Improved Nyquist filter characteristics using spline interpolation

This paper presents and investigates a novel approach for constructing a family of intersymbol interference (ISI)-free pulses that shows comparable or better ISI performance in the presence of sampling errors, compared with some recently proposed pulses. We propose and discuss a new parametric method for the design of Nyquist filter characteristics using constraints in frequency characteristics construction. The method for constructing the filter characteristics uses a piecewise polynomial approximation of an ideal optimized staircase characteristic by spline functions. The spline polynomials are used to approximate a function that must pass through specified points. The performances of new ISI-free pulses are studied with respect to the ISI error probability. This family provides flexibility in designing an appropriate pulse even after the roll-off factor has been chosen. The results for error probability outperform the fourth-degree polynomial pulse [4].     

Generalized raised-cosine filters

Data transmission over bandlimited channels requires pulse shaping to eliminate or control intersymbol interference (ISI). Nyquist filters provide ISI-free transmission. Here we introduce a phase compensation technique to design Nyquist filters. Phase compensation can be applied to the square-root of any zero-phase bandlimited Nyquist filter with normalized excess bandwidth less than or equal to one. The resulting phase compensated square-root filter is also a Nyquist filter. In the case of a raised-cosine spectrum, the phase compensator has a simple piecewise-linear form. Such a technique is particularly useful to accommodate two different structures for the receiver, one with a filter matched to the transmitting filter and one without a matched filter. We also use the phase compensation technique to characterize a more general family of Nyquist filters which subsumes raised-cosine spectra. These generalized raised-cosine filters offer more flexibility in filter design. For instance, the rate of asymptotic decay of the filter impulse response may be increased, or the residual ISI, introduced by truncation of the impulse response, may be minimized. Design examples are provided to illustrate these choices     

Differential phase shift keying in two-path Rayleigh channel withadjacent channel interference

A formula is derived for the error probability of M-ary differential phase-shift keying with differential phase detection in a two-path Rayleigh fading channel taking into account adjacent channel interference (ACI), cochannel interference (CCI), intersymbol interference (ISI), and Doppler frequency shift. Square-root Nyquist filters are used with roll-off, β, the transmitter and receiver as in the proposed US digital mobile radio system. The presence of the second path has a profound effect on increasing the bit error probability (BEP) because it causes ISI. In the absence of ISI, ACI has a smaller effect on BEP than CCI. In the presence of ISI their effect is essentially the same. For a given bit energy-to-noise ratio, the binary system has the lowest BEP; however, the bit rate is also the lowest for a given bandwidth. When the main interference is ACI or CCI, a quaternary system has a lower BEP than the octal system. When the main interference is ISI, this is reversed     

Parametric construction of Nyquist-I pulses

A novel parametric approach for constructing families of intersymbol-interference (ISI)-free pulses is presented and examined. Some new pulses so constructed have smaller maximum distortion, a more open receiver eye, and a smaller probability of error in the presence of symbol-timing error than the Nyquist raised-cosine pulse for the same excess bandwidth. The parametric approach gives more degrees of freedom in the design of ISI-free pulses, and subsumes previous ISI-free pulses as special cases. A number of theorems that relate time-domain behaviors of a pulse to the pulse's frequency spectrum are proved. A previously known result relating pulse tail-time decay to discontinuity of the pulse-frequency spectrum is corrected and clarified.     

Digital signal processing techniques in Nyquist-WDM transmission systems

In single-carrier wavelength-division multiplexing (WDM) systems, the spectral efficiency can be increased by reducing the channel spacing through digital signal processing (DSP). Two major issues with using tight filtering are cross talk between channels and inter-symbol interference (ISI) within a channel. By fulfilling the Nyquist criterion, Nyquist spectral-shaped WDM systems can achieve narrow channel spacings close to the symbol rate \((\hbox {R}_{\mathrm{S}})\) with negligible cross talk and ISI. In principle, DSP can generate any signals with arbitrary waveforms and spectrum shapes. However, the complexity of DSP is limited by its cost and power consumption. It is necessary to optimize the DSP to achieve the required performance at a minimum complexity. In this paper, we first introduced the background of digital signal processing for Nyquist spectral shaping in optical fiber WDM systems. Then, we investigated the use of digital finite impulse response (FIR) filters to generate Nyquist-WDM 16-ary quadrature amplitude modulation (16QAM) signals with the raised-cosine (RC) and root-raised-cosine (RRC) shape spectra. The system performance of both the RC and RRC spectra is also examined. Moreover, we explored the various methods to reduce digital-to-analog converter (DAC) sampling speed, such as using super-Gaussian electrical filters (E-filter) and spectral pre-emphasis. We also discussed receiver-side matched filter design for Nyquist-WDM receiver optimization.     

