Amplitude Equalization Research Articles

Technique to generate equal amplitude, higher-orderopticalpulses in rational harmonically modelocked fibre ring lasers

A novel technique of pulse amplitude equalisation in higher-order optical pulses in a rational harmonically modelocked fibre ring laser is proposed and demonstrated. The combination of intra-cavity optical filtering, and even-order modulation sideband generation using nonlinear characteristics of a Mach-Zehnder intensity modulator can effectively eliminate pulse amplitude instability at higher-order rational harmonic modelocking. The generated optical pulse trains exhibit equal amplitudes with a high degree of spectral purity in terms of a large suppression of supermode noise, low amplitude noise, phase noise, and timing jitter.

Theoretical and experimental study of pulse-amplitude-equalization in a rational harmonic mode-locked fiber ring laser

A simple technique, based on nonlinear polarization rotation, for the amplitude equalization of high repetition rate pulses generated from a rational harmonic mode-locked fiber ring laser was demonstrated. Amplitude equalized pulses at 10 GHz (the fourth rational harmonic) were obtained with a harmonic component suppression ratio up to 30 dB. A theoretical explanation was given in detail, which indicates that, after pulse amplitude equalization, the situation of unequal pulse spacing can be improved to a certain extend.

Equality of length-form and velocity-form transition amplitudes in relativistic many-body perturbation theory

Rules for obtaining transition amplitudes that are equal in length form and velocity form, order-by-order in relativistic many-body perturbation theory are presented. Explicit formulas are derived for first-, second-, and third-order amplitudes for transitions between valence states in alkali-metal atoms. Numerical codes are developed to evaluate amplitudes through third order and applied to $3s\ensuremath{-}{3p}_{1/2}$ and $3s\ensuremath{-}{3p}_{3/2}$ transitions in sodium and sodiumlike ions. The present calculations for sodiumlike ions are compared with other accurate theoretical calculations.

Polarisation Analysis: What is it? Why do you need it? How do you do it?

Polarisation analysis quantitatively describes the particle motion of a seismic wavefield. It is the fundamental vector processing technique applied to multi-component seismic data. Synthetic and real VSP examples illustrate the application of polarisation analysis via particle-motion hodograms, and an automated single-trace time-domain method.Polarisation analysis can facilitate the extraction of pure P and S-wave sections, removal of unwanted noise events, and recovery of information relating to fracturing, porosity and lithology from multi-component data. Two applications of polarisation analysis are demonstrated, namely the extraction of pure P and S-wave sections, and S-wave splitting analysis.The success of polarisation analysis depends on the accuracy with which the recorded seismic wavefield represents the true vector wavefield. Care must be taken to ensure particle motion is not distorted during acquisition and preprocessing. Sensor response and coupling must be matched across components. Amplitude equalisation must be identical on all components. Frequency and/or velocity filtering should be designed to remove only noise, so as not to modify the underlying signal.The effect of the analysis window length is demonstrated, with the best compromise between resolution and stability being provided by a window approximately equal to the dominant period of the recorded signal. If more than one seismic event exists within the analysis window, single-trace polarisation analysis cannot accurately recover infoimation on the individual wave types. A comparison of polarisation analysis in the t-x and T-p domains highlights the value of utilising both slowness and polarisation information to enhance the accuracy of discriminating between interfering wave types.

Performance of cumulant based inverse filters for blind deconvolution

Chi and Wu (1963) proposed a class of inverse filter criteria J/sub r,m/ using rth-order and rth-order cumulants (where r is even and m>r/spl ges/2) for blind deconvolution (equalization) of a (nonminimum phase) linear time-invariant (LTI) system with only non-Gaussian measurements. The inverse filter criteria J/sub r,m/ for r=2 are frequently used such as Wiggins' (1978) criterion, Donoho's (1981) criteria, and Tugnait's (1993) inverse filter criteria for which the identifiability of the LTI system is based on infinite signal-to-noise ratio (SNR). We analyze the performance of the inverse filter criteria J/sub 2,m/ (r=2) when the SNR is finite. The analysis shows that the inverse filter associated with J/sub 2,m/ is related to the minimum mean square error (MMSE) equalizer in a nonlinear manner, with some common properties such as perfect phase (but not perfect amplitude) equalization. Furthermore, the former approaches the latter either for higher SNR, cumulant-order m, or for wider system bandwidth. Moreover, as the MMSE equalizer does, the inverse filter associated with J/sub 2,m/, also performs noise reduction besides equalization. Some simulation results, as well as some calculation results, are provided to support the proposed analytic results.

