Showing papers on "Bandwidth (signal processing) published in 1998"

Impulse radio: how it works

Abstract: Impulse radio, a form of ultra-wide bandwidth (UWB) spread-spectrum signaling, has properties that make it a viable candidate for short-range communications in dense multipath environments. This paper describes the characteristics of impulse radio using a modulation format that can be supported by currently available impulse signal technology and gives analytical estimates of its multiple-access capability under ideal multiple-access channel conditions.

On the robustness of ultra-wide bandwidth signals in dense multipath environments

Abstract: The results of an ultra-wide bandwidth (UWB) signal propagation experiment, using bandwidth in excess of 1 GHz, performed in a typical modern office building are presented. The robustness of the UWB signal in multipath is quantified through cumulative distribution functions of the signal quality in various locations of the building. The results show that an UWB signal does not suffer multipath fading.

The role of synchronization in digital communications using chaos. II. Chaotic modulation and chaotic synchronization

Abstract: For pt. I see ibid., vol. 44, p. 927-36 (1997). In a digital communications system, data are transmitted from one location to another by mapping bit sequences to symbols, and symbols to sample functions of analog waveforms. The analog waveform passes through a bandlimited (possibly time-varying) analog channel, where the signal is distorted and noise is added. In a conventional system the analog sample functions sent through the channel are weighted sums of one or more sinusoids; in a chaotic communications system the sample functions are segments of chaotic waveforms. At the receiver, the symbol may be recovered by means of coherent detection, where all possible sample functions are known, or by noncoherent detection, where one or more characteristics of the sample functions are estimated. In a coherent receiver, synchronization is the most commonly used technique for recovering the sample functions from the received waveform. These sample functions are then used as reference signals for a correlator. Synchronization-based coherent receivers have advantages over noncoherent receivers in terms of noise performance, bandwidth efficiency (in narrow-band systems) and/or data rate (in chaotic systems). These advantages are lost if synchronization cannot be maintained, for example, under poor propagation conditions. In these circumstances, communication without synchronization may be preferable. The theory of conventional telecommunications is extended to chaotic communications, chaotic modulation techniques and receiver configurations are surveyed, and chaotic synchronization schemes are described.

Recent advances in dielectric-resonator antenna technology

Abstract: This paper features some of the advances in dielectric-resonator antenna technology at the Communications Research Centre. Several novel elements are presented that offer significant enhancements to parameters such as impedance bandwidth, circular-polarization bandwidth, gain, or coupling to various feed structures. Several linear and planar arrays are also presented, to illustrate the performance of dielectric-resonator antenna elements in the array environment.

Capacity and mutual information of broadband multipath fading channels

Abstract: We investigate the capacity and mutual information of a broadband fading channel consisting of a finite number of time-varying paths. We show that the capacity of the channel in the wideband limit is the same as that of a wideband Gaussian channel with the same average received power. However, the input signals needed to achieve the capacity must be "peaky" in time or frequency. In particular, we show that if white-like signals are used instead (as is common in spread-spectrum systems), the mutual information is inversely proportional to the number of resolvable paths L/spl tilde/ with energy spread out, and in fact approaches 0 as the number of paths gets large. This is true even when the paths are assumed to be tracked perfectly at the receiver. A critical parameter L/spl tilde//sub crit/ is defined in terms of system parameters to delineate the threshold on L over which such overspreading phenomenon occurs.

Means and method for a synchronous network communications system

Abstract: Nodes on a network are synchronized with each other using a clock transfer system (16). The communications channels between the nodes are then measured (164) and calibrated (163) for optimal bandwidth. The optimized channels and synchronization enable a new form of signaling based on precise control of the frequency, amplitude, and phase of the waveform of the signal. Receiving nodes receive information in order to locate the signal at the frequency, phase and amplitude. Precision control (165, 166) of these parameters also serves as a unique signature of the transmitting node preventing security breaches (162) as the signal's characteristics are unique to the transmitting node. The channel is continuously updated with a precision control system (165, 166) to insure that the nodes are not out of phase.

