Yih-Chyun Jenq

Performance Analysis of a Packet Switch Based on Single-Buffered Banyan Network

Banyan networks are being proposed for interconnecting memory and processor modules in multiprocessor systems as well as for packet switching in communication networks. This paper describes an analysis of the performance of a packet switch based on a single-buffered Banyan network. A model of a single-buffered Banyan network provides results on the throughput, delay, and internal blocking. Results of this model are combined with models of the buffer controller (finite and infinite buffers). It is shown that for balanced loads, the switching delay is low for loads below maximum throughput (about 45 percent per input link) and the blocking at the input buffer controller is low for reasonable buffer sizes.

Digital spectra of nonuniformly sampled signals: fundamentals and high-speed waveform digitizers

A digital spectral representation of a nonuniformly sampled signal is derived, and a spectrum analysis of a nonuniformly sampled sinusoid is presented. It is found that the spectrum of a nonuniformly sampled sinusoid comprises uniformly spaced line spectra; in addition, the signal-to-noise ratio is obtained in closed form. The theories are then applied to analyze the harmonic distortion introduced in high-speed waveform digitizers due to time-base errors. Specifically, waveform digitizers are analyzed which utilize interleaving/multiplexing and random equivalent time-sampling techniques and the monolithic A/D converter technology to extend their capabilities. Theoretical results are confirmed by experimental results with a real waveform digitizer. >

Digital spectra of nonuniformly sampled signals: a robust sampling time offset estimation algorithm for ultra high-speed waveform digitizers using interleaving

The author presents an algorithm for estimating the sampling time offsets encountered at the parallel sampling paths of an ultra-high-speed waveform digitizing system which is realized by interleaving many sample-hold and A/D (analog/digital) converter modules. One obvious application of this algorithm is to feed these estimates back to adjustable delay units in all the sampling paths to compensate the sampling-time offsets. Simulation results indicate that with an 8-bit quantizer the residual timing error can be reduced to just about 0.05% of the sampling period. >

Perfect reconstruction of digital spectrum from nonuniformly sampled signals

In this paper, we consider the problem of reconstructing the digital spectrum from a set of nonuniformly spaced time samples of a signal. Specifically, we deal with the situation where the timing offsets of each sampling instance are known and have a periodic structure. Examples include the random equivalent time sampling system of a digital scope, and an ultra high speed waveform digitizing system with interleaved A/D converters. An algorithm which allows one to reconstruct the digital spectrum perfectly is derived, and a numerical example is presented. The algorithm is non-iterative and precise, and should prove to be useful in many applications.

Digital spectra of nonuniformly sampled signals. II. Digital look-up tunable sinusoidal oscillators

For Part I see ibid., vol.37, no.2, June 1988. The author presents theories and applications of a digital spectrum analysis technique for a class of nonuniformly sampled signals. The structure of the harmonic components present in a digitally synthesized sine wave is analyzed using a table look-up method. The digital table look-up method offers several desirable features, such as high-frequency stability and precision control of both the frequency and the phase of the generated sine wave. However, undesirable spurious harmonic components are generated when one tries to tune to different frequencies by manipulating the memory-addressing mechanism rather than loading a new waveform sample into the waveform memory, which is generally time-consuming and sometimes infeasible. The frequencies, amplitudes, and phrases of all the spurious harmonic components are derived in closed form. >

Measuring harmonic distortion and noise floor of an A/D converter using spectral averaging

The author proposes to use spectral averaging techniques to measure the harmonic distortion and noise floor of an analog/digital (A/D) digitizing subsystem. The noise floor of an ideal B-bit A/D converter is derived in closed form. It is shown that this noise floor is a function of the A/D resolution B, the record length N, and the equivalent noise bandwidth E/sub B/ of the window function used in the discrete-Fourier-transform (DFT) computation. For an example, the noise floor is given for the case in which the magnitude square of the spectrum is averaged. Both experimental and simulation results are presented and it is shown that they are in good agreement with the theoretical results. >

Sinewave parameter estimation algorithm with application to waveform digitizer effective bits measurement

A high-performance algorithm to estimate the four parameters (amplitude, DC offset, frequency and phase) of a sine wave from a sampled data record is presented. The estimation errors are obtained in closed form and can be controlled. The algorithm is non iterative and extremely fast. A Turbo Pascal implementation on the IBM PC/AT requires only a couple of seconds to do a 256-point fit. A method to measure a digitizers effective bits using this algorithm is presented. Simulation results indicate that the method gives excellent estimates of the true resolution of the simulated ideal digitizer. A 10-point effective-bits plot of a waveform digitizer under test can be accomplished in seconds instead of minutes or even hours as with other iterative algorithms. >

Direct digital synthesizer with jittered clock

Since the direct digital synthesizer (DDS) can potentially be used as a flexible clock source, it is of interest to study its spectrum purity as well as jitter characteristic. In this paper, we investigate the jitter transfer characteristic of the DDS clock driven by a jittered digital-to-analog converter (DAC) clock. We first derive the dosed form expressions of the spectrum of the DAC output signal with jittered driving clock. These expressions are then used to investigate the spectral structure of the DDS clock. Equations are derived for the calculation of the SNR. For a small phase noise power in the driving clock, the DDS clock SNR is obtained in a simple closed form and is shown to be lower than that of the input driving clock by the amount of 20 log(f/sub s//d/sub d/) dB, where f/sub s/ is the nominal driving clock frequency and f/sub d/ is the desirable DDS output clock frequency.

Digital spectra of non-uniformly sampled signals: theories and applications. IV. Measuring clock/aperture jitter of an A/D system

Theories and applications of a digital spectrum analysis technique for a class of nonuniformly sampled signals are described. A method based on asynchronous spectral averaging is presented to measure the standard deviation of a clock/aperture jitter of an A/D (analog/digital) system. A sine wave with frequency f/sub 0/ is used as the input test signal to an A/D system. Spectral averaging is performed on many asynchronously acquired data records with length N. The jitter standard deviation is calculated from the measured signal-to-noise (S/N) floor ratio. The expression which relates the S/N to the standard deviation, sigma /sub r/, of the jitter, r, is derived in closed form. Graphs showing good agreement between the theoretical equation and the simulation results are presented. >

High-precision sinusoidal frequency estimator based on weighted least square method

The estimation of the frequency of a sine wave is a fundamental task in many test and measurement systems. In this report, a frequency estimator based on the weighted least-square method (WLSM) is derived. The estimator is optimal in the sense that it is unbiased, and it has the smallest standard deviation among the whole class of linear estimators. A well-approximated normalized standard deviation of the estimator is obtained in closed form. It is shown that the normalized standard deviation of the optical estimator is of the form 2.2σ/[m×n3]1/2, where m is the average number of samples per period, n is the number of half periods covered by the observation interval, and σ is the standard deviation of the additive noise. There are three potential applications of this result: precision frequency measurement in white-noise environment; confidence interval display in frequency meter; and waveform digitizer effective-bits characterization.