Pulse-amplitude equalization of rational harmonic mode-locked fiber laser using a semiconductor optical amplifier loop mirror

The authors demonstrate, for the first time to our knowledge, the amplitude equalization of high-repetition-rate pulses generated from a rational harmonic mode-locked fiber laser using a semiconductor optical amplifier loop mirror. Here, the loop mirror acts as an all-optical pulse-amplitude equalizer. Optimized parameters of the loop mirror for pulse-amplitude equalization were determined by a simulation. The pulse-amplitude equalization was successfully demonstrated up to the thirteenth rational harmonic mode-locked pulse train (∼14 GHz).

Pulse-amplitude-equalized output from a rational harmonic mode-locked fiber laser

We report, for the first time to our knowledge, the demonstration of amplitude equalization of high-repetition-rate pulses generated from a rational harmonic mode-locked Er-doped fiber laser. The output pulses are injected into another fiber laser with a nonlinear optical loop mirror. This scheme provides pulse-amplitude equalization up to the ninth rational harmonic mode-locked pulse train.

External fibre laser based pulse amplitude equalisationscheme forrational harmonic modelocking in a ring-type fibre laser

The authors have obtained, for the first time to their knowledge, pulse amplitude equalisation in a high repetition rate (up to 22.6 GHz) pulse train, which is generated from rational harmonic modelocking of an Er-doped fibre ring laser, by using an equalising fibre laser. The equalising fibre laser is based on a passively modelocked laser with an NALM (nonlinear amplifying loop mirror) and a Faraday rotating mirror.

10GHz Sky Survey Project, Waseda FFT Interferometer

Large-field radio interferometer at 10.65GHz have been developed to search for transient radio objects such as radio supernovae and radio bursts in stellar systems (Daishido et al. 1984). This is a spatial fast-fourier transform (FFT) type radio interferometer, being an equally-spaced, maximum redundant, two-dimensional (2D) array in an 8 × 8 configuration. Sixty-four identically-designed frontend elements are comprised of 2.4 m diameter cassegrain antennas and 200K HEMT receivers. These are steerable in elevetion and are fixed in azimuth. Although it is only partially operating, the completed system having 64 beams in the northern hemisphere is expected to provide maps having 0.1° angular resolution and a sensitivity of 50 mJy. The beams are formed by a newly-developed “Digital Lens” (complex amplitude equalizer + 2D FFT pipelined processor), with the array’s overall size being 20 × 20m.

A current-mode biquadratic amplitude equalizer

A boost biquad transfer function with two symmetrical zeros on the real axis is derived; it provides a technique for amplitude equalization with a second-order continuous-timegm-C section using current injection. The synthesis procedure yields a differential boost biquad consisting of three double-input OTAs and a single-input high-gmboost OTA. SPICE simulations show that for boost gain up to 20 dB the phase of the biquad is essentially unaffected. The presented technique is found suitable for amplitude equalization of disk-drive read channels operating in the range of 100 MHz.

Complex correction of data acquisition channels using FIR equalizer filters

The common conviction about FIR (finite impulse response) digital filters is that the number of necessary taps, to reach the same performance as provided by IIR (infinite impulse response) digital filters, is usually too large. Moreover, the standard FIR filter design algorithm (Remez exchange) allows the design of linear-phase filters only. Therefore, IIR filters are often preferred over FIR ones, without any further investigations. This paper presents a case study of complex (amplitude and phase) equalization of the passband of a commercial anti-aliasing filter. The novelty is the usage of an FIR filter for this purpose (or an FIR one, combined with a low-order IIR filter), and a thorough discussion of the special design aspects. It turns out that for the given anti-aliasing filter (a Cauer filter of order 11) an FIR filter of length 60...100 can perform as well as a 26/26 (numerator order/denominator order) IIR one. The properties are even better if a low-order IIR filter is used in combination with an FIR one (orders, e.g., 1/1+40/0). Because of the absence of stability problems and the ease of implementation, the use of FIR filters is suggested. >

