Further results on Nyquist's third criterion

It is shown that a band-limited Nyquist 3 pulse is expressible as a weighted infinite sum of delayed versions of a corresponding Nyquist 1 pulse. Weightings are derived explicitly for the minimum-bandwidth case. Also, a baseband system using Nyquist 3 shaping and integration at the receiver (over one symbol interval) is studied. An optimal band-limited Nyquist 3 system using integration at the receiver is shown to have the same error performance as that of an optimal Nyquist 1 system which uses sampling at the receiver.     

Disturbance suppression beyond Nyquist frequency in hard disk drives

In conventional hard disk drives, a control system compensates for vibration in which the frequency is higher than the Nyquist frequency by using a multi-rate filter that decreases the gain above the Nyquist frequency. However, such a control system can only avoid instability and cannot suppress disturbances above the Nyquist frequency. To overcome this problem, a control system design method that suppresses disturbances beyond the Nyquist frequency is proposed. This method uses frequency responses of a controlled object and a digital controller to calculate the gain of the sensitivity function in a sampled-data system without requiring complex calculations involving matrices, and realizes a stable resonant filter that decreases the gain of the sensitivity function above the Nyquist frequency. Significant suppression of the vibrations caused by the disturbances beyond the Nyquist frequency is demonstrated by implementing this method in the head-positioning system of a hard disk drive.     

视频信号的Nyquist分析

Nyquist体积是对信号进行分析的有效方法和手段,本文以我国的PAL制电视系统为例,采用Nyquist体积分析方法,对其中的亮度信息、彩色副载波等进行了分析,并针对Nyquist体积的不足,提出了区分Nyquist体积内部不同信号的方法.     

On computing the minimum distance for faster than Nyquist signaling

The degradation suffered when pulses satisfying the Nyquist criterion are used to transmit binary data at a rate faster than the Nyquist rate over the ideal band-limited (brick-wall) channel is studied. The minimum distance between received signals is used as a performance criterion. It is well-known that when Nyquist pulses (i.e. pulses satisfying the Nyquist criterion) are sent at the Nyquist rate, the minimum distance between signal points is the same as the pulse energy. The main result is to show that the minimum distance between received signals is the same as the pulse energy for rates of transmission about 25% beyond the Nyquist rate, which is the best possible result. In fact, one can even identify the precise error event and signaling rate that causes the minimum distance to be no longer equal to the pulse energy. The mathematical formulation of the problem is analyzed     

Discussion on Barkhausen and Nyquist stability criteria

Most textbooks on analog circuits and signal processing describe the Barkhausen criterion pertaining to the determination of sinusoidal oscillations in a closed-loop system. On the other hand, the Nyquist stability criterion is well known, as discussed in most textbooks on control systems. Recently, some examples in which the Barkhausen criterion fails to produce the correct condition for startup of oscillations have been reported. In the present paper, an explanation of oscillation startup based on the Nyquist stability criterion is given and the close relationship between the Barkhausen and the Nyquist criteria highlighted. It is shown that the Nyquist criterion (which is a rigorous technique) is a more robust approach than the Barkhausen criterion concerning the determination of sinusoidal oscillations in a closed-loop system and that the Barkhausen criterion (whenever it yields the correct result) is subsumed by the Nyquist criterion as a special case. The textbooks usually describe the Barkhausen criterion as a separate topic, i.e., do not discuss the relationship of this criterion with the Nyquist criterion. It is, therefore, felt that the present discussion will go a long way to put the subject in a broader perspective.     

Pulse Shape Design for Teletext Data Transmission

This paper studies the problem of designing a suitable pulse shape for teletext data transmission. The following four criteria are used: 1) Nyquist I criterion, 2) Nyquist II criterion, 3) degree of overshoots in the channel signal, and 4) robustness to sampling phase jitter. For system bandwidths less than the inverse-baud rate, it is not possible to satisfy all these criteria simultaneously; tradeoffs that have to be made are illustrated. Several candidate pulse shapes are given and a composite criterion developed. A pulse shape, which satisfies the Nyquist I criterion and is closest to satisfying the Nyquist II criterion, in a sum-of-squares-of-deviations sense, is recommended.     

