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111
From theory to practice: SubNyquist sampling of sparse wideband analog signals
 IEEE J. SEL. TOPICS SIGNAL PROCESS
, 2010
"... Conventional subNyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind subNyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum. ..."
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Cited by 142 (55 self)
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Conventional subNyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind subNyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum. Our primary design goals are efficient hardware implementation and low computational load on the supporting digital processing. We propose a system, named the modulated wideband converter, which first multiplies the analog signal by a bank of periodic waveforms. The product is then lowpass filtered and sampled uniformly at a low rate, which is orders of magnitude smaller than Nyquist. Perfect recovery from the proposed samples is achieved under certain necessary and sufficient conditions. We also develop a digital architecture, which allows either reconstruction of the analog input, or processing of any band of interest at a low rate, that is, without interpolating to the high Nyquist rate. Numerical simulations demonstrate many engineering aspects: robustness to noise and mismodeling, potential hardware simplifications, realtime performance for signals with timevarying support and stability to quantization effects. We compare our system with two previous approaches: periodic nonuniform sampling, which is bandwidth limited by existing hardware devices, and the random demodulator, which is restricted to discrete multitone signals and has a high computational load. In the broader context of Nyquist sampling, our scheme has the potential to break through the bandwidth barrier of stateoftheart analog conversion technologies such as interleaved converters.
Explicit analysis of channel mismatch effects in timeinterleaved ADC systems
 IEEE Transactions on Circuits and Systems I
, 2001
"... Abstract—A timeinterleaved A–D converter (ADC) system is an effective way to implement a highsamplingrate ADC with relatively slow circuits. In the system, several channel ADCs operate at interleaved sampling times as if they were effectively a single ADC operating at a much higher sampling rate. ..."
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Cited by 44 (0 self)
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Abstract—A timeinterleaved A–D converter (ADC) system is an effective way to implement a highsamplingrate ADC with relatively slow circuits. In the system, several channel ADCs operate at interleaved sampling times as if they were effectively a single ADC operating at a much higher sampling rate. However, mismatches such as offset, gain mismatches among channel ADCs as well as timing skew of the clocks distributed to them degrade S/N of the ADC system as a whole. This paper analyzes the channel mismatch effects in the timeinterleaved ADC system. Previous analysis showed the effect for each mismatch individually,however in this paper we derive explicit formulas for the mismatch effects when all of offset, gain and timing mismatches exist together. We have clarified that the gain and timing mismatch effects interact with each other but the offset mismatch effect is independent from them, and this can be seen clearly in frequency domain. We also discuss the bandwidth mismatch effect. The derived formulas can be used for calibration algorithms to compensate for the channel mismatch effects. Index Terms—A–D converter, analog circuit, calibration, channel mismatch, interleave, track/hold circuit. I.
Reconstruction of nonuniformly sampled bandlimited signals by means of digital fractional delay filters
 IEEE Trans. Signal Processing
, 2002
"... Abstract – This paper deals with reconstruction of nonuniformly sampled bandlimited continuoustime signals using timevarying discretetime FIR filters. The points of departures are that the signal is slightly oversampled as to the average sampling frequency and that the sampling instances are know ..."
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Cited by 44 (8 self)
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Abstract – This paper deals with reconstruction of nonuniformly sampled bandlimited continuoustime signals using timevarying discretetime FIR filters. The points of departures are that the signal is slightly oversampled as to the average sampling frequency and that the sampling instances are known. Under these assumptions, a representation of the reconstructed sequence is derived that utilizes a timefrequency function. This representation enables a proper utilization of the oversampling and reduces the reconstruction problem to a design problem that resembles an ordinary filter design problem. Furthermore, for an important special case, corresponding to a certain type of periodic nonuniform sampling, it is shown that the reconstruction problem can be posed as a filterbank design problem, thus with requirements on a distortion transfer function and a number of aliasing transfer functions. 1.