ACT-enabled 100 MHz channel equalizer (for magnetic recording application)

An acoustic charge transport (ACT) equalizer with 128 taps and a 180-MHz tap sampling rate is demonstrated with a variety of head responses. The standard programmable transversal filter (PTF) product has been modified for magnetic recording applications by the addition of an instrumentation interface and specialized analog circuitry for low-frequency equalization. The resulting module, when combined with controlling software is known as a filter/equalizer development station (FEDS). A laboratory system employing two such FEDS modules for separate amplitude and zero-crossing equalization in a digital saturated magnetic recording peak detection channel is modeled and demonstrated. Equalizer impacts on system speed, packing density, and error rates are predicted with a channel model.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Automatic amplitude and phase equalization of n similar periodic signals of the same frequency

Automatic amplitude and phase equalization of n similar periodic signals of the same frequency (ω) is studied. To demonstrate the technique, first automatic amplitude and phase equalization of n sinusoidal signals of the same frequency (ω) is considered using a new method. The method is then elaborated upon for similar periodic signals. Through proof of a theorem, the proposed system can be enlarged for any degree of accuracy desired without encountering any stability problem whatsoever! The proposed technique is very straightforward, low-cost and accurate, and does not involve any approximation or limitation on amplitudes, phase angles or frequency (ω) of the signals. Two examples, simulated on an analogue computer for sinusoidal and periodic signals, support the theoretical results.

Automatic amplitude, phase and frequency equalization of “n” sinusoidal signals

Automatic amplitude, phase and frequency equalization of “n” sinusoidal signals is studied in this paper. In a completely unique way it will be shown how this objective can be fulfilled—without limitation on the values of any of them, as well as total avoidance of any approximation technique whatsoever.

Automatic amplitude and phase equalization of “n” sinusoidal signals of the same frequency

Automatic amplitude and phase equalization of “n” sinusoidal signals of the same frequency ω are studied. To demonstrate the technique, first amplitude and phase equalization of “two” such signals are considered and then the method is extended for the “n-signal” case. It will be seen that the proposed technique is very straightforward and accurate and does not involve any approximation or limitation on amplitudes, phase angles and the frequency ω of signals. Also, no instability problem is encountered if “three” simple rules are observed. An analogue computer simulation for the “2-signal” case is presented, which shows how accurate and attractive the method is.

FFT Processor as a Digital Lens in Grid Array VLBI

Correlator type processors have been currently used in VLBI, in which the number of correlators increases as N(N-1)/2 where N is the number of antennas. In a large elements VLBI array in future, this will introduce difficulty in constructing the processor. If we took the grid array configuration of antenna, FFT processor could be used in VLBI processing instead. FFT processor is used as a digital lens for a directional finding facility of the arrival waves. In FFT, the number of multiplications increases only as N log N. Although it gives maximum redundancy of Fourier components, the next step of the research on crustal motion will require measuring the velocities as a vector fields. Higher S/N ratio is also obtained in the VLBI maps.The present processor, which was originally constructed for a pilot system of the radio patrol camera at Waseda University, is formed by a FFT Processor and eight Complex Amplitude Equalizers(1,2). When it is used as an VLBI processor, phase and amplitude fluctuations due to local oscillators and/or propagation effects are absorbed by the quick control of the Complex Amplitude Equalizers.Here, we show examples of the computer controlled phase adjustment using the Equalizers(3). Our telescope is an 8 elements Very Short Baseline Interferometer (only 2m) at 10 GHz. Fig.1 is the block diagram of the present system. In VLBI system the recording facilities should exist between A/Ds and the Equalizers. The FFT processor is an error free ideal lens, and from the sampling theorem it makes eight independent beams in our system. Fig.2 is the dirty beams before removing phase errors, and Fig.3 the beams after the error removed. Both are 180 deg beam switched, while non switched in Fig.4.

