackman windows (1) and their modifications (2) based on raised-cosine functions. Some other famous windows are Dolph-Chebyshev and Kaiser, which have been optimized using various criteria - the first one is the effect of the minimization of the sidelobes level without decay and the second one is sub-optimal in the energetic sense minimizing the sidelobes to the mainlobe energy ratio.

Uniform Illumination Rendering Using an Array of LEDs: A Signal Processing Perspective

An array of a large number of LEDs will be widely used in future indoor illumination systems. In this paper, we investigate the problem of rendering uniform illumination by a regular LED array on the ceiling of a room. We first present two general results on the scaling property of the basic illumination pattern, i.e., the light pattern of a single LED, and the setting of LED illumination levels, respectively. Thereafter, we propose to use the relative mean squared error as the cost function to measure the uniformity of the realized illumination pattern, and provide an analysis for this cost function. Based on the analysis, the design of a basic illumination pattern is discussed. The performances of a few basic illumination patterns are compared, and an approach for optimizing the basic illumination pattern through a weighted combination of these basic patterns is also proposed. A weighted combination of Gaussian and raised-cosine functions is found to yield the best results. Finally, three basic regular grid shapes for an LED array are compared. The results show that 13% and 39% of LEDs can be saved for the same degree of uniformity, using the hexagonal instead of the rectangular and triangular grid, respectively.

Compensation of Loudspeaker Nonlinearity in Acoustic Echo Cancellation Using Raised-Cosine Function

Compensation of Loudspeaker Nonlinearity in Acoustic Echo Cancellation Using Raised-Cosine Function

Optimal design of coupling waveguide structure for adiabatic optical directional full couplers weighted by sin-square and raised-cosine functions

The optimal design of coupling waveguide structure for adiabatic optical directional full couplers (AODFC) based on weighted sin-square function (SSF) and raised-cosine function (RCF) are investigated in this paper. The coupling lengths with a crosstalk smaller than −30 dB at the operating wavelength of 1.57 μm resulted in a value of 3.0 and 2.4 mm for the SSF and RCF cases, respectively. Under the same level of crosstalk, the wavelength ranges obtained by weighted SSF and RCF could be varied about 1.33–1.70 μm and 1.27–1.70 μm with coupler lengths of 6.0 and 5.5 mm, respectively. Clearly, the AODFC weighted by RCF has the superior performances of both short coupling length and broad wavelength ranges.

Real-Time Dynamic Articulations in the 2-D Waveguide Mesh Vocal Tract Model

Time domain articulatory vocal tract modeling in one-dimensional (1-D) is well established. Previous studies into two-dimensional (2-D) simulation of wave propagation in the vocal tract have shown it to present accurate static vowel synthesis. However, little has been done to demonstrate how such a model might accommodate the dynamic tract shape changes necessary in modeling speech. Two methods of applying the area function to the 2-D digital waveguide mesh vocal tract model are presented here. First, a method based on mapping the cross-sectional area onto the number of waveguides across the mesh, termed a widthwise mapping approach is detailed. Discontinuity problems associated with the dynamic manipulation of the model are highlighted. Second, a new method is examined that uses a static-shaped rectangular mesh with the area function translated into an impedance map which is then applied to each waveguide. Two approaches for constructing such a map are demonstrated; one using a linear impedance increase to model a constriction to the tract and another using a raised cosine function. Recommendations are made towards the use of the cosine method as it allows for a wider central propagational channel. It is also shown that this impedance mapping approach allows for stable dynamic shape changes and also permits a reduction in sampling frequency leading to real-time interaction with the model

Compensation of Loudspeaker Nonlinearity in Acoustic Echo Cancellation Using Raised-Cosine Function