The impact of combined channel mismatch effects in timeinterleaved ADCs
 IEEE Transactions on Instrumentation and Measurement
, 2005
"... converter (ADC) achieves high sampling rates with the drawback of additional distortions caused by channel mismatches. In this paper, we consider the dependency of the signaltonoiseanddistortion ratio (SINAD) on the combination of several different channel mismatch effects. By using either expli ..."
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Cited by 28 (15 self)
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converter (ADC) achieves high sampling rates with the drawback of additional distortions caused by channel mismatches. In this paper, we consider the dependency of the signaltonoiseanddistortion ratio (SINAD) on the combination of several different channel mismatch effects. By using either explicitly given mismatch parameters or given parameter distributions, we derive closedform equations for calculating the explicit or the expected SINAD for an arbitrary number of channels. Furthermore, we extend the explicit SINAD by the impact of timing jitter. We clarify how channel mismatches interact and perform a worst case analysis of the explicit SINAD for individual mismatch errors. We also show that equations describing the expected SINAD of individual mismatch errors are special cases of our general formulation. We indicate how to use the expected SINAD for finding efficient optimization priorities and demonstrate the importance of worst case analyses. Index Terms—Analogtodigital converter (ADC), channel mismatch, error analysis, signaltonoiseanddistortion ratio (SINAD), timeinterleaving, timing jitter.
Calibration of sampletime error in a twochannel timeinterleaved analogtodigital converter
 IEEE TRANS. CIRCUITS SYST. I
, 2004
"... Offset mismatch, gain mismatch, and sampletime error between timeinterleaved channels limit the performance of timeinterleaved analogtodigital converters (ADCs). This paper focuses on the sampletime error. Techniques for correcting and detecting sampletime error in a twochannel ADC are desc ..."
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Cited by 26 (0 self)
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Offset mismatch, gain mismatch, and sampletime error between timeinterleaved channels limit the performance of timeinterleaved analogtodigital converters (ADCs). This paper focuses on the sampletime error. Techniques for correcting and detecting sampletime error in a twochannel ADC are described, and simulation results are presented.
Blind Adaptive Equalization of Mismatch Errors in Time Interleaved A/D Converter System
, 2003
"... To significantly increase the sampling rate of an A/D converter (ADC), a time interleaved ADC system is a good option. The drawback of a time interleaved ADC system is that the ADCs are not exactly identical due to errors in the manufacturing process. This means that time, gain and o#set mismatc ..."
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Cited by 25 (2 self)
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To significantly increase the sampling rate of an A/D converter (ADC), a time interleaved ADC system is a good option. The drawback of a time interleaved ADC system is that the ADCs are not exactly identical due to errors in the manufacturing process. This means that time, gain and o#set mismatch errors are introduced in the ADC system. These errors cause distortion in the sampled signal.
An 8Bit 150MHz CMOS A/D Converter
, 1999
"... OF THE DISSERTATION An 8Bit 150MHz CMOS A/D Converter by YunTi Wang Doctor of Philosophy in Electrical Engineering University of California, Los Angeles, 1999 Professor Behzad Razavi, Chair Highspeed analogtodigital converters (ADCs) with resolutions of 8 bits find wide application in instrume ..."
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Cited by 20 (3 self)
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OF THE DISSERTATION An 8Bit 150MHz CMOS A/D Converter by YunTi Wang Doctor of Philosophy in Electrical Engineering University of California, Los Angeles, 1999 Professor Behzad Razavi, Chair Highspeed analogtodigital converters (ADCs) with resolutions of 8 bits find wide application in instrumentation and communication systems. For example, portable digital oscilloscopes use 8bit ADCs with sampling rates above one hundred megahertz. Also, the Gigabit Ethernet standard with CAT5 copper cable requires four 125MHz ADCs having a resolution of 7 to 8 bits to perform the frontend analogtodigital data conversion. This dissertation presents an 8bit, 5stage interleaved and pipelined ADC that performs analog processing only by means of openloop circuits such as differential pairs and source followers, thereby achieving a high conversion rate. The concept of "sliding interpolation" is proposed to obviate the need for a large number of comparators or interstage digitaltoanalog conve...