An experimental and theoretical study of the offset launch technique for the enhancement of the bandwidth of multimode fiber links

Abstract: This paper reports an experimental and theoretical study of bandwidth enhancement in multimode fiber links achieved by using offset launch techniques. It is found, both from theory and experiment, that an up to four-fold bandwidth enhancement can be obtained compared to standard overfilled launch techniques despite exciting over 50% of the fiber modes, thus allowing good stability. The enhancement technique is found to be achieved for a range of fibers with different core diameters and core refractive index profiles. The level of bandwidth enhancement depends upon the inherent bandwidth of the fiber, being particularly effective in improving the performance of low bandwidth "worst case" fibers. The launch is found to be stable with respect to environmental variations, showing bandwidth enhancement for injection positions or connector offsets of up to 5 /spl mu/m from optimum. In addition, unlike many restricted launch techniques, it is found to be tolerant to angular fiber misalignment for angles up to 6/spl deg/ from normal.

Communications channel selection

Abstract: A communications system (10) is provided for sending and receiving information relative to a mobile unit in which a number of network channels are available through which the information can be transferred. The system includes a link selector (64) for selecting an acceptable network channel using application requirements for the particular channel, together with channel operating parameter values. When such a channel does not become available, the link selector (64) is also involved with recovery procedures. These network channel operating parameters include bandwidth, information transfer costs and information transfer packet loss, latency and jitter. Weighting vectors are also utilized with such channel operating parameters in determining suitability values associated with the available network channels. The link selector (64) communicates with a link scheduler (70) that has responsability for determining when information should be transferred including when there should be a change in the timing of the information transfer.

Tunable optical filters for dense WDM networks

Abstract: WDM is currently taking over as the leading technology in point-to-point transmission links. For optical implementation of WDM networks, logical functionalities such as wavelength (channel) selection should be carried out in the wavelength domain; thus, the development of dynamic optical devices is required. One key device is a tunable optical filter. Important features of such a filter include low insertion loss, narrow bandwidth, high sidelobe suppression, large dynamic range, fast tuning speed, a simple control mechanism, small size, and cost effectiveness. Here, an extensive overview of the different technologies used to produce tunable optical filters is presented. Among them, fiber filters such as fiber Bragg gratings and fiber Fabry Perot are the most commercialized, yet inherently limited in their dynamic speeds. For high demanding dynamics, micro-machined and acousto-optic filters can offer a good solution for microsecond tuning speeds. Faster tunable devices, in nanosecond tuning speeds, might emerge out of microresonators, electrooptic filters, and active DBR filters.

Dispersive properties of optical filters for WDM systems

Abstract: Wavelength division multiplexing (WDM) communication systems invariably require good optical filters meeting stringent requirements on their amplitude response, the ideal being a perfectly rectangular filter. To achieve high bandwidth utilization, the phase response of these filters is of equal importance, with the ideal filter having perfectly linear phase and therefore constant time delay and no dispersion. This aspect of optical filters for WDM systems has not received much attention until very recently. It is the objective of this paper to consider the phase response and resulting dispersion of optical filters in general and their impact on WDM system performance. To this end we use general concepts from linear systems, in particular, minimum and nonminimum phase response and the applicability of Hilbert transforms (also known as Kramers-Kronig relations). We analyze three different classes of optical filters, which are currently being used in WDM systems and compare their performance in terms of their phase response. Finally, we consider possible ways of linearizing the phase response without affecting the amplitude response, in an attempt to approximate the ideal filter and achieve the highest bandwidth utilization.

Bandwidth selection for the smoothing of distribution functions

Abstract: SUMMARY Several approaches can be made to the choice of bandwidth in the kernel smoothing of distribution functions. Recent proposals by Sarda (1993) and by Altman & Leger (1995) are analogues of the 'leave-one-out' and 'plug-in' methods which have been widely used in density estimation. In contrast, a method of crossvalidation appropriate to the smoothing of distribution functions is proposed. Selection of the bandwidth parameter is based on unbiased estimation of a mean integrated squared error curve whose minimising value defines an optimal smoothing parameter. This procedure is shown to lead to asymptotically optimal bandwidth choice, not just in the usual first-order sense but also in the second-order sense in which kernel methods improve on the standard empirical distribution function. Some general theory on the performance of optimal, data-based methods of bandwidth choice is also provided, leading to results which do not have analogues in the context of density estimation. The numerical performances of all the methods discussed in the paper are compared. A bandwidth based on a simple reference distribution is also included. Simulations suggest that the crossvalidatory proposal works well, although the simple reference bandwidth is also quite effective.

A low bandwidth broadcasting protocol for video on demand

Abstract: Broadcasting protocols can improve the efficiency of video on demand services by reducing the bandwidth required to transmit videos that are simultaneously watched by many viewers. We present a polyharmonic broadcasting protocol that requires less bandwidth than the best extant protocols to achieve the same low maximum waiting time. We also show how to modify the protocol to accommodate very long videos without increasing the buffering capacity of the set-top box.

