Showing papers on "Sampling (signal processing) published in 2009"

Compressed Sensing of Analog Signals in Shift-Invariant Spaces

Abstract: A traditional assumption underlying most data converters is that the signal should be sampled at a rate exceeding twice the highest frequency. This statement is based on a worst-case scenario in which the signal occupies the entire available bandwidth. In practice, many signals are sparse so that only part of the bandwidth is used. In this paper, we develop methods for low-rate sampling of continuous-time sparse signals in shift-invariant (SI) spaces, generated by m kernels with period T . We model sparsity by treating the case in which only k out of the m generators are active, however, we do not know which k are chosen. We show how to sample such signals at a rate much lower than m/T, which is the minimal sampling rate without exploiting sparsity. Our approach combines ideas from analog sampling in a subspace with a recently developed block diagram that converts an infinite set of sparse equations to a finite counterpart. Using these two components we formulate our problem within the framework of finite compressed sensing (CS) and then rely on algorithms developed in that context. The distinguishing feature of our results is that in contrast to standard CS, which treats finite-length vectors, we consider sampling of analog signals for which no underlying finite-dimensional model exists. The proposed framework allows to extend much of the recent literature on CS to the analog domain.

Modified Current Control Schemes for High-Performance Permanent-Magnet AC Drives With Low Sampling to Operating Frequency Ratio

Abstract: These days, high-frequency permanent-magnet synchronous motors (PMSMs) are used in industry; their maximum synchronous frequency is higher than 1 kHz. However, the sampling and switching frequencies of the digital inverter that consists of the digital controller and pulsewidth-modulation voltage source inverters are limited due to the cost and efficiency reasons. As a result, the current regulation loop has some problems when the high-frequency PMSM runs around its maximum speed and the ratio of the sampling frequency over the synchronous frequency, F ratio = (f samp/fr), is small. In this paper, the problems of the current regulation loop caused by small F ratio in the high-frequency PMSM drive are carefully investigated. Two problems are discussed in this paper: the stability problem and the sampling error. In addition, solutions for the problems are developed; a complex proportional and integral controller with predicted active damping terms is developed to stabilize the current regulation loop, and a model-based error estimator is offered to compensate the sampling error. The developed solutions are verified by simulations and experiments.

Beyond bandlimited sampling

Abstract: Digital applications have developed rapidly over the last few decades. Since many sources of information are of analog or continuous-time nature, discrete-time signal processing (DSP) inherently relies on sampling a continuous-time signal to obtain a discrete-time representation. Consequently, sampling theories lie at the heart of signal processing devices and communication systems. Examples include sampling rate conversion for software radio and between audio formats, biomedical imaging, lens distortion correction and the formation of image mosaics, and super-resolution of image sequences.

Simulation and Analysis of Random Decision Errors in Clocked Comparators

Abstract: Clocked comparators have found widespread use in noise sensitive applications including analog-to-digital converters, wireline receivers, and memory bit-line detectors. However, their nonlinear, time-varying dynamics resulting in discrete output levels have discouraged the use of traditional linear time-invariant (LTI) small-signal analysis and noise simulation techniques. This paper describes a linear, time-varying (LTV) model of clock comparators that can accurately predict the decision error probability without resorting to more general stochastic system models. The LTV analysis framework in conjunction with the linear, periodically time-varying (LPTV) simulation algorithms available from RF circuit simulators can provide insights into the intrinsic sampling and decision operations of clock comparators and the major contribution sources to random decision errors. Two comparators are simulated and compared with laboratory measurements. A 90-nm CMOS comparator is measured to have an equivalent input-referred random noise of 0.73 mVrms for dc inputs, matching simulation results with a short channel excess noise factor ? = 2.

