We show that stacking the columns of a Costas array one below the other yields a Golomb ruler, pr... more We show that stacking the columns of a Costas array one below the other yields a Golomb ruler, provided several blank rows have been appended at the bottom of the array first, and we prove rigorously an upper bound for the necessary number of rows. We then provide a method to determine the numbers of blank rows appended for which the construction succeeds, and we also determine by simulation the smallest such number over all Costas arrays of a given order. We argue that these Golomb rulers, though suboptimal, have applications in channels affected by multi-path interference and periodic bursts of noise, thanks to their special structure. We finally study briefly alternative unwrapping strategies.
Using only the audio signals from two real microphones and the distance separating them, we synth... more Using only the audio signals from two real microphones and the distance separating them, we synthesize the audio that would have been heard at any point along the line connecting the two microphones. The method is valid in anechoic environments. The interpolated audio can be calculated directly, with no need to estimate the number of sources present in the environment or to separate the sources from the received audio mixtures. However, additionally estimating the mixing parameters is shown to dramatically improve results for speech mixtures. Experimental results are presented, and sample sound files can be found on the authors' web site,
The Doppler effect, the apparent change in the frequency of a signal caused by contractions/dilat... more The Doppler effect, the apparent change in the frequency of a signal caused by contractions/dilations of time when transmitter and receiver have relative motion, can be derived using either Newtonian or relativistic mechanics. One may be led to believe that the Newtonian Doppler effect is applicable to sound waves, while the relativistic Doppler effect is applicable to electromagnetic waves, but this is, of course, not the case; there are not two Doppler effects. The relativistic model represents a more accurate description for both acoustic and electromagnetic waves, but for typical (non-relativistic) speeds in acoustic settings, the classic model is sufficient. In this paper, we derive from first principles both the Newtonian and the relativistic input-output relationships for transmitter and receiver moving directly towards or away from each other with constant speed. We compare the two models and show how the non-relativistic model can be seen as can be seen as approximation of the relativistic one, when velocities are small.
ThenewemergingtheoryofCompressiveSamplinghasdemon- strated that by exploiting the structure of a ... more ThenewemergingtheoryofCompressiveSamplinghasdemon- strated that by exploiting the structure of a signal, it is possible to sample a signal below the Nyquist rate and achieve perfect reconstruction. In this short note, we employ Non-negative Matrix Factori- sation in the context of Compressive Sampling and propose two NMF algorithms for signal recovery—one of which utilises It- eratively Reweighted Least Squares. The algorithms are ap- pliedtocompressivelysamplednon-negativedata, whereasparse non-negative basis and corresponding non-negative coefficients for the original uncompressed data are discovered directly in the compressively sampled domain.
The new emerging theory of Compressive Sampling has demonstrated that by exploiting the structure... more The new emerging theory of Compressive Sampling has demonstrated that by exploiting the structure of a signal, it is possible to sample a signal below the Nyquist rate and achieve perfect reconstruction. In this paper, we consider a special case of Compressive Sampling where the uncompressed signal is non-negative, and propose an extension of Non-negative Quadratic Programming—which utilises Iteratively Reweighted Least Squares—for the recovery of non-negative minimum 'p-norm solutions, 0 p 1. Furthermore, we investigate signal recovery performance where the sampling matrix has entries drawn from a Gaussian distribution with decreasing number of negative values, and demonstrate that—unlike standard Compressive Sampling— the standard Gaussian distribution is unsuitable for this special case.
We offer a pedagogical study of the Doppler effect as a channel, and derive a mathematical model ... more We offer a pedagogical study of the Doppler effect as a channel, and derive a mathematical model of the input-output relation in both classical and relativistic settings. We then show for the derived channel models the well known result that the classical model is the limit of the relativistic one at low speeds. We also derive the relativistic channel model in two independent ways and show they are compatible. We infer from these two observations that there is essentially only one Doppler effect in different disguises. Finally, we observe that the channel models we derive correctly demonstrate that, although the Doppler effect is a rescaling, it can be approximated by an additive frequency shift under the usual narrowband assumption in communications. We conclude with a brief survey of the myriad of applications that exploit the Doppler effect in both classical and relativistic form.
The DUET and DESPRIT blind source separation algorithms attempt to recover J sources from I mixtu... more The DUET and DESPRIT blind source separation algorithms attempt to recover J sources from I mixtures of these sources, in the interesting case where J > I, with minimal information about the mixing environment of underling sources statistics. We present a semi-blind generalization of the DUET-DESCRIPT approach which allows arbitary placement of the sensors and demixes the sources given the room impulse response. We learn a sparse representation of the mixtures on an over-complete spatial signatures dictionary. We localize and separate the constituent sources via binary masking of a power weighted histogram in location space or in attenuation-delay space. We demonstrate the robustness of this technique using synthetic room experiments.