Low-loss micromachined filters for millimeter-wave communication systems

Abstract: High-performance planar micromachined filters at 37 and 60 GHz are presented. The filters consist of a 3.5% bandwidth two-pole Chebyshev filter with transmission zeros at 37 GHz, 2.7% and 4.3% bandwidth four- and five-pole Chebyshev filters at 60 GHz, and an 8% bandwidth elliptic filter at 60 GHz. Silicon micromachining techniques combined with micropackaging have been applied to allow for very high-Q resonators resulting in low-loss filters. The 37-GHz two-pole filter exhibits a 2.3-dB port-to-port insertion loss. The 2.7% and 4.3% four- and five-pole Chebyshev filters at 60 GHz exhibit 2.8- and 3.4-dB insertion loss, and the 8% elliptic filter exhibits a 1.5-dB insertion loss. These values show a large reduction of insertion loss compared to conventional planar techniques, and can be used for planar low-cost millimeter-wave wireless communication systems.

System and method for multiresolution scalable audio signal encoding

Abstract: An audio signal analyzer and encoder is based on a model that considers audio signals to be composed of deterministic or sinusoidal components, transient components representing the onset of notes or other events in an audio signal, and stochastic components. Deterministic components are represented as a series of overlapping sinusoidal waveforms. To generate the deterministic components, the input signal is divided into a set of frequency bands by a multi-complementary filter bank. The frequency band signals are oversampled so as to suppress cross-band aliasing energy in each band. Each frequency band is analyzed and encoded as a set of spectral components using a windowing time frame whose length is inversely proportional to the frequency range in that band. Low frequency bands are encoded using longer time frames than higher frequency bands. Transient components are represented by parameters denoting sinusoidal shaped waveforms produced when the transient components are transformed into a real valued frequency domain waveform. Stochastic or noise components are represented as a series of spectral envelopes. The parameters representing the three signal components compose a stream of compressed encoded audio data that can be further compressed so as to meet a specified transmission bandwidth limit by the deleting the least significant bits of quantized parameter values, reducing the update rates of parameters, and/or deleting the parameters used to encode higher frequency bands until the bandwidth of the compressed audio data meets the bandwidth requirement. Signal quality degrades in a graduated manner with successive reductions in the transmitted data rate.

A fully integrated VCO at 2 GHz

Abstract: An integrated voltage-controlled oscillator (VCO) at a frequency of 2 GHz is implemented in a f/sub T/= 25 GHz standard bipolar process. The phase noise of the VCO is -136 dBc/Hz at 4.7 MHz frequency offset. The LC-resonator uses vertically coupled on-chip inductors and integrated tuning diodes. Due to the poor performance of integrated resonators on silicon ICs, oscillators with phase noise meeting requirements of wireless applications are difficult to integrate. With fully integrated designs only the standards for cordless phones, for instance DECT, can be achieved. The critical point in the DECT-specification is the emission of the transmitter due to intermodulation in the third adjacent channel, that must be <-47 dBm. This value is measured with an integration bandwidth of 1 MHz centered at the nominal center frequency. With a channel-spacing of 1.728 MHz the third adjacent channel is located 5.184 MHz from the actual transmit channel frequency. The beginning of the integration bandwidth is at an offset frequency of 4.684 MHz related to the nominal frequency of the transmit channel. This is the offset frequency, at which the specification must be met. The resulting noise requirement is -132 dBc/Hz at a offset frequency of 4.684 MHz, when the integration bandwidth and the transmit output power of 25 dBm are taken into account.

Combined GPS and wide bandwidth radiotelephone terminals and methods

Abstract: Wireless mobile terminals include a GPS Radio Frequency (RF) receiver and a wide bandwidth radiotelephone RF receiver having bandwidth that is at least half as wide as the GPS RF signal chip frequency The wireless mobile terminals also include a shared Intermediate Frequency (IF) section that is responsive to both the GPS RF receiver and to the wide bandwidth radiotelephone RF receiver A demodulator such as a CDMA despreader is responsive to the shared IF section Thus, common circuitry may be provided except for the separate GPS RF receiver and wide bandwidth radiotelephone RF receiver Low cost manufacturing and high efficiency operations may thereby be provided

Q-enhanced LC bandpass filters for integrated wireless applications

Abstract: Q-enhanced LC filter technology offers an alternative to the use of direct conversion techniques for implementing fully integrated receivers. Design and performance issues for QE LC filters are discussed and a fully integrated 850 MHz, two-pole, bandpass filter with an 18 MHz 3 dB bandwidth is reported. The prototype design is implemented in a standard 0.8 /spl mu/m CMOS process and achieves a rejection of over 50 dB at 100 MHz offset, an in-band dynamic range of 75 (90) dB when used in a system with a 1 MHz (30 kHz) final IF bandwidth, and a third-order intercept point that exceeds +25 dBm at an 80 MHz offset from the passband center,.