Criteria for the onset of oscillation in microwave circuits

A commonly used criterion for oscillator startup is demonstrated not to be universally valid. In order to investigate startup conditions, the Nyquist stability criterion is written in terms of microwave quantities. It is shown that widely available microwave CAD can be used to create Nyquist stability plots. Since the Nyquist criterion gives only global stability information, a convenient graphical criterion is developed to determine whether an oscillation will start up near a particular resonance frequency     

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     

Fractionally Nyquist Sample Spaced ARMA Blind Equalizer for Direct Signal Recovery in Passive Bistatic Radar

This paper proposes a modified signal pro-cessing structure based on the fractionally Nyquist sample spaced structure for passive bistatic radar. To recover the direct signal from the multipath clutter, an equalizer of the Auto regressive moving average (ARMA) type is pro-posed based on the fractionally Nyquist sample spaced con-stant modulus algorithm. Compared with the conventional Nyquist sample spaced equalizer, the equalizer of the frac-tionally Nyquist sample spaced ARMA structure is more effective in dealing with deep fading multipath channels with zeros near the unit circle. Computer simulations and real data tests indicate that the proposed approach out-performs the conventional processing structure in terms of both clutter residual and mean square error.     

Nyquist 3 Pulse Shaping in Continuous Phase Modulation

Continuous phase modulation (CPM) schemes, using Nyquist 3 pulse shaping and correlative codes, are popular candidates for mobile radio applications. This paper presents a detailed study of the effects of Nyquist 3 pulse shaping on the spectral characteristics of CPM schemes with a modulation index of 1/2. The influence of pulse parameters such as its shape, bandwidth, coding polynomial, and truncation length on spectral characteristics such as main lobe, fractional power bandwidths, and out-of-band power levels is thoroughly investigated; error performance is also briefly analyzed. Among uncoded schemes, a new scheme using a pulse satisfying both Nyquist 3 and Nyquist 2 criteria is pointed out as a promising candidate and as a good compromise between spectral and power efficiencies.     

Parallel-path digital-to-analog converters for Nyquist signal generation

Nyquist-rate digital-to-analog converters (DACs) can generate frequencies up to half the sampling frequency. It is, however, impractical to generate such high frequencies. Due to its nature, the converter will not only generate the desired signal itself but also, often undesired, image frequencies. For frequencies near the Nyquist frequency, an image with almost exactly the same amplitude appears very close to the signal. An extremely steep filter is required. Therefore, real-life systems do provide oversampling to locate the Nyquist image further away from the wanted signal. In practice, the signal frequency has to be reduced if the maximum sampling rate is reached. We propose a technique that conversely removes this Nyquist image so that only further away Nyquist images with lower amplitudes have to be filtered off. The proposed technique is applied to the design of a dual 6-bit binary current-steering DAC running at 250 MS/s.     

Image flicker control by CCD-chip-shift and wobble operation at double-enhanced Nyquist regions

CCD-chip-shift operation can double the Nyquist limit to give a high-resolution CCD imager. Image flickers, however, are apt to appear at highly resolved images near the double-enhanced Nyquist limit. The flickers are, in nature, field-time-dependent image flickers inherent in the operation principle. In order to suppress image flickers, a CCD-chip wobbling was superimposed at swung sites for the CCD-chip-shift imager by utilizing piezoelectric bimorph acutators, on which the CCD chip was mounted. By wobbling, apparent horizontal pixel apertures were enlarged to overlap each other, resulting in MTF control at the double-enhanced Nyquist regions.     