Using only the audio signals from two real microphones and the distance separating them, we synth... more Using only the audio signals from two real microphones and the distance separating them, we synthesize the audio that would have been heard at any point along the line connecting the two microphones. The method is valid in anechoic environments. The interpolated audio can be calculated directly, with no need to estimate the number of sources present in the environment or to separate the sources from the received audio mixtures. However, additionally estimating the mixing parameters is shown to dramatically improve results for speech mixtures. Experimental results are presented, and sample sound files can be found on the authors' web site [1]. 1.
Conference on Information Sciences and Systems, 2000
In which representation is speech most sparse? Time-scale? Time-frequency? Which window generator... more In which representation is speech most sparse? Time-scale? Time-frequency? Which window generator and length should be used to create the sparsest decomposition? To answer these questions, we propose the Gini index, which is twice the area between the Lorenz curve and the 45 degree line, as a measure of signal sparsity. The Gini index, introduced in 1912, is one of
Costas arrays are permutation matrices with ideal auto-ambiguity properties; No two of the the N ... more Costas arrays are permutation matrices with ideal auto-ambiguity properties; No two of the the N choose 2 line segments between pairs of 1's in the matrix have the same slope and length. This paper presents a search technique based on the periodicity properties of the existing construction techniques which nds previously unknown Costas arrays for N = 29, N =
2008 IEEE Workshop on Machine Learning for Signal Processing, 2008
Traditional Nyquist-Shannon sampling dictates that a continuous time signal be sampled at twice i... more Traditional Nyquist-Shannon sampling dictates that a continuous time signal be sampled at twice its bandwidth to achieve perfect recovery. However, It has been recently demonstrated that by exploiting the structure of the signal, it is possible to sample a signal below the Nyquist rate and achieve perfect reconstruction using a random projection, sparse representation and an 1 -norm minimisation. These methods constitute a new and emerging theory known as Compressive Sampling (or Compressed sensing).
Proceedings of Conference on Intelligent Transportation Systems, 1997
The ability to perform automatic vehicle location (AVL) is a requirement for a variety of applica... more The ability to perform automatic vehicle location (AVL) is a requirement for a variety of applications in intelligent transportation systems like vehicle guidance, dynamic route optimization, scheduling, bus stop annunciation, security, fleet tracking, etc. We describe a new approach to AVL where data from a simple low-bandwidth sensor producing 1-dimensional visual data is matched against a stored database to determine position, in combination with standard dead-reckoning. Our system is completely self-contained in that it requires no infrastructure external to the vehicle such as beacons or satellites
2008 42nd Annual Conference on Information Sciences and Systems, 2008
Costas array enumeration is an NP-complete problem with a highly parallelize-able solution. This ... more Costas array enumeration is an NP-complete problem with a highly parallelize-able solution. This paper examines the implementation of a solution to this problem on an FPGA platform and examines the elements of what makes the most efficient solution to this problem. This paper compares the performance of the hardware solution against the performance of the best known software solution and finds an approximate 40 times speedup from using hardware.
Using only the audio signals from two real microphones and the distance separating them, we synth... more Using only the audio signals from two real microphones and the distance separating them, we synthesize the audio that would have been heard at any point along the line connecting the two micro- phones. The method is valid in anechoic environments. The inter- polated audio can be calculated directly, with no need to estimate the number of sources present in the environment or to separate the sources from the received audio mixtures. However, addition- ally estimating the mixing parameters is shown to dramatically improve results for speech mixtures. Experimental results are pre- sented, and sample sound files can be found on the authors' web site (1). In this paper, our goal is to understand when there is enough infor- mation contained in the audio signals received at two microphones to produce the audio that would have actually been heard had a third microphone been present in the environment. We show that for anechoic environments, when the virtual microphone is located along ...
Sparse representations are being used to solve problems pre- viously thought insolvable. For exam... more Sparse representations are being used to solve problems pre- viously thought insolvable. For example, we can separate more sources than sensors using an appropriate transforma- tion of the mixtures into a domain where the sources are sparse. But what do we mean by sparse? What attributes should a sparse measure have? And how can we use this sparsity to separate sources? We investigate these questions and, as a result, conclude that sparse sources are separated sources, as long as you use the correct measure.
Page 1. NMF of Compressively Sampled Non-Negative Signals Paul O'Grady & Scott Rickard .... more Page 1. NMF of Compressively Sampled Non-Negative Signals Paul O'Grady & Scott Rickard ... Compressive Sampling Paul O'Grady & Scott Rickard Sparse Signal Processing Group, Complex & Adaptive Systems Laboratory, University College Dublin, Ireland. ...