The nonlinearity of a power amplifier or loudspeaker in a large-signal situation gives rise to a nonlinear distortion of acoustic signal. A conventional acoustic echo canceller using linear adaptive filters is not able to eliminate the nonlinear echo component. In this brief, a novel nonlinear echo cancellation technique is presented by using a nonlinear transformation in conjunction with a conventional linear adaptive filter. The nonlinear transformation is derived from a raised-cosine function and is exploited to compensate for the nonlinearity of a loudspeaker. The transformation parameters are updated using the normalized least mean square algorithm according to the unknown nonlinear characteristic of the loudspeaker. Computer simulations show that the proposed method yields, in general, a satisfactory cancellation performance while having a very low computational complexity

Experimental demonstration of a long-period grating based on the sampling theorem

We demonstrate experimentally the feasibility of a long-period grating whose index change pattern is in the form of sampling a raised-cosine function. We call such a grating a long-period grating based on the sampling theorem (LPGST). The LPGST is thermo-optically induced by an array of electrodes with individual widths. The array period is equal to the sampling period of 100μm, and the period of the sampled function is 395μm. A fabricated polymer long-period waveguide grating using the LPGST has a desired resonance band in its transmission spectrum, which is generated by the periodicity of the sampled function.

Behavior of different ansätze in the generalized projection operator method

Abstract Using the recently reported generalized projection operator method for the nonlinear Schrodinger equation, we derive the generalized pulse parameters equations for ansatze like hyperbolic secant and raised cosine functions. In general, each choice of the phase factor θ in the projection operator gives a different set of ordinary differential equations. For θ = 0 or θ = π /2, the corresponding projection operator scheme is equivalent to the Lagrangian variation method or the bare approximation of the collective variable theory. We prove that because of the inherent symmetric property between the pulse parameters of a Gaussian ansatz results the same set of pulse parameters equations for any value of the generalized projection operator parameter θ . Finally we prove that after the substitution of the ansatze function, the Lagrange function simplifies to the same functional form irrespective of the ansatze used because of a special property shared by all the anatze chosen in this work.

A novel OFDM receiver with second order polynomial nyquist window function

A class of time domain second order polynomial Nyquist window functions and a new receive method are proposed and applied to orthogonal frequency-division multiplexing for reducing frequency offset induced inter-carrier interference (ICI) in the receiver. As far as the delay spread is shorter than the guard interval, we can find a member of the class providing better signal to ICI ratio than the rectangular function and raised cosine function.

Detection of auditory "events" based on amplitude and frequency modulation.

These experiments examined the ability of subjects to detect auditory "events" composed of a brief modulation in the temporal center of an otherwise steady sinusoid. In experiment 1, psychometric fluctuations were measured for detecting either amplitude modulation (AM) or frequency modulation (FM) composed of a single cycle of a raised-cosine function (either positive going or negative going); the modulation frequency was 10 Hz, so the event lasted for 100 ms. Then, psychometric functions were measured for stimuli with both AM and FM, using pairs of values of AM and FM that were equally detectable; pairs were always modulated in the same direction, so a positive amplitude excursion went together with a positive frequency excursion. Performance was compared with the "reference" detectability that would be predicted from the optimal combination of independent sources of information. When the AM and FM were synchronous, detectability was better than the reference detectability. When the FM was delayed by 100 ms relative to the AM, detectability was mostly equal to or less than the reference detectability. The better performance with synchronous AM and FM is consistent with an explanation based on an excitation-pattern model. Experiment 2 was similar to experiment 1, except that the event was a single cycle of sinusoidal modulation starting at 0 degree phase or 180 degrees phase. When the AM and FM were synchronous and in phase, detectability was better than the reference detectability. When the AM was delayed by 200 ms relative to the FM or had opposite starting phase, detectability was close to or below the reference detectability. However, for the case where the delay was 100 ms and the modulation had the same starting phase for AM and FM, detectability was better than the reference detectability. A control experiment using two successive cycles of either AM or FM showed a similar, but slightly smaller, effect. It appears that detectability can be enhanced when two successive events form a regular temporal pattern.

