Ashkan Ashrafi

Arbitrary waveform DDFS utilizing Chebyshev polynomials interpolation

A new technique of arbitrary waveform direct digital frequency synthesis (DDFS) is introduced. In this method, one period of the desired periodic waveform is divided into m sections, and each section is approximated by a series of Chebyshev polynomials up to degree d. By expanding the resultant Chebyshev polynomials, a power series of degree d is produced. The coefficients of this power series are obtained by a closed-form direct formula. To reconstruct the desired signal, the coefficients of the approximated power series are placed in a small ROM, which delivers the coefficients to the inputs of a digital system. This digital system contains digital multipliers and adders to simulate the desired polynomial, as well as a phase accumulator for generating the digital time base. The output of this system is a reconstructed signal that is a good approximation of the desired waveform. The accuracy of the output signal depends on the degree of the reconstructing polynomial, the number of subsections, the wordlength of the truncated phase accumulator output, as well as the word length of the DDFS system output. The coefficients are not dependent on the sampling frequency; therefore, the proposed system is ideal for frequency sweeping. The proposed method is adopted to build a traditional DDFS to generate a sinusoidal signal. The tradeoff between the ROM capacity, number of sections, and spectral purity for an infinite output wordlength is also investigated.

A Direct Digital Frequency Synthesizer Based on the Quasi-Linear Interpolation Method

This paper introduces a novel direct digital frequency synthesizer (DDFS) with an architecture based on the quasi-linear interpolation method (QLIP). The QLIP method is a hybrid polynomial interpolation in which the first quarter of a cosine function is approximated by two sets of linear and parabolic polynomials. The section of the cosine function that is closer to its peak is interpolated by parabolic polynomials, due to its resemblance to a parabola. The rest of the function, which is closer to where it approaches zero, is interpolated by linear polynomials. The paper describes the proposed interpolation method and its VLSI implementation. The performance of the proposed implementations is compared to several state-of-the-art DDFS designs.

Theoretical Upperbound of the Spurious-Free Dynamic Range in Direct Digital Frequency Synthesizers Realized by Polynomial Interpolation Methods

In this paper, a universal mathematical method is proposed to determine the upperbound of the spurious-free dynamic range (SFDR) in direct digital frequency synthesizers (DDFSs) realized by piecewise polynomial interpolation methods. The Fourier series is used to establish a linear matrix relationship between the frequency spectrum of the interpolated sinusoidal signal and the coefficients of the interpolating polynomials. This matrix relationship can be considered as a linear overdetermined system of equations, which can be solved for the ideal spectrum where the fundamental harmonic has an amplitude of one and the other harmonics are zero. It is shown that the Moore-Penrose pseudoinverse and Chebyshev minimax methods find the coefficients corresponding to the largest signal-to-noise ratio and maximum SFDR designs, respectively. The proposed method is used to show that the maximum SFDR of a DDFS based on the even fourth-order polynomial interpolation is 74.35 dBc. A DDFS based on the aforementioned method is designed and its architecture is optimized to obtain an SFDR of 72.2 dBc. A VLSI implementation of the proposed DDFS is also reported.

Harmonic oscillator utilizing double-fold integral, traditional and second-order sliding mode control

To stabilize both amplitude and frequency of the second-order harmonic oscillator double-fold sliding mode control is employed. The first, integral sliding mode control, is used to compensate for the disturbance/uncertainty, which is unmatched by the second control. The second sliding mode control is designed to achieve the stabilization of the harmonic oscillator system while the system is in the integral sliding mode. The first (integral) and second sliding mode controls are implemented in both formats: traditional sliding mode control that requires high-frequency oscillating control action and second-order sliding mode (super-twisting) control that is continuous and provides for the higher accuracy of stabilization. It is shown that the output of the double-fold sliding mode controlled second-order harmonic oscillator is robust to bounded disturbances and model parameter uncertainties. Computer simulations are performed to manifest the theoretical analysis.