A High-Speed Low-Noise CMOS Image Sensor With 13-b Column-Parallel Single-Ended Cyclic ADCs

Abstract: A high-performance CMOS image sensor (CIS) with 13-b column-parallel single-ended cyclic ADCs is presented The simplified single-ended circuits for the cyclic ADC are squeezed into a 56-mum-pitch single-side column The proposed internal reference generation and return-to-zero digital signal feedback techniques enhance the ADC to have low read noise, a high resolution of 13 b, and a resulting dynamic range of 71 dB An ultralow vertical fixed pattern noise of 01 erms - is attained by a digital CDS technique, which performs A/D conversion twice in a horizontal scan period (6 mus) The implemented CIS with 018-mum technology operates at 390 frames/s and has 707-V/lx middots sensitivity, 61- muV/e- conversion gain, 49-erms - read noise, and less than 04 LSB differential nonlinearity

Access Point Localization Using Local Signal Strength Gradient

Abstract: Many previous studies have examined the placement of access points (APs) to improve the community's understanding of the deployment and behavioral characteristics of wireless networks. A key implicit assumption in these studies is that one can estimate the AP location accurately from wardriving-like measurements. However, existing localization algorithms exhibit high error because they over-simplify the complex nature of signal propagation. In this work, we propose a novel approach that localizes APs using directional information derived from local signal strength variations. Our algorithm only uses signal strength information, and improves localization accuracy over existing techniques. Furthermore, the algorithm is robust to the sampling biases and non-uniform shadowing, which are common in wardriving measurements.

A Unified Approach to Sparse Signal Processing

Abstract: A unified view of sparse signal processing is presented in tutorial form by bringing together various fields. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described succinctly. The common benefits of significant reduction in sampling rate and processing manipulations are revealed. The key applications of sparse signal processing are sampling, coding, spectral estimation, array processing, component analysis, and multipath channel estimation. In terms of reconstruction algorithms, linkages are made with random sampling, compressed sensing and rate of innovation. The redundancy introduced by channel coding in finite/real Galois fields is then related to sampling with similar reconstruction algorithms. The methods of Prony, Pisarenko, and MUSIC are next discussed for sparse frequency domain representations. Specifically, the relations of the approach of Prony to an annihilating filter and Error Locator Polynomials in coding are emphasized; the Pisarenko and MUSIC methods are further improvements of the Prony method. Such spectral estimation methods is then related to multi-source location and DOA estimation in array processing. The notions of sparse array beamforming and sparse sensor networks are also introduced. Sparsity in unobservable source signals is also shown to facilitate source separation in SCA; the algorithms developed in this area are also widely used in compressed sensing. Finally, the multipath channel estimation problem is shown to have a sparse formulation; algorithms similar to sampling and coding are used to estimate OFDM channels.

Digital Carrier Modulation and Sampling Issues of Matrix Converters

Abstract: Although the modulation of AC-AC matrix converters using space vector theory has long been established, their carrier-based modulation principles have only recently attracted some attention. Reasons commonly stated for evaluating the carrier-based alternative include simpler converter control because of its inherent autosequencing process, and easier implementation using fast on-chip timers embedded in most modern digital signal processors. Motivated by these likely merits, which have previously been proven for DC-AC inverters, an investigation is now pursued here to develop appropriate digital carrier modulation schemes for controlling conventional (direct) and indirect matrix converters with minimized semiconductor commutation count and smooth sextant transitions with no erroneous states produced. For guaranteeing the latter two features, correct digital sampling instants and state sequence reversal must be chosen appropriately, as demonstrated in the paper for the two different topological options, which, to date, have not yet been discussed in the existing literature. To validate the concepts discussed, experimental testing on the implemented conventional and indirect matrix laboratory prototypes was performed with their respective results captured and presented in the paper for visual confirmation.

A precision relaxation oscillator with a self-clocked offset-cancellation scheme for implantable biomedical SoCs

Abstract: Recently, there has been an increasing demand for SoCs in the biomedical field [1]. In implantable applications, SoCs are designed under very stringent power and area constraints. The analog and mixed-signal circuits as well as digital circuits in those SoCs require a clock source, because clock-based signal-processing techniques, such as sampling and chopper stabilization, are often used. The primary clock source for such SoCs needs to provide good accuracy and long-term stability of the oscillation frequency ƒ OSC to minimize variations and drifts of the system characteristics. A fairly pure clock signal is required to avoid signal distortion when sampling or chopping techniques are applied. Considering such a source is typically a free-running oscillator, and biomedical signals of typical interest reside at low frequencies, the close-in phase noise is important.