The new emerging theory of Compressive Sampling has demonstrated that by exploiting the structure... more The new emerging theory of Compressive Sampling has demonstrated that by exploiting the structure of a signal, it is possible to sample a signal below the Nyquist rate and achieve perfect reconstruction.
The new emerging theory of Compressive Sampling has demonstrated that by exploiting the structure... more The new emerging theory of Compressive Sampling has demonstrated that by exploiting the structure of a signal, it is possible to sample a signal below the Nyquist rate and achieve perfect reconstruction.
It is hard to avoid ASCII Art in today's digital world, from the ubiquitous emoticons-;)-to the e... more It is hard to avoid ASCII Art in today's digital world, from the ubiquitous emoticons-;)-to the esoteric artistic creations that reside in many people's e-mail signatures, everybody has come across ASCII art at some stage. The origins of ASCII art can be traced back to the days when computers had a high price, slow operating speeds and limited graphics capabilities, which forced computer programmers and enthusiasts to develop some innovative ways to render images using the limited graphics blocks available, viz., text characters. Here, we treat automatic ASCII art conversion of binary images as an optimisation problem, and present an application of our work on Non-Negative Matrix Factorisation to this task-where a basis constructed from monospace font glyphs is fitted to a binary image using a winner-takes-all assignment.
We show that stacking the columns of a Costas array one below the other yields a Golomb ruler, pr... more We show that stacking the columns of a Costas array one below the other yields a Golomb ruler, provided several blank rows have been appended at the bottom of the array first, and we prove rigorously an upper bound for the necessary number of rows. We then provide a method to determine the numbers of blank rows appended for which the construction succeeds, and we also determine by simulation the smallest such number over all Costas arrays of a given order. We argue that these Golomb rulers, though suboptimal, have applications in channels affected by multi-path interference and periodic bursts of noise, thanks to their special structure. We finally study briefly alternative unwrapping strategies.
Using only the audio signals from two real microphones and the distance separating them, we synth... more Using only the audio signals from two real microphones and the distance separating them, we synthesize the audio that would have been heard at any point along the line connecting the two microphones. The method is valid in anechoic environments. The interpolated audio can be calculated directly, with no need to estimate the number of sources present in the environment or to separate the sources from the received audio mixtures. However, additionally estimating the mixing parameters is shown to dramatically improve results for speech mixtures. Experimental results are presented, and sample sound files can be found on the authors' web site,
The Doppler effect, the apparent change in the frequency of a signal caused by contractions/dilat... more The Doppler effect, the apparent change in the frequency of a signal caused by contractions/dilations of time when transmitter and receiver have relative motion, can be derived using either Newtonian or relativistic mechanics. One may be led to believe that the Newtonian Doppler effect is applicable to sound waves, while the relativistic Doppler effect is applicable to electromagnetic waves, but this is, of course, not the case; there are not two Doppler effects. The relativistic model represents a more accurate description for both acoustic and electromagnetic waves, but for typical (non-relativistic) speeds in acoustic settings, the classic model is sufficient. In this paper, we derive from first principles both the Newtonian and the relativistic input-output relationships for transmitter and receiver moving directly towards or away from each other with constant speed. We compare the two models and show how the non-relativistic model can be seen as can be seen as approximation of the relativistic one, when velocities are small.
ThenewemergingtheoryofCompressiveSamplinghasdemon- strated that by exploiting the structure of a ... more ThenewemergingtheoryofCompressiveSamplinghasdemon- strated that by exploiting the structure of a signal, it is possible to sample a signal below the Nyquist rate and achieve perfect reconstruction. In this short note, we employ Non-negative Matrix Factori- sation in the context of Compressive Sampling and propose two NMF algorithms for signal recovery—one of which utilises It- eratively Reweighted Least Squares. The algorithms are ap- pliedtocompressivelysamplednon-negativedata, whereasparse non-negative basis and corresponding non-negative coefficients for the original uncompressed data are discovered directly in the compressively sampled domain.
The new emerging theory of Compressive Sampling has demonstrated that by exploiting the structure... more The new emerging theory of Compressive Sampling has demonstrated that by exploiting the structure of a signal, it is possible to sample a signal below the Nyquist rate and achieve perfect reconstruction. In this paper, we consider a special case of Compressive Sampling where the uncompressed signal is non-negative, and propose an extension of Non-negative Quadratic Programming—which utilises Iteratively Reweighted Least Squares—for the recovery of non-negative minimum 'p-norm solutions, 0 p 1. Furthermore, we investigate signal recovery performance where the sampling matrix has entries drawn from a Gaussian distribution with decreasing number of negative values, and demonstrate that—unlike standard Compressive Sampling— the standard Gaussian distribution is unsuitable for this special case.