Children with heavy prenatal alcohol exposure have different frequency domain signal characteristics when producing isometric force

To extend our current understanding of the teratogenic effects of prenatal alcohol exposure on the control of isometric force, the present study investigated the signal characteristics of power spectral density functions resulting from sustained control of isometric force by children with and without heavy prenatal exposure to alcohol. It was predicted that the functions associated with the force signals would be fundamentally different for the two groups. Twenty-five children aged between 7 and 17 years with heavy prenatal alcohol exposure and 21 non-alcohol exposed control children attempted to duplicate a visually represented target force by pressing on a load cell. The level of target force (5 and 20% of maximum voluntary force) and the time interval between visual feedback (20 ms, 320 ms and 740 ms) were manipulated. A multivariate spectral estimation method with sinusoidal windows was applied to individual isometric force-time signals. Analysis of the resulting power spectral density functions revealed that the alcohol-exposed children had a lower mean frequency, less spectral variability, greater peak power and a lower frequency at which peak power occurred. Furthermore, mean frequency and spectral variability produced by the alcohol-exposed group remained constant across target load and visual feedback interval, suggesting that these children were limited to making long-time scale corrections to the force signal. In contrast, the control group produced decreased mean frequency and spectral variability as target force and the interval between visual feedback increased, indicating that when feedback was frequently presented these children used the information to make short-time scale adjustments to the ongoing force signal. Knowledge of these differences could facilitate the design of motor rehabilitation exercises that specifically target isometric force control deficits in alcohol-exposed children.

Comments on "A 13-bit resolution ROM-less direct digital frequency synthesizer based on a trigonometric quadruple angle formula"

In this brief, the first- and second-order approximation of the quadruple angle formula (QAF) interpolation methods introduced in the paper by Wang et al. in 2004, are revisited. The limitations of those methods are completely overlooked in the paper. One of the limitations is maximum achievable spurious-free dynamic range (SFDR) of the generated sinusoidal signals, which are significantly overestimated. In this paper, it is mathematically proven that the best achievable spurious-free dynamic ranges using QAF interpolation methods are significantly less than the values given in the paper by Wang et al. Moreover, the corrected and complete digital implementation of the second-order approximation is introduced.

A novel ROM-less direct digital frequency synthesizer based on Chebyshev polynomial interpolation

In this paper a novel ROM-less direct digital frequency synthesizer (DDFS) is introduced. The phase-to-sine mapping section of this new scheme is designed based on approximation of the first half cycle of a cosine signal by a fourth order Chebyshev polynomial. The spurious free dynamic range (SFDR) of the proposed method is 64.2 dBc while the maximum achievable SFDR is theoretically obtained equal to 66.2 dBc. The proposed method is also implemented using the Xilinx Vertex-II FPGA and the experimental results exhibit the maximum clock frequency around 25 MHz.

A Fingerprint Verification Algorithm Using the Smallest Minimum Sum of Closest Euclidean Distance

In this paper, a Euclidean distance based minutia matching algorithm is proposed to improve the matching accuracy in fingerprint verification system. This algorithm extracts matched minutia pairs from input and template fingerprints by using the smallest minimum sum of closest Euclidean distance (SMSCED), corresponding rotation angle and empirically chosen statistical threshold values. Instead of using the minutia type and orientation angle, which are widely employed in existing algorithms, the proposed algorithm uses only the minutia location, to reduce the effect of non-linear distortion. Experimental results show that the proposed method has higher accuracy with improved verification rate and rejection rate.

An optimized direct digital frequency synthesizer based on even fourth order polynomial interpolation

In this paper, an optimized direct digital frequency synthesizer (DDFS) utilizing even fourth order polynomial is introduced. The spurious free dynamic range (SFDR) upper bound of the design is evaluated and an optimized digital system is designed to implement the method. It is shown that SFDR of the implemented digital system is 72.2dBc, which is only 2.15dBc less than the theoretical SFDR upper bound. Finally, the proposed system is realized in a chip using a 0.13mum standard cell library. The maximum clock frequency, the chip area and the chip power consumption are calculated equal to 210 MHz, 1048mum2 and 11.57 muW/MHz, respectively

A direct digital frequency synthesizer utilizing quasi-linear interpolation method

In this paper, a novel direct digital frequency synthesizer (DDFS) is introduced in which a combination of linear and even piecewise parabolic polynomial interpolation (EPIP) is used to interpolate the first quadrant of a cosine signal. An appropriate combination of these two methods is employed to maximize the spurious free dynamic range and reduce the complexity of the entire system. The even parabolic polynomial can be treated as a linear interpolation with respect to the squared of the accumulators output, thus the proposed system is called quasi linear interpolation (QLIP) direct digital frequency synthesizer.