A new adaptive recursive RLS-based fast-array IIR filter for active noise and vibration control systems

Infinite impulse response filters have not been used extensively in active noise and vibration control applications. The problems are mainly due to the multimodal error surface and instability of adaptive IIR filters used in such applications. Considering these, in this paper a new adaptive recursive RLS-based fast-array IIR filter for active noise and vibration control applications is proposed. At first an RLS-based adaptive IIR filter with computational complexity of order O(n²) is derived, and a sufficient condition for its stability is proposed by applying passivity theorem on the equivalent feedback representation of this adaptive algorithm. In the second step, to reduce the computational complexity of the algorithm to the order of O(n) as well as to improve its numerical stability, a fast array implementation of this adaptive IIR filter is derived. This is accomplished by extending the existing results of fast-array implementation of adaptive FIR filters to adaptive IIR filters. Comparison of the performance of the fast-array algorithm with that of Erikson’s FuLMS and SHARF algorithms confirms that the proposed algorithm has faster convergence rate and ability to reach a lower minimum mean square error which is of great importance in active noise and vibration control applications.     

Novel droop-compensated comb decimation filter with improved alias rejections

This paper presents a novel two-stage comb decimator with the improved magnitude characteristic. Simple multiplierless corrector filters, which are designed using the frequency sampling and IFIR methods, are introduced. The proposed filters compensate the comb passband droop in the wideband passband region and increase the attenuations in the folding bands. Using the multirate identity the filters may be moved to a lower rate. The filter design depends only on the number of the cascaded comb filters and do not depend on the decimation factor M.     

Approximation of Löwdin orthogonalization to a spectrally efficient orthogonal overlapping PPM design for UWB impulse radio

In this paper we consider the design of spectrally efficient time-limited pulses for ultra-wideband (UWB) systems using an overlapping pulse position modulation scheme. For this we investigate an orthogonalization method, which was developed in 1950 by Löwdin [1] and [2]. Our objective is to obtain a set of N orthogonal (Löwdin) pulses, which remain time-limited and spectrally efficient for UWB systems, from a set of N equidistant translates of a time-limited optimal spectral designed UWB pulse. We derive an approximate Löwdin orthogonalization (ALO) by using circulant approximations for the Gram matrix to obtain a practical filter implementation as a tapped-delay-line [7]. We show that the centered ALO and Löwdin pulses converge pointwise to the same square-root Nyquist pulse as N tends to infinity. The set of translates of the square-root Nyquist pulse forms an orthonormal basis for the shift-invariant-space generated by the initial spectral optimal pulse. The ALO transformation provides a closed-form approximation of the Löwdin transformation, which can be implemented in an analog fashion without the need of analog to digital conversions. Furthermore, we investigate the interplay between the optimization and the orthogonalization procedure by using methods from the theory of shift-invariant-spaces. Finally we relate our results to wavelet and frame theory.     

Nyquist 1 universal filters

The Nyquist (1928) 1 filters (NFls) with both nonlinear phase response and amplitude response of nonspecified symmetry are investigated. It is shown that one of the filter's responses (amplitude or phase) can be chosen almost arbitrary. The second one is then derived from the condition of zero intersymbol interference (ISI) in data transmission synchronous systems. As a specific application of the presented theory, a simple procedure for calculating NFl's with ISI-free matched and unmatched filter properties is proposed     

Techniques to Generate ISI and Jitter-Free Bandlimited Nyquist Signals and a Method to Analyze Jitter Effects