New Spectrum Leakage Correction Algorithm for Frequency Estimation of Power System Signals

Abstract: A new algorithm for the estimation of the frequency of single-tone signals is presented in this paper. The algorithm works in the frequency domain and is based on best fitting a theoretical spectrum of a single-tone signal that is windowed using a rectangular window on the spectrum of the sampled signal. Using this iterative process, the algorithm compensates the spectrum leakage caused by incoherent sampling and a finite number of samples. Due to leakage compensation, the algorithm provides accurate estimates of the signal's frequency, amplitude, and phase. The influence of noise and harmonic and interharmonic distortions on the proposed algorithm was investigated and is reported here. The algorithm's performance was compared with several other frequency-estimation algorithms (mostly those working in the frequency domain). Since the algorithm is intended for power quality measurements (although it is not limited to this application), it was also tested on signals measured in a single-phase power system.

Compressive sensing for sparsely excited speech signals

Abstract: Compressive sensing (CS) has been proposed for signals with sparsity in a linear transform domain. We explore a signal dependent unknown linear transform, namely the impulse response matrix operating on a sparse excitation, as in the linear model of speech production, for recovering compressive sensed speech. Since the linear transform is signal dependent and unknown, unlike the standard CS formulation, a codebook of transfer functions is proposed in a matching pursuit (MP) framework for CS recovery. It is found that MP is efficient and effective to recover CS encoded speech as well as jointly estimate the linear model. Moderate number of CS measurements and low order sparsity estimate will result in MP converge to the same linear transform as direct VQ of the LP vector derived from the original signal. There is also high positive correlation between signal domain approximation and CS measurement domain approximation for a large variety of speech spectra.

Signal processing for picosecond resolution timing measurements

Abstract: The development of large-area homogeneous photo-detectors with sub-millimeter path-lengths for direct Cherenkov light and for secondary electrons opens the possibility of large time-of-flight systems for relativistic particles with resolutions in the picosecond range. Modern ASIC techniques allow fast multi-channel front-end electronics capable of sub-picosecond resolution directly integrated with the photo-detectors. However, achieving resolution in the picosecond range requires a precise knowledge of the signal generation process in order to understand the pulse waveform, the signal dynamics, and the noise induced by the detector itself, as well as the noise added by the processing electronics. Using the parameters measured for fast photo-detectors such as micro-channel plates photo-multipliers, we have simulated and compared the time resolutions for four signal processing techniques: leading edge discriminators, constant fraction discriminators, multiple-threshold discriminators and pulse waveform sampling.

Generation of optical OFDM signals using 21.4 GS/s real time digital signal processing.

Abstract: We demonstrate a field programmable gate array (FPGA) based optical orthogonal frequency division multiplexing (OFDM) transmitter implementing real time digital signal processing at a sample rate of 214 GS/s The QPSK-OFDM signal is generated using an 8 bit, 128 point inverse fast Fourier transform (IFFT) core, performing one transform per clock cycle at a clock speed of 1672 MHz and can be deployed with either a direct-detection or a coherent receiver The hardware design and the main digital signal processing functions are described, and we show that the main performance limitation is due to the low (4-bit) resolution of the digital-to-analog converter (DAC) and the 8-bit resolution of the IFFT core used We analyze the back-to-back performance of the transmitter generating an 836 Gb/s optical single sideband (SSB) OFDM signal using digital up-conversion, suitable for direct-detection Additionally, we use the device to transmit 836 Gb/s SSB OFDM signals over 200 km of uncompensated standard single mode fiber achieving an overall BER<10(-3)

Near field rf communicators

Abstract: A near field RF communicator has an inductive coupler (102) to couple inductively to an H field of an RF signal from another near field RF communicator in near field range to provide a received signal, a demodulator (300) coupled to extract any modulation from a source signal representing a received RF signal to provide an extracted modulation signal; and a controller (107) coupled to receive an extracted modulation signal from the demodulator. The demodulator (300) has a sampler (400) to sample the source signal in sampling periods and to compare signal samples with at least one of other signal samples and a clock or reference signal to remove or reject the carrier of the received RF signal and to extract the modulation.