SubNyquist Sampling  Bridging theory and practice
, 2011
"... Signal processing methods have changed substantially over the last several decades. In modern applications, an increasing number of functions is being pushed forward to sophisticated software algorithms, leaving only delicate finely tuned tasks for the circuit level. Sampling theory, the gate to th ..."
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Cited by 14 (5 self)
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Signal processing methods have changed substantially over the last several decades. In modern applications, an increasing number of functions is being pushed forward to sophisticated software algorithms, leaving only delicate finely tuned tasks for the circuit level. Sampling theory, the gate to the digital world, is the key enabling this revolution, encompassing all aspects related to the conversion of continuoustime signals to discrete streams of numbers. The famous ShannonNyquist theorem has become a landmark: a mathematical statement that has had one of the most profound impacts on industrial development of digital signal processing (DSP) systems. Over the years, theory and practice in the field of sampling have developed in parallel routes. Contributions by many research groups suggest a multitude of methods, other than uniform sampling, to acquire analog signals [1]–[6]. The math has deepened, leading to abstract signal spaces and innovative sampling techniques. Within generalized sampling theory, bandlimited signals have no special preference, other than historic. At the same time, the market adhered to the Nyquist paradigm;
Reconstruction of nonuniformly sampled bandlimited signals using a differentiatormultiplier cascade
 IEEE Trans. Circuits Syst. I, Reg. Papers
, 2008
"... Abstract—This paper considers the problem of reconstructing a bandlimited signal from its nonuniform samples. Based on a discretetime equivalent model for nonuniform sampling, we propose the differentiator–multiplier cascade, a multistage reconstruction system that recovers the uniform samples from ..."
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Cited by 13 (9 self)
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Abstract—This paper considers the problem of reconstructing a bandlimited signal from its nonuniform samples. Based on a discretetime equivalent model for nonuniform sampling, we propose the differentiator–multiplier cascade, a multistage reconstruction system that recovers the uniform samples from the nonuniform samples. Rather than using optimally designed reconstruction filters, the system improves the reconstruction performance by cascading stages of linearphase finite impulse response (FIR) filters and timevarying multipliers. Because the FIR filters are designed as differentiators, the system works for the general nonuniform sampling case and is not limited to periodic nonuniform sampling. To evaluate the reconstruction performance for a sinusoidal input signal, we derive the signaltonoiseratio at the output of each stage for the twoperiodic and the general nonuniform sampling case. The main advantage of the system is that once the differentiators have been designed, they are implemented with fixed multipliers, and only some general multipliers have to be adapted when the sampling pattern changes; this reduces implementation costs substantially, especially in an application like timeinterleaved analogtodigital converters (TIADCs) where the timing mismatches among the ADCs may change during operation. Index Terms—Discretetime differentiator, Farrow structure, nonuniform sampling, Taylor series expansion, timeinterleaved analogtodigital converter (TIADC), timevarying multiplier. I.
Bandwidth mismatch and its correction in timeinterleaved analogtodigital converters
 IEEE Trans. Circuits Syst. II
, 2006
"... 3/27/2006>REPLACE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLECLICK HERE TO EDIT)< Abstract—The sampleandhold amplifier (SHA) in each channel of a timeinterleaved analogtodigital converter system has finite bandwidth, and these bandwidths may be mismatched. This paper analyzes the effec ..."
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Cited by 12 (0 self)
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3/27/2006>REPLACE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLECLICK HERE TO EDIT)< Abstract—The sampleandhold amplifier (SHA) in each channel of a timeinterleaved analogtodigital converter system has finite bandwidth, and these bandwidths may be mismatched. This paper analyzes the effect of such mismatches. Correction for bandwidth mismatch in the digital domain is described and demonstrated. Index Terms—Analogdigital conversion, FIR digital filters, Sample and hold circuit, Bandwidth mismatch.