An analytical method to predict the data pattern dependent jitter is presented. Results obtained are shown to be in excellent agreement with those obtained by computer simulation and laboratory measurement. In order to find methods that can generate an ISI (intersymbol interference) and jitter-free bandlimited Nyquist signal, a double-intervaled raised cosine and its spectral characteristics are studied. Based on this, a search for new double-intervaled pulses having low spectral sidelobes is conducted. Pulses having desirable spectral characteristics and their application in communication systems are discussed. Two methods for the generation of ISI and jitter-free Nyquist signals are described. The first one uses the concept of pulse overlapping while the second one incorporates the nonlinear switching concept. These two methods are equivalent as they can generate the same output signals. Hardware implementation and measured results on this nonlinear switching filter are given. The simplicity of its design and its low cost will enable this type of nonlinear switching filter suitable for use in low bit rate satellite communication systems.     

A design of linear-phased IIR Nyquist filters

This paper discusses a new method of designing linear-phased IIR Nyquist filters with zero intersymbol interference. The filters designed by this method possess linear-phase characteristics and are lower in order than other Nyquist filters designed by existing methods. Expressions are derived for zero-phased IIR Nyquist filters and efficient design methods are examined for them. The opted design method is based on an iteration process, and in each iteration step a modified version of the Remez exchange algorithm is used. In addition, the implementation of the designed zero-phased IIR filters is considered. Finally, the proposed design method is demonstrated through various design examples     

A family of ISI-free polynomial pulses

A family of ISI free polynomial pulses that can have an asymptotic decay rate of t/sup -k/ for any integer value of k has been proposed. The proposed family provides flexibility in designing bandlimited pulses in accordance with the desired application, even after the roll-off factor /spl alpha/ has been chosen. Pulses obtained from this family have been found to be better than the currently known good pulses.     

Low-Voltage CMOS Nonlinear Transconductors and Their Application to Companding Current-Mode Filters

Two novel nonlinear CMOS transconductors that can be employed for building CMOS current-mode filters are presented and their performances compared to formerly proposed topologies aimed at the same goal. The first one is based on a previous topology proposed by the authors, where a new biasing procedure leads to an improved performance for low supply voltages. The second one follows a novel approach, based on cascading a transresistor and a transconductor. The analysis is complemented with a more general approach based on the identification of translinear loops present in the circuit. Both nonlinear transconductors can operate at supply voltages as low as one V _GS plus two V _DS of a saturated MOSFET. CMOS current-mode filters based on these blocks are built following companding techniques, and their correct operation is validated by simulation and experimental results.     

Laser formation of Pt-Si Schottky barriers on silicon

135 nsec pulses ofλ = 1.06μm light from a Nd: YAG laser have been used to form Schottky barriers by irradiation of a 500Å thick metal film on n-type silicon. Large area barriers were fabricated by over-lapping individual 30μ diameter laser pulses of from 4 to 12 J/cm². The barrier height was 0.73 ± 0.03 V, independent of the laser power. The barrier quality, as assessed by measurement of the forward current characteristic, decreased with laser power to a value of n = 1.5 at 12 J/cm².     

Weighted median filters with sigma-delta modulation encoding

Digital decimation filters play a fundamental role in oversampled sigma-delta A/D decoders. In this paper, we first show that weighted median (WM) filtering of a demodulated sequence (at the Nyquist rate) can be implemented concurrently in the A/D decoder. Through a simple modification of the binary time-series outputted by the A/D modulator, the sequence obtained after the sigma-delta modulation (SDM) decoder is shown to be equivalent to WM filtering the multilevel sequence at the Nyquist rate. Second, we show that WM filters can be used for SDM decimation filters and that these filters are readily implemented in the SDM binary domain. A very promising characteristic of SDM converters equipped with WM decimating filters is that sharp discontinuities (edges) can be preserved and acquired. Thus, the bandlimited constraint imposed on the input signals can be relaxed making SDM more attractive to A/D conversion of signals containing sharp transitions. The proposed signal processing algorithms, in essence, combine A/D sigma-delta converters and WM filters into a single programmable system     

Two-parameter nyquist pulses with better performance

We present three novel Nyquist (intersymbol interference free) pulses that outperform two sophisticated pulses reported in literature by Bealieu et al. and Assalini and Tonello. The pulses are based on the concept of inner and outer functions, which was recently explored by the authors. Apart from requiring only two design parameters, the proposed pulses offer an enhanced error performance for various values of roll-off factor and timing jitter along with a smaller maximum distortion.     

