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Blind Multiband Signal Reconstruction: Compressed Sensing for Analog Signals
"... We address the problem of reconstructing a multiband signal from its subNyquist pointwise samples, when the band locations are unknown. Our approach assumes an existing multicoset sampling. Prior recovery methods for this sampling strategy either require knowledge of band locations or impose stric ..."
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Cited by 98 (62 self)
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We address the problem of reconstructing a multiband signal from its subNyquist pointwise samples, when the band locations are unknown. Our approach assumes an existing multicoset sampling. Prior recovery methods for this sampling strategy either require knowledge of band locations or impose strict limitations on the possible spectral supports. In this paper, only the number of bands and their widths are assumed without any other limitations on the support. We describe how to choose the parameters of the multicoset sampling so that a unique multiband signal matches the given samples. To recover the signal, the continuous reconstruction is replaced by a single finitedimensional problem without the need for discretization. The resulting problem is studied within the framework of compressed sensing, and thus can be solved efficiently using known tractable algorithms from this emerging area. We also develop a theoretical lower bound on the average sampling rate required for blind signal reconstruction, which is twice the minimal rate of knownspectrum recovery. Our method ensures perfect reconstruction for a wide class of signals sampled at the minimal rate. Numerical experiments are presented demonstrating blind sampling and reconstruction with minimal sampling rate.
The pros and cons of compressive sensing for wideband signal acquisition: Noise folding vs. dynamic range
, 2011
"... Compressive sensing (CS) exploits the sparsity present in many common signals to reduce the number of measurements needed for digital acquisition. With this reduction would come, in theory, commensurate reductions in the size, weight, power consumption, and/or monetary cost of both signal sensors an ..."
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Cited by 24 (5 self)
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Compressive sensing (CS) exploits the sparsity present in many common signals to reduce the number of measurements needed for digital acquisition. With this reduction would come, in theory, commensurate reductions in the size, weight, power consumption, and/or monetary cost of both signal sensors and any associated communication links. This paper examines the use of CS in the design of a wideband radio receiver in a noisy environment. We formulate the problem statement for such a receiver and establish a reasonable set of requirements that a receiver should meet to be practically useful. We then evaluate the performance of a CSbased receiver in two ways: via a theoretical analysis of the expected performance, with a particular emphasis on noise and dynamic range, and via simulations that compare the CS receiver against the performance expected from a conventional implementation. On the one hand, we show that CSbased systems that aim to reduce the number of acquired measurements are somewhat sensitive to signal noise, exhibiting a 3dB SNR loss per octave of subsampling which parallels the classic noisefolding phenomenon. On the other hand, we demonstrate that since they sample at a lower rate, CSbased systems can potentially attain a significantly larger dynamic range. Hence, we conclude that while a CSbased system has inherent limitations that do impose some restrictions on its potential applications, it also has attributes that make it highly desirable in a number of important practical settings. 1
BlockBased Compressed Sensing of Images and Video
 Foundations and Trends in Signal Processing
, 2012
"... A number of techniques for the compressed sensing of imagery are surveyed. Various imaging media are considered, including still images, motion video, as well as multiview image sets and multiview video. A particular emphasis is placed on blockbased compressed sensing due to its advantages in terms ..."
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Cited by 16 (4 self)
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A number of techniques for the compressed sensing of imagery are surveyed. Various imaging media are considered, including still images, motion video, as well as multiview image sets and multiview video. A particular emphasis is placed on blockbased compressed sensing due to its advantages in terms of both lightweight reconstruction complexity as well as a reduced memory burden for the randomprojection measurement operator. For multipleimage scenarios, including video and multiview imagery, motion and disparity compensation is employed to exploit frametoframe redundancies due to object motion and parallax, resulting in residual frames which are more compressible and thus more easily reconstructed from compressedsensing measurements. ExFoundations and Trends R ○ in Signal Processing, to appear, 2012. tensive experimental comparisons evaluate various prominent reconstruction algorithms for stillimage, motionvideo, and multiview scenarios in terms of both reconstruction quality as well as computational
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;
60 GHz radio: prospects and future directions
"... Abstract─This paper addresses the basic issues regarding the design and development of wireless systems that will operate in the 60 GHz band. The 60 GHz band is of much interest since this is the band in which a massive amount of spectral space (5 to 7 GHz) has been allocated for dense wireless loca ..."