Effect of contrast and adaptation on the perception of the direction and speed of drifting gratings

Three experiments were conducted to analyse the effect of contrast and adaptation state on the ability of human observers to discriminate the motion of drifting gratings. In the first experiment, subjects judged the direction of briefly presented gratings, which slowly drifted leftward or rightward. The test gratings were enveloped in space by a raised cosine function and in time by a Gaussian. The centre of the spatial envelope was either 2 deg left or right of the fixation point. An adaptive staircase procedure was used to find the velocities, at which the observer judged the motion direction in 75% of the presentations as leftwards or rightwards, respectively. In the second experiment, subjects judged the relative speed of two simultaneously presented gratings. Stimulus contrast was varied in both experiments from 0.01 to 0.32. Discrimination threshold vs contrast functions were measured before and after adaptation to a high-contrast (0.4) grating drifting at rates between 2 and 32 Hz. In a third experiment, subjects matched, before and after adaptation, the relative speed of a test stimulus, which had a constant contrast (0.04 or 0.08) and a variable speed, to that of a reference stimulus having a variable contrast but a constant speed. The results indicate that, before adaptation, direction and speed discrimination thresholds are independent of test contrast, except when test contrast approaches the detection threshold level. Adaptation to a drifting grating increases the lower threshold of motion (LTM) and the speed discrimination threshold (ΔV/V) for low test contrasts. In addition, the point of subjective stationarity (PSS) shifts towards the adapted direction and this shift is more pronounced for low test contrasts. The perceived speed of a drifting grating increases with increasing contrast level. Adaptation to a drifting grating shifts the perceived speed vs log contrast function downwards and to the right (toward higher contrast levels) and this shift is greatest for adaptation frequencies between 8 and 16 Hz. We further explored the effects of adaptation contrast (0.04, 0.4 and 0.9) and adaptation drift direction (iso- or contra-directional) on the perceived speed versus contrast function. The effect of adaptation is greatest for iso-directional drift and increases with increasing adaptation contrast. The results are discussed in terms of a contrast gain control model of adaptation.

Design of low VSWR axisymmetric subreflector

The design of a low VSWR axisymmetric subreflector using the method of moments is described. To reduce the power reflected back into the waveguide horn the surface of the hyperbolic subreflector is deformed using raised-cosine functions. The method of moments technique is then validated by comparing experimental and theoretical results.

Restoration of noisy images using a raised cosine function approximation

In order to implement image restoration techniques on a digital computer an accurate representation of the image in discrete form is required. A new set of functions called raised cosine functions is suggested for this purpose. These functions have properties similar to those of the spline functions which are useful for image representation and inversion of the degrading phenomenon. The singular value decomposition in the raised cosine function domain is used for restoration of noisy degraded images.

Raised cosine function for image restoration

In this paper, a new set of raised cosine functions is proposed. These functions have all the useful properties of the spline functions with the additional advantage of continuous infinite derivatives as against only a finite number of derivatives in case of the spline functions. Because of this property they exhibit a smoother behaviour. The property of smoothness, coupled with convolution, makes the raised cosine functions readily applicable to the image restoragtion problem, where the degradation is through a shift invariant blurring function. The results confirm the superior behaviour of these functions in comparison to spline functions.

Raised cosine function for image data interpolation

Spline functions because of their smoothing and interpolating properties are gaining popularity in engineering applications and image processing. In the present paper a new set of functions is proposed which has all the useful properties of spline function but are more smooth and are practically a band-limited type. These functions are the convolved raised cosine functions. The performance of image data reconstruction through the raised cosine functions is found to be better than that of spline functions for the two representative images.

Optical-Waveguide Band-Rejection Filters: Design

A method for designing optical-waveguide band-rejection filters is presented that allows side-lobe levels to be reduced by several orders of magnitude while the rolloff rate of the response characteristics is not appreciably degraded. The method is based upon the control of the shape of the perturbation-amplitude envelope. We discuss in detail the particular case where the coupling coefficient of the waveguide filter takes the form of a modified raised cosine function along the length of the waveguide. Side-lobe level and rolloff can be traded off by appropriately choosing the index p of the function. Design curves are included that allow the optimization of filter responses for side-lobe levels or rolloff characteristics.