Transient distortion and nth order filtering in deep level transient spectroscopy (DnLTS)

Problems associated with intrinsic sensitivity and time constant selectivity of capacitive DLTS systems are discussed as well as intrinsic limitations in predominantly deep level doped semiconductors.A previously published figure of merit for the optimized exponential correlator for capacitive DLTS studies is shown to be too high because of improper consideration of effects of level restoration: when correctly compared, a filter with a 12% lower figure of merit can be constructed based purely on gating and a weighted phase inversion before the integrator and a phase sensitive detector has a 20% lower figure of merit. The exponential DLTS correlator is also inadequate for analysis of continuous spectra because of its slow drop off in response (∝ T_S for T_S shorter than the peak response time constant and ∝ T_S^?1 for longer times). Blanking is necessary to achieve more selectivity relative to short time constants. When performed on-line, D²LTS gives a response ∝ T_S^?2 for longer times. Still more selective filters of order n, or DⁿLTS, are considered based on weighted averages over time intervals in geometric progression that are suitable for DLTS and a system with ±1 weighting and suitably chosen time intervals for use with DDLTS. For these filters there is no penalty in figure of merit associated with choice of DDLTS which also appears to be easier to achieve than DLTS. On-line filters with long time constant responses ∝ T_S^?3 or higher order are shown to exact a large penalty in figure of merit. Equivalent filters can, however, be synthesized with much better figure of merit by a software compensation of multichannel data. The channels are then selected so that the responses of successive channels peak a factor of 2 away in T_S and the number of pulses used is decreased by a factor of two. Relative to a multipoint averager, the software compensated analyzer requires a factor of 100 less in measurement time for comparable accuracy when a spectrum must cover a range of 1000:1 in relaxation times. There are also comparable improvements in the holding time specifications and the number of A/D conversions if the system is to be coupled to a computer.When the deep level concentration is comparable to the shallow doping concentration, the peak responses of both DLTS and DDLTS are broadened, the sensitivity increases, the response peaks are shifted to larger relaxation times, and the system becomes essentially nonlinear in response to the individual deep level constituents. This distortion can, in principle, be corrected by going to a constant capacitance mode of operation both during the initial driving pulse and during the recovery transient.     

Noise in near-ballistic n+nn+ and n+pn+ gallium arsenide submicron diodes

Direct-current (d.c.) characteristics and noise measurements in the range 1 Hz-25 kHz are reported for n⁺nn⁺ and n⁺pn⁺ near-ballistic devices, with n regions (p regions) of 0.4 μm (0.45 μm), fabricated by molecular beam epitaxy at Cornell. The n⁺nn⁺ mesa structures show very low 1/? noise. indicating a Hooge parameter α_H = 6.0 × 10^?. This very low noise is attributed to the near absence of phonon collisions. The thermal (? like) noise above 1 kHz is equal to Nyquist noise at the lowest currents, rising to slightly above Nyquist noise for high currents, indicating the presence of carrier drag effects. The n⁺pn⁺ noise, on the contrary, is quite high. It seems to be associated with the ambipolar effects occurring for low injection of electrons in the p region. The importance of noise measurements for confirming ballistic or near-ballistic behavior is discussed.     

基于新型优化窗的多维全相位数字滤波器设计

提出一种通用的多维全相位数字滤波器的设计方法.基于一维原型全相位数字滤波器(APDF),通过多维抽取变换,设计出具有任意平行六面体通带的多维APDF,并保持奈奎斯特约束特性和零相位特性.利用一种新型优化窗函数设计了性能优异的一维加窗APDF,将其作为一维原型滤波器,生成了不可分离的多维加窗APDF.实例表明,在滤波器长...     

A family of pulse-shaping filters with ISI-free matched andunmatched filter properties

The raised-cosine pulse-shaping filter plays an important role in digital communications due to its intersymbol interference (ISI)-free property. The ISI-free property holds after matched filtering is performed. In this letter, we propose a new family of pulse-shaping filters. These filters are ISI free with or without matched filtering. Using these new pulse-shaping filters, the computational load, and therefore the hardware cost in demodulation for modem design, might be reduced in some applications