A New Approach to Interference Excision in Radio Astronomy: Real-Time Adaptive Cancellation

Abstract: Every year, an increasing amount of radio-frequency (RF) spectrum in the VHF, UHF, and microwave bands is being utilized to support new commercial and military ventures, and all have the potential to interfere with radio astronomy observations. Such services already cause problems for radio astronomy even in very remote observing sites, and the potential for this form of light pollution to grow is alarming. Preventive measures to eliminate interference through FCC legislation and ITU agreements can be effective; however, many times this approach is inadequate and interference excision at the receiver is necessary. Conventional techniques such as RF filters, RF shielding, and postprocessing of data have been only somewhat successful, but none has been sufficient. Adaptive interference cancellation is a real-time approach to interference excision that has not been used before in radio astronomy. We describe here, for the first time, adaptive interference cancellation in the context of radio astronomy instrumentation, and we present initial results for our prototype receiver. In the 1960s, analog adaptive interference cancelers were developed that obtain a high degree of cancellation in problems of radio communications and radar. However, analog systems lack the dynamic range, noised performance, and versatility required by radio astronomy. The concept of digital adaptive interference cancellation was introduced in the mid-1960s as a way to reduce unwanted noise in low-frequency (audio) systems. Examples of such systems include the canceling of maternal ECG in fetal electrocardiography and the reduction of engine noise in the passenger compartments of automobiles. These audio-frequency applications require bandwidths of only a few tens of kilohertz. Only recently has high-speed digital filter technology made high dynamic range adaptive canceling possible in a bandwidth as large as a few megahertz, finally opening the door to application in radio astronomy. We have built a prototype adaptive canceler that consists of two receivers: the primary channel (input from the main beam of the telescope) and a separate reference channel. The primary channel receives the desired astronomical signal corrupted by RFI (radio-frequency interference) coming in the sidelobes of the main beam. A separate reference antenna is designed to receive only the RFI. The reference channel input is processed using a digital adaptive filter and then subtracted from the primary channel input, producing the system output. The weighting coefficients of the digital filter are adjusted by way of an algorithm that minimizes, in a least-squares sense, the power output of the system. Through an adaptive-iterative process, the canceler locks onto the RFI, and the filter adjusts itself to minimize the effect of the RFI at the system output. We have designed the adaptive canceler with an intermediate frequency (IF) of 40 MHz. This prototype system will ultimately be functional with a variety of radio astronomy receivers in the microwave band. We have also built a prototype receiver centered at 100 MHz (in the FM broadcast band) to test the adaptive canceler with actual interferers, which are well characterized. The initial laboratory tests of the adaptive canceler are encouraging, with attenuation of strong frequency-modulated (FM) interference to 72 dB (a factor of more than 10 million), which is at the performance limit of our measurements. We also consider requirements of the system and the RFI environment for effective adaptive canceling.

How narrow is narrowband

Abstract: The "narrowband" assumption is often made in the analysis of array signal processing algorithms. The author provides a definition for the notion of narrowband, and the derivation of an expression which is useful in determining if a particular scenario qualifies as narrowband. The expression derived correctly predicts where the narrowband assumption fails for some super-resolution algorithms, the Cramer-Rao bound on angle estimation and the signal-to-interference plus noise performance of adaptive beamformers.

Automated home control using existing electrical lines as a communications medium

Abstract: A home control system as described herein uses existing electrical power lines in a home for communications. A system includes one or more analog signal sources connected to transmit analog signals using high-bandwidth frequency channels on the electrical power lines, at relatively high bandwidths. The analog signal sources receive control data using a low-bandwidth frequency channel on the same electrical power lines, at a comparatively low bandwidth. One or more analog signal receivers are connected to receive the analog signals using the high-bandwidth frequency channels, and to receive control data using the low-bandwidth frequency channel. A controller is configured to designate one or more source/receiver groups from the analog signal sources and receivers. The controller is connected to send control data to the source and receiver of each group using the low-bandwidth frequency channel. The control data instructs each group to use a different one of the light-bandwidth frequency channels.