A multi-threshold sampling method for TOF PET signal processing

Abstract: As an approach to realizing all-digital data acquisition for positron emission tomography (PET), we have previously proposed and studied a multi-threshold sampling method to generate samples of a PET event waveform with respect to a few user-defined amplitudes. In this sampling scheme, one can extract both the energy and timing information for an event. In this paper, we report our prototype implementation of this sampling method and the performance results obtained with this prototype. The prototype consists of two multi-threshold discriminator boards and a time-to-digital converter (TDC) board. Each of the multi-threshold discriminator boards takes one input and provides up to 8 threshold levels, which can be defined by users, for sampling the input signal. The TDC board employs the CERN HPTDC chip that determines the digitized times of the leading and falling edges of the discriminator output pulses. We connect our prototype electronics to the outputs of two Hamamatsu R9800 photomultiplier tubes (PMTs) that are individually coupled to a 6.25×6.25×25mm(3) LSO crystal. By analyzing waveform samples generated by using four thresholds, we obtain a coincidence timing resolution of about 340 ps and an ∼18% energy resolution at 511 keV. We are also able to estimate the decay-time constant from the resulting samples and obtain a mean value of 44ns with an ∼9 ns FWHM. In comparison, using digitized waveforms obtained at a 20 GSps sampling rate for the same LSO/PMT modules we obtain ∼300 ps coincidence timing resolution, ∼14% energy resolution at 511 keV, and ∼5 ns FWHM for the estimated decay-time constant. Details of the results on the timing and energy resolutions by using the multi-threshold method indicate that it is a promising approach for implementing digital PET data acquisition.

Multiple frequency range imaging to remove measurement ambiguity

Abstract: Range imaging systems use a specialised sensor to capture an image where object distance (range) is measured for every pixel using time-of-flight. The scene is illuminated with an amplitude modulated light source, and the phase of the modulation envelope of the reflected light is measured to determine flight time, hence object distance for each pixel. As the modulation waveform is cyclic, an ambiguity problem exists if the phase shift exceeds 2π radians. To overcome this problem we demonstrate a method that superposes two different modulation frequencies within a single capture. This technique reduces the associated overhead compared with performing two sequential measurements, allowing the system to retain high range measurement precision at rapid acquisition rates. A method is also provided to avoid interference from aliased harmonics during sampling, which otherwise contaminate the resulting range measurement. Experimental results show the potential of the multiple frequency approach; producing high measurement precision while avoiding ambiguity. The results also demonstrate the limitation of this technique, where large errors can be introduced through a combination of a low signal to noise ratio and suboptimal selection of system parameters.

Real-Time FPGA Processing for High-Speed Optical Frequency Domain Imaging

Abstract: We present a novel algorithm for reconstructing interferograms acquired in optical frequency domain imaging (OFDI). The algorithm was developed specifically for processing in field programmable gate arrays (FPGAs) and featured the use of a finite-impulse-response (FIR) filter implementation of B-spline interpolation for efficiently re-sampling k-space. When implemented in FPGAs, the algorithm allowed for real-time processing of interferograms acquired with a high-speed OFDI system at 54 kHz and a sampling rate of 100 MS/s.

Potentials of Digitally Sampling Scintillation Pulses in Timing Determination in PET

Abstract: We investigate the potentials of digitally sampling scintillation pulses techniques for positron emission tomography (PET) in this paper, focusing on the determination of the event time We have built, and continue building, a digital library of PET event waveforms generated with various combinations of photo-detectors and scintillator materials, with various crystal sizes Events in this digital library are obtained at a high sampling of 20 GSps (Giga-samples per second) so that their waveforms are recorded with high accuracy To explore the potential advantages of digitally sampling scintillation pulses, we employ a dataset in the above-mentioned library to evaluate two methods for digitizing the event pulses and linear interpolation techniques to analyze the resulting digital samples Our results show that the two digitization methods that we studied can yield a coincidence timing resolution of about 300 ps FWHM when applied to events generated by a pair of LSO + PMT detector units This timing resolution is comparable with that is achieved by the same detector pair with a constant fraction discriminator (CFD) As a benchmark, regular-time sampling (RTS) method, usually implemented with very fast traditional analog-to-digital converters (ADCs) for digitizing scintillation pulses, is not feasible for a multi-channel system like a PET system Digitizing scintillation pulses with multi-voltage threshold (MVT) method could be implemented at a reasonable cost for a PET system With digitized PET event samples, various digital signal processing (DSP) techniques can be implemented to determine event arrival time Our results have therefore demonstrated the promising potentials of digitally sampling scintillation pulses techniques in PET imaging

Compressive sensor array system and method

Abstract: A compressive sensor array (CSA) system and method uses compressive sampling techniques to acquire sensor data from an array of sensors without independently sampling each of the sensor signals. In general, the CSA system and method uses the compressive sampling techniques to combine the analog sensor signals from the array of sensors into a composite sensor signal and to sample the composite sensor signal at a sub-Nyquist sampling rate. At least one embodiment of the CSA system and method allows a single analog-to-digital converter (ADC) and single RF demodulation chain to be used for an arbitrary number of sensors, thereby providing scalability and eliminating redundant data acquisition hardware. By reducing the number of samples, the CSA system and method also facilitates the processing, storage and transmission of the sensor data.