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Cited by 9 (1 self)
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Abstract─This paper addresses the basic issues regarding the design and development of wireless systems that will operate in the 60 GHz band. The 60 GHz band is of much interest since this is the band in which a massive amount of spectral space (5 to 7 GHz) has been allocated for dense wireless local communications.
Random observations on random observations: Sparse signal acquisition and processing
 RICE UNIVERSITY
, 2010
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A subsampling UWB radio architecture by analytic signalling
 Proc. ICASSP
, 2004
"... This paper describes a signal processing technique which allows a reduction in the complexity of a transceiver for a 3.110.6 GHz UltraWideband radio. The proposed system transmits passband pulses using a pulser and antenna, and the receiver frontend downconverts the signal frequency by subsamplin ..."
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Cited by 8 (2 self)
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This paper describes a signal processing technique which allows a reduction in the complexity of a transceiver for a 3.110.6 GHz UltraWideband radio. The proposed system transmits passband pulses using a pulser and antenna, and the receiver frontend downconverts the signal frequency by subsampling, thus, requiring substantially less hardware than a traditional narrowband approach. By exploring the properties of analytic signals, the system allows hardware reduction and a time resolution finer than the sampling period, which is useful for locationing or ranging applications. 1.
1 Wideband, bandpass and versatile Hybrid Filter Bank A/D conversion for software radio
, 2009
"... Abstract—This paper deals with analogtodigital (A/D) conversion for future software/cognitive radio systems. For these applications, A/D converters should convert wideband signals and offer high resolutions. In order to achieve this and to overcome technological limitations, the A/D conversion sys ..."
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Cited by 5 (1 self)
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Abstract—This paper deals with analogtodigital (A/D) conversion for future software/cognitive radio systems. For these applications, A/D converters should convert wideband signals and offer high resolutions. In order to achieve this and to overcome technological limitations, the A/D conversion systems should be versatile, i.e. it should be possible to adapt the conversion characteristics (resolution and bandwidth) by software. This work studies and adapts Hybrid Filter Banks (HFBs) in this context. First, HFBs, which can provide large conversion bandwidth, are extended to bandpass sampling, thus minimizing the sampling frequency. Then, we provide efficient ways of improving the HFB resolution in a smaller frequency band, only by reprogramming the digital part. Moreover, this study takes into account the main drawback of HFBs which is their very high sensitivity to analog imperfections. Simulation results are presented to demonstrate the performance of HFBs. Index Terms—Analogtodigital conversion, hybrid filter
Exact Interpolation and Iterative Subdivision Schemes
 IEEE Trans. Signal Processing
, 1995
"... In this paper we examine the circumstances under which a discretetime signal can be exactly interpolated given only every Mth sample. After pointing out the connection between designing an M fold interpolator and the construction of an M channel perfect reconstruction filter bank, we derive nece ..."
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Cited by 4 (1 self)
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In this paper we examine the circumstances under which a discretetime signal can be exactly interpolated given only every Mth sample. After pointing out the connection between designing an M fold interpolator and the construction of an M channel perfect reconstruction filter bank, we derive necessary and sufficient conditions on the signal under which exact interpolation is possible. Bandlimited signals are one obvious example, but numerous others exist. We examine these and show how the interpolators may be constructed. A main application is to iterative interpolation schemes, used for the efficient generation of smooth curves. We show that conventional bandlimited interpolators are not suitable in this context. We illustrate that a better criterion is to use interpolators that are exact for polynomial functions. Further, we demonstrate that these interpolators converge when iterated. We show how these may be designed for any polynomial degree N and any interpolation factor M . Th...
Direct Downconversion of Multiband RF Signals Using Bandpass Sampling
"... Abstract — Bandpass sampling can be used by radio receivers to directly digitize the radio frequency (RF) signals. Although the bandpass sampling theory for singleband RF signals is well established, its counterpart for multiband RF signals is relatively immature. In this paper, we propose a novel ..."
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Cited by 3 (0 self)
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Abstract — Bandpass sampling can be used by radio receivers to directly digitize the radio frequency (RF) signals. Although the bandpass sampling theory for singleband RF signals is well established, its counterpart for multiband RF signals is relatively immature. In this paper, we propose a novel and efficient method to find the ranges of valid bandpass sampling frequency for direct downconverting multiband RF signals. Simple formulas for the ranges of valid bandpass sampling frequency in terms of the frequency locations of the multiple RF bands are derived. The result can be used to design a multiband receiver for software defined radios. Index Terms — Software defined radio, bandpass sampling, sampling methods, analogdigital conversion, signal sampling. I.