On the rising total cross-section and the new approach to high-energy hadron-hadron scattering

A new approach to high-energy hadron-hadron scattering is proposed, based on the spontaneously broken non-Abelian gauge theory with observable baryons as fundamental fermions and gauge field quanta corresponding to observable vector mesons. It is shown that rising total cross-section, positive ratio of real to imaginary part of the forward scattering amplitude and asymptotic equality of the baryon-baryon and baryon-antibaryon total cross-sections appear naturally in this model at high energies, in the leading-logarithm approximation. The expression for the total baryon-baryon cross-section is shown to be consistent with experimental data on pp and p\(\bar p\) scattering in the ISR and SPS energy range, and to give reasonable predictions for higher energies. An asymptotic expression for the ratio of real to imaginary part of the forward scattering amplitude is obtained, and is also in agreement with pp and p\(\bar p\) data.

A high-performance custom standard-cell CMOS equalizer for telecommunications applications

A high-performance CMOS programmable amplitude equalizer has been implemented with a dynamic range greater than 100 dB and supply rejection greater than 60 dB at 1 kHz from both supplies. This was accomplished using a balanced architecture. A nonreturn-to-zero sample-and-hold circuit is proposed that is also parasitic-insensitive. The circuits are implemented using a standard-cell methodology.

Pseudoerror Monitor for 16 QAM 140 Mbit/s Digital Radio

This paper presents the performance of a pseudoerror monitoring technique for a 16 QAM 140 Mbit/s digital radio in presence of multipath dispersive fading. The so-called pseudoerrors, generated by means of a threshold modification of two, namely, secondary receivers are entered into an extrapolating function to obtain a fast bit error ratio (BER) calculation. A counting time of 10 ms was retained in order to follow fading depth changes up to 100 dB/s and fading notch speeds up to 300 MHz/s approximately. We have considered three structures for the receiver: without equalization, with IF amplitude equalization, and decision feedback equalization (DFE). The results obtained show the estimated and real BER within a margin that includes the two recommended CCIR values: 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> and10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> . In particular, the estimated signature obtained in the case of using IF equalization reveals that this fast BER calculation could be an effective choice to control a frequency diversity switch, even in the presence of a fading activity with rapid variations.

Synchrony and “synchrony suppression” in primary auditory neurons

Synchrony of discharge to two‐tone stimuli and “synchrony suppression” are analyzed by examining the implications of the definition of vector strength. “Synchrony suppression,” defined as the reduction in the vector strength for one tone when a second is added, occurs by definition when half‐wave rectification occurs in an otherwise linear system. The usual shifts of empirical vector strength curves occur, disproving the necessity for compressive nonlinearity. “Synchrony suppression,” has been defined incompatibly as the shift in dB of a vector strength curve—said to be the magnitude of suppression. The identification of half‐wave rectification with vector strength reduction disproves this conception, which is a logical fallacy as well. Curve shift is here defined as the shift of the crossover point at which a vector strength growth curve intersects the paired decay curve of the fixed‐level tone. Crossover is the point of equality of the output amplitudes, hence vector strengths, in the period histogram. When the vector strength definition is applied to a complex waveform at the output of a compressive nonlinearity that compresses equal inputs equally, the shifts of the crossover points necessarily equal those in the linear case. But differences in unequal inputs will be accentuated in the relative output levels in the histogram, leading to greater differences of the vector strengths, at those relative input levels, than in the linear case. More visible effects of compression result from waveform distortion, which reduces vector strength saturation, and crossover, values and causes them to recede at higher levels. If the auditory periphery includes nonlinearities that compress equal inputs unequally, the basic curve shifts caused by half‐wave rectification will change by the amount of differential compression. Since data suggest such nonlinearities may exist, it could be useful in new studies to use the crossover point of the growth and decay curves, as an index of equal output, to seek their confirmation and to infer something about them. [Work supported by NSERC.]