A W-band dielectric-lens-based integrated monopulse radar receiver

Abstract: An integrated monopulse radar receiver has been developed for tracking applications at W-band frequencies. The receiver is based on dielectric-lens-supported, coplanar-waveguide-fed slot-ring antennas integrated with /spl times/2 uniplanar subharmonic mixers. The slot-ring antenna is capable of supporting two orthogonal modes offering the possibility of dual/multiple receive polarizations. The design center frequency is 94 GHz and the IF bandwidth is 2-4 GHz. The measured DSB conversion losses of the individual receiver channels range from 14.4 to 14.7 dB at an LO frequency of 45.0 GHz and an IF of 1.4 GHz. This includes the lens reflection and absorption losses, backside radiation, RF feedline loss, mixer conversion loss, and IF distribution loss. Excellent monopulse patterns are achieved with better than 45 dB difference pattern nulls using IF monopulse processing. This translates to submilliradian angular accuracy for a 24 mm aperture. Better than 25 dB nulls are possible over a 600 MHz bandwidth. The receiver is robust with respect to RF frequency.

Characterization of UHF radio propagation channels in tunnel environments for microcellular and personal communications

Abstract: Narrowband and wideband propagation measurements have been conducted in five tunnels. The effects of pedestrians, vehicles, and curvature on propagation are included in the characterization. The narrowband propagation is characterized in terms of power distance law, slow fading, and fast fading statistics: wideband propagation, rms delay spread, and its statistics. The results show that the power distance law is insensitive to the location of the transmit antenna in the cross section of a tunnel, but not to the antenna insertion loss. The lognormal distribution basically fits the slow variation of the received signals, whereas the Rician distribution, the fast fading in the straight empty sections of the tunnels. In the curved tunnel sections, the Rayleigh distribution does not fit the fast fading variation as is expected. Tunnel radio propagation channels are dependent strongly upon frequency. Higher frequency signals exhibit more severe fluctuations and larger rms delay spread. The rms delay spreads are found to be generally less than 25 and 103 ns for the emptied and occupied tunnel conditions, respectively. One can conclude that the tunnel channels have a broad coherent bandwidth and can support the data rate up to 1 Mb per second without equalization.

Novel compact elliptic-function narrow-band bandpass filters using microstrip open-loop resonators with coupled and crossing lines

Abstract: Novel compact elliptic-function narrow-band bandpass filters have been designed and fabricated. This new configuration consists of two identical microstrip open-loop resonators with coupled and crossing lines. A theoretical investigation has confirmed that this novel configuration is capable of providing elliptic-function filtering. Furthermore, the feasibility of this filter is verified experimentally. Centered at 2.039 GHz, the fabricated microstrip bandpass filter shows a measured 3-dB bandwidth of 2% and two deep notches in its stopband. In addition, the main circuit of this filter occupies only 2.5 cm/spl times/1.5 cm using a substrate with dielectric constant of 10.5, making it very attractive for applications in the mobile and personal communication systems (PCS's).

Mechanical design and control of a high-bandwidth shape memory alloy tactile display

Abstract: We have constructed a tactile shape display which can be used to convey small scale shape in teleoperation and virtual environments. A line of 10 pins spaced 2 mm on center are each actuated with a shape memory alloy wire. A combination of careful mechanical design and liquid cooling allows a simple proportional controller with constant current feed forward to achieve 40 Hz bandwidth. To quantify the value of increased bandwidth, an experiment involving a prototypical search task has been conducted using the display. A digital filter limited the frequency response of the display to three cutoff frequencies: 1, 5 and 30 Hz. Subjects were able to complete the search more than 6 times as quickly with 30 Hz bandwidth than with 1 Hz.

Optimization of the advanced earth observing satellite ii global imager channels by use of radiative transfer calculations

Abstract: The channel specifications of the Global Imager onboard the Advanced Earth Observing Satellite II have been determined by extensive numerical experiments. The results show that there is an optimum feasible position for each ocean color channel. The bandwidth of the 0.763-microm channel should be less than 10 nm for good sensitivity to the cloud top height and geometric thickness of the cloud layer; a 40-nm bandwidth is suitable for the 1.38-microm channel to have the strongest contrast between cloudy and clear radiance with a sufficient radiant energy; and a 3.7-microm channel is better than a 3.95-microm channel for estimation of the sea surface temperature (SST) and determination of the cloud particle size when the bandwidth of the channel is 0.33 microm. A three-wavelength combination of 6.7, 7.3, and 7.5 microm is an optimized choice for water vapor profiling. The combination of 8.6, 10.8, and 12.0 microm is suitable for cloud microphysics and SST retrievals with the split-window technique.