Bandwidth expansion for robust, low-complexity communication overfading dispersive channels

In this paper, we derive pulses that yield Nyquist or near Nyquist properties when convolved with the initial terms of the series model of a slow fading dispersive channel. For the f-power series these are the so called powers of Nyquist pulses. For a Karhunen-Loeve series, model pulses are found that maximize the ratio of the mean peak-sample energy to mean residual intersymbol interference energy for a given bandwidth expansion factor. Under certain conditions, the approach significantly lessens the need for, or complexity of, equalization. Other benefits attributable to the use of the derived pulses, including those related to timing recovery, are discussed     

宽带奈奎斯特FIR滤波器的设计与实现

本文根据奈奎斯特（Nyquist）FIR滤波器的设计原理，结合宽带无线接入网的技术要求，给出了一种适用于高速率通信网的宽带Nyquist FIR滤波器的设计方案，并在FPGA单片系统上予以实现，其性能指标通过计算机仿真测试，达到了设计要求。     

宽带带通信号的直接采样定理

对起、止频率为ｆｓ_ｆｅ_的带通信号的直接采样,传统上要求信号是窄带的９即ｆ≥ｆ_ｅ／２）,否则只能用经典的Ｓｈａｎｎｏｎ采样定理,以不低于２ｆ_ａ的采样率来采样才能恢复信号。本文采取半均匀采样技巧,突破了这一限制。对满足ｆ_ｓ≥ｆ_ｅ／３的宽带带通信号,建立了精确的恢复公式,采样率为４ｆｅ／３,低于Ｎｙｑｕｉｓｔ率;如果ｆ_ｓ＜ｆ_ｅ／３,用ｔｉｌｉｎｇ分析技术可以证明无论是均匀还是半均匀采样,最低采样率必然是２ｆ_ｅ。这表明本文所给出的宽带条件是最优的。     

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     

Dependence of intersymbol interference upon the signalling rate

When the channel characteristics of a digital communications system are known, it is possible in theory to modify the system to meet any one of Nyquiat's criteria to eliminate intersymbol interference. This paper examines the performance of such a system when signalling rate changes by about ± 40% about the Nyquist optimum value. The results are presented in a graphical form in terms of the eye parameters. The cases considered are Nyquist I (with cosine roll-off factor of 0, 0·25, 0·50, 0·75 and 1·0 respectively) and Nyquist II (with cosine roll-off factor of 0 and 1·0 respectively).     

使用基于二阶多项式Nyquist波形降低同信道干扰的影响

本文讨论了在Nakagami衰落条件下,使用一类基于二阶多项式Nyquist波形的BPSK系统中的同信道干扰问题。我们发现在新提出的这类脉冲波形中总可以找到合适的成员,较升余弦Nyquist脉冲相比,具有更强的抗同信道干扰能力。     

Exploiting the Faster Than Nyquist Concept in WavelengthDivision Multiplexing Systems Using Duobinary Shaping

This paper begins with Nyquist wavelength-division multiplexing (WDM) and then introduces faster-than-Nyquist. In faster-than-Nyquist, a certain amount of inter-symbol interference (ISI) is accepted, which violates the fundamental principle of Nyquist WDM. This results in much-relaxed transceiver bandwidth and simpler spectral design. However, in faster-than-Nyquist, implementation complexity is shifted from the transmitter side to the receiver side. Therefore, successful application of faster-than-Nyquist depends on innovation in the receiver structure. In this paper, we discuss the guidelines for implementing suboptimum, low-complexity receivers based on faster-than-Nyquist. We suggest that duobinary shaping is a good technique for trading off achievable spectral efficiency, detection performance, and implementation complexity and might be preferable to Nyquist WDM. Experiments are conducted to verify robustness of the proposed technique.     

Fractional delay filter design when sampling rate higher thanNyquist rate

Fractional delay filter design is used to approximate the delay filter exp(-jωD) with a delay D for the full band |ω|<π using FIR filters or IIR allpass filters. The author shows that the fractional delay filter design is necessary only when sampling is critical, i.e. Nyquist sampling. It is shown that, when the sampling rate is higher than the Nyquist rate, the ideal delay filter exp(-jωD) for the baseband |ω|<π/r only needs to be approximated, where r is the ratio of sampling rate over the Nyquist rate. Numerical simulations are presented to illustrate the theory