Objective filtering of ensemble‐based background‐error variances

Abstract: Flow-dependent background-error variances can be estimated by means of an ensemble of assimilations. However, the finite size of the ensemble implies a sampling noise, which is detrimental for the variance estimation. This article presents a filtering procedure for ensemble-estimated variance fields, which relies on an estimate of spectral signal/noise ratios. It is first demonstrated that the sampling noise covariance can be expressed analytically as a simple function of the background-error covariance. The resulting formula shows in particular that the spatial structure of the sampling noise is closely related to the spatial structure of background error (i.e. to its correlation function). It is then explained how this relation can be used to calculate an objective filter. Investigations are first conducted in a highly idealized 1D framework, to show that the proposed filter is able to remove most of the sampling noise, while extracting the signal of interest. Application to an ensemble of Meteo-France Arpege forecasts is then considered. This objective filter reveals a vertical-level dependence, with a larger signal/noise ratio near the surface, and a scale separation between signal and noise which is more pronounced in altitude. The results also indicate that, after applying such an optimized filter, variance estimates obtained from a six-member ensemble have a residual estimation error variance around 10%. Some insights are then given into the spatio-temporal dynamics of the variance field. It is observed that the globally averaged background-error variance is fairly stable in time, while spatial patterns of the variance field are closely linked to the meteorological situation, with high values found in the vicinity of troughs. Finally, impact studies in the Arpege system show that the filtering of vorticity variances has a positive impact on the quality of the NWP system. Copyright © 2009 Royal Meteorological Society

The Influence of Windowing on Bias and Variance of DFT-Based Frequency and Phase Estimation

Abstract: In sinusoidal parameter-estimation problems for measurement applications, discrete spectra with high dynamic range are often under investigation. To suppress unwanted interference effects (ldquoleakagerdquo) in the discrete Fourier transform (DFT) spectrum, the application of data windows is common practice. In this paper, the influence of windowing on the bias and variance of the frequency and phase estimates, calculated via the DFT, is investigated. Furthermore, the effect of choosing different sampling start times on both the bias and the variance is discussed.

Electro-optical device and electronic apparatus

Abstract: PROBLEM TO BE SOLVED: To provide an electro-optical device that has suppressed streak-like sequential display unevenness that occurs due to parasitic capacitance caused by a wiring structure of a data line, and an electronic apparatus including the electro-optical deviceSOLUTION: A liquid crystal device 100 as an electro-optical device includes image signal lines 111 to which image signals are supplied, data lines 6a, and sampling transistors (S-TFTs) 71 as first and second transistors that are electrically connected between the data lines 6a and image signal lines 111 and supply the image signals to the data lines 6a, where the S-TFTs 71 have at least two types different in the overlapping amount in which a gate electrode of the S-TFT 71 and the data line 6a overlap via an insulating film This configuration generates parasitic capacitance between the gate electrode and data line 6a, and the overlapping amount can be made different to adjust parasitic capacitance structurally included in each of the data lines 6a and suppress streak-like sequential display evennessSELECTED DRAWING: Figure 2

Current sensing for high voltage buck converter

Abstract: Methods, systems, and devices are described for providing output (e.g., current) sensing and feedback in high-voltage switching power converter topologies. Certain aspects of high voltage switching converter topologies may make output (e.g., current) sensing difficult. In some embodiments, a sampling module implements sample-and-hold techniques in a low-side switch converter topology to provide reliable current sensing. Embodiments of the sampling module provide certain functionality, including integration, blanking, buffering, and adjustable sampling frequency. Further, some embodiments include feedback functionality for generating a converter driver signal (for driving the switching converter) and/or a sample driver signal (for driving the sampling module) as a function of sensed output feedback from the sampling module.