Spread spectrum at phase lock loop (PLL) feedback path

Abstract: A plurality of four bit modulation read only memory (ROM) codes are generated with a PLL feedback divider. The output of a single phase lock loop is modulated to spread the bandwidth of a synthesized clock signal. By spreading the bandwidth, the amplitude of the synthesized clock signal is decreased with respect to its fundamental and its harmonics. As a result of reducing the peak amplitudes, the radiated electromagnetic emission level is significantly lower. Input phase lock loop system data is received as to selected phase lock loop characteristics. A continuous FBD is selected, and a bandwidth and system stability calculation is performed. A state variable system is determined and a numerical model for programming by finite differences is developed. A best path is determined to produce output data and ROM code by a least squares error method.

Apparatus for expanding narrowband speech to wideband speech by codebook correspondence of linear mapping functions

Abstract: Apparatus for expanding the bandwidth of speech signals such that a narrowband speech signal is input and digitized, the spectral envelope information and residual information are extracted from the digitized signal by linear predictive coding analysis, the spectral envelope information is expanded into wideband information by a spectral envelope converter, the residual information is expanded into wideband information by a residual converter, the converted spectral envelope information and residual information are combined to produce a wideband speech signal, frequency information not contained in the input signal is extracted from the obtained wideband speech signal by a filter, and the resulting signal is added to the original digitized input signal, and the obtained signal is converted into an analog signal as the output signal of the apparatus. The apparatus comprises a linear mapping function codebook used for converting spectral parameters, and a weights calculator and an adder for weighing and summing function outputs.

A wide-band tuning system for fully integrated satellite receivers

Abstract: The building blocks for a low-power tuning system that reduces the phase noise of integrated VCO's are described. The multimodulus prescaler, the phase frequency detector, and the wide-band charge pump have been integrated in a standard bipolar technology with 9-GHz n-p-n transistors and 200-MHz p-n-p transistors. The maximum input frequency of the multimodulus prescaler is 3.2 GHz, the maximum reference frequency of the phase frequency detector is 380 MHz, and the 3-dB bandwidth of the charge pump is 41 MHz at a reference frequency of 300 MHz. The achieved performance enables the use of fully integrated VCO's with relatively high phase noise for reception of satellite digital signals.

Efficient simulation of constant Q using coarse-grained memory variables

Abstract: Improvements in computing speed have progressively increased the usable bandwidth of seismic wave-field simulations computed with time-stepped numerical schemes (e.g., finite difference, finite element, pseudospectral). As computational bandwidth increases, anelastic losses become increasingly significant for some important applications such as earthquake ground-motion modeling, whole earth seismogram simulation, and exploration seismic profile modeling, and these losses need to be included in the simulations. As bandwidth increases, however, the memory variables necessary to incorporate realistic anelastic losses account for an increasing proportion of total computational storage requirements, a consequence of the broad relaxation spectrum of typical earth materials. To reduce these storage requirements, we introduce a new method in which the memory variables are coarse grained, that is, redistributed in such a way that only a single relaxation time is represented at each node point (and therefore a single memory variable per stress component is required). Guided by a perturbation analysis, we effect this redistribution in such a way that spatial variability of this single relaxation time simulates the full relaxation spectrum. Such coarse graining reduces memory-variable storage requirements by a factor of 8 for 3D problems or a factor of 4 for 2D problems. In fourth-order finite-difference computations for the 3D acoustic-wave equation, the method simulates frequency-independent Q within a 3% tolerance over 2 decades in frequency, and it is highly accurate and free of artifacts over the entire usable bandwidth of the underlying finite-difference scheme. These results should also hold for the elastodynamic equations. The method is readily generalized to approximate specific frequency-dependent Q models such as power laws or to further reduce memory requirements. In its present implementation, the main limitation of the method is that it generates artifacts at wavelengths equal to 4 grid cell dimensions and shorter, which may, in some limited circumstances, overlap the usable bandwidth of very high-order finite-difference and/or pseudospectral schemes.