Computationally efficent radar processing method and sytem for SAR and GMTI on a slow moving platform

Abstract: A method and system for processing radar data from a movable platform comprising passing a radar signal through a low noise amplifier; down converting the signal to a lower frequency; filtering out harmonics; sampling using A/D converter at or above Nyquist frequency; determining a scene center; performing a two stage averaging scheme of the received signals with a variable window function based upon the velocity, acceleration of the platform and scene center; coherently averaging N pulses to create an average pulse; performing an inverse Fourier transform; compensating to the scene center by multiplying by a complex exponential based upon GPS and inertial navigational system; summing the average pulses using a low pass filter; repeating the determination of an average pulse for a time period that is less than the Nyquist sample time interval to generate second average pulses; and performing a 2D inverse Fourier transform to obtain SAR image.

Soft clock delay for OCT system and method therefor

Abstract: An optical coherence analysis system comprises a swept source laser for generating optical signals that are tuned over a scan band; an interferometer for transmitting the optical signals over a sample arm and reference arm and combining the optical signals; a k-clock for generating a sampling clock indicating non-linearities in the frequency tuning of the optical signals over the scan band, the k-clock being not delay matched to propagation delays for the optical signals in the interferometer; a sampling system for sampling the optical signals from the interferometer in response to the k-clock to generate interference signals; and a processing system for determining non-linearities in the sampling clock and for transforming the interference signals into an image of a sample in response to the non-linearities. The system compensates for the lack of an electronic delay of k-clock using a nonuniform discrete Fourier transform.

Introduction To Digital Signal Processing: Computer Musically Speaking

Abstract: This book offers an introduction to digital signal processing (DSP) with an emphasis on audio signals and computer music. It covers the mathematical foundations of DSP, important DSP theories including sampling, LTI systems, the z-transform, FIR/IIR filters, classic sound synthesis algorithms, various digital effects, topics in time and frequency-domain analysis/synthesis, and associated musical/sound examples. Whenever possible, pictures and graphics are included when presenting DSP concepts of various abstractions. To further facilitate understanding of ideas, a plethora of MATLAB code examples are provided, allowing the reader tangible means to connect dots via mathematics, visuals, as well as aural feedback through synthesis and modulation of sound. This book is designed for both technically and musically inclined readers alike folks with a common goal of exploring digital signal processing. Contents: Acoustics, Hearing Limitations, and Sampling Time-Domain Signal Processing I Time-Domain Processes II Sine Waves Linear Time-Invariant Systems Frequency Response Filters Frequency-Domain and the Fourier Transform Spectral Analysis, Vocoders, and Other Goodies

Compressive image sampling with side information

Abstract: Compressive sampling is a novel framework that exploits sparsity of a signal in a transform domain to perform sampling below the Nyquist rate. In this paper, we apply compressive sampling to reduce the sampling rate of images/video. The key idea is to exploit the intra- and inter-frame correlation to improve signal recovery algorithms. The image is split into non-overlapping blocks of fixed size, which are independently compressively sampled exploiting sparsity of natural scenes in the Discrete Cosine Transform (DCT) domain. At the decoder, each block is recovered using useful information extracted from the recovery of a neighboring block. In the case of video, a previous frame is used to help recovery of consecutive frames. The iterative algorithm for signal recovery with side information that extends the standard orthogonal matching pursuit (OMP) algorithm is employed. Simulation results are given for Magnetic Resonance Imaging (MRI) and video sequences to illustrate advantages of the proposed solution compared to the case when side information is not used.

An Agile, Ultra-Wideband Pulse Radio Transceiver With Discrete-Time Wideband-IF

Abstract: A pulse-based CMOS ultra-wideband transmitter and receiver have been realized using a standard digital 90 nm CMOS process. The transceiver uses digital templates stored in high-speed memories for pulse generation on the transmit side and for correlation on the receive side. This allows fast band switching for multi-band operation and interferer avoidance without the requirement for fast-settling phase-locked loops. The receiver contains a 3.1-9.5 GHz broadband front-end and discrete-time intermediate frequency correlators that achieve a pulse rate of 100 Mpulses/s and has a die area of 1 mm2 while consuming 130 mA from a 1.2 V supply. The transmitter uses interleaved, intermediate frequency digital-to-analog converters followed by partial-order hold reconstruction filters that eliminate sampling images, and a quadrature RF up-converter. 1.25 nJ is spent per transmitted pulse for a pulse-repetition rate of 100 MHz while achieving a broadband image cancellation of 42 dB.