We offer a pedagogical study of the Doppler effect as a channel, and derive a mathematical model ... more We offer a pedagogical study of the Doppler effect as a channel, and derive a mathematical model of the input-output relation in both classical and relativistic settings. We then show for the derived channel models the well known result that the classical model is the limit of the relativistic one at low speeds. We also derive the relativistic channel model in two independent ways and show they are compatible. We infer from these two observations that there is essentially only one Doppler effect in different disguises. Finally, we observe that the channel models we derive correctly demonstrate that, although the Doppler effect is a rescaling, it can be approximated by an additive frequency shift under the usual narrowband assumption in communications. We conclude with a brief survey of the myriad of applications that exploit the Doppler effect in both classical and relativistic form.
The DUET and DESPRIT blind source separation algorithms attempt to recover J sources from I mixtu... more The DUET and DESPRIT blind source separation algorithms attempt to recover J sources from I mixtures of these sources, in the interesting case where J > I, with minimal information about the mixing environment of underling sources statistics. We present a semi-blind generalization of the DUET-DESCRIPT approach which allows arbitary placement of the sensors and demixes the sources given the room impulse response. We learn a sparse representation of the mixtures on an over-complete spatial signatures dictionary. We localize and separate the constituent sources via binary masking of a power weighted histogram in location space or in attenuation-delay space. We demonstrate the robustness of this technique using synthetic room experiments.
Using only the audio signals from two real microphones and the distance separating them, we synth... more Using only the audio signals from two real microphones and the distance separating them, we synthesize the audio that would have been heard at any point along the line connecting the two microphones. The method is valid in anechoic environments. The interpolated audio can be calculated directly, with no need to estimate the number of sources present in the environment or to separate the sources from the received audio mixtures. However, additionally estimating the mixing parameters is shown to dramatically improve results for speech mixtures. Experimental results are presented, and sample sound files can be found on the authors' web site [1]. 1.
Conference on Information Sciences and Systems, 2000
In which representation is speech most sparse? Time-scale? Time-frequency? Which window generator... more In which representation is speech most sparse? Time-scale? Time-frequency? Which window generator and length should be used to create the sparsest decomposition? To answer these questions, we propose the Gini index, which is twice the area between the Lorenz curve and the 45 degree line, as a measure of signal sparsity. The Gini index, introduced in 1912, is one of
Costas arrays are permutation matrices with ideal auto-ambiguity properties; No two of the the N ... more Costas arrays are permutation matrices with ideal auto-ambiguity properties; No two of the the N choose 2 line segments between pairs of 1's in the matrix have the same slope and length. This paper presents a search technique based on the periodicity properties of the existing construction techniques which nds previously unknown Costas arrays for N = 29, N =
2008 IEEE Workshop on Machine Learning for Signal Processing, 2008
Traditional Nyquist-Shannon sampling dictates that a continuous time signal be sampled at twice i... more Traditional Nyquist-Shannon sampling dictates that a continuous time signal be sampled at twice its bandwidth to achieve perfect recovery. However, It has been recently demonstrated that by exploiting the structure of the signal, it is possible to sample a signal below the Nyquist rate and achieve perfect reconstruction using a random projection, sparse representation and an 1 -norm minimisation. These methods constitute a new and emerging theory known as Compressive Sampling (or Compressed sensing).
Proceedings of Conference on Intelligent Transportation Systems, 1997
The ability to perform automatic vehicle location (AVL) is a requirement for a variety of applica... more The ability to perform automatic vehicle location (AVL) is a requirement for a variety of applications in intelligent transportation systems like vehicle guidance, dynamic route optimization, scheduling, bus stop annunciation, security, fleet tracking, etc. We describe a new approach to AVL where data from a simple low-bandwidth sensor producing 1-dimensional visual data is matched against a stored database to determine position, in combination with standard dead-reckoning. Our system is completely self-contained in that it requires no infrastructure external to the vehicle such as beacons or satellites
2008 42nd Annual Conference on Information Sciences and Systems, 2008
Costas array enumeration is an NP-complete problem with a highly parallelize-able solution. This ... more Costas array enumeration is an NP-complete problem with a highly parallelize-able solution. This paper examines the implementation of a solution to this problem on an FPGA platform and examines the elements of what makes the most efficient solution to this problem. This paper compares the performance of the hardware solution against the performance of the best known software solution and finds an approximate 40 times speedup from using hardware.
Using only the audio signals from two real microphones and the distance separating them, we synth... more Using only the audio signals from two real microphones and the distance separating them, we synthesize the audio that would have been heard at any point along the line connecting the two micro- phones. The method is valid in anechoic environments. The inter- polated audio can be calculated directly, with no need to estimate the number of sources present in the environment or to separate the sources from the received audio mixtures. However, addition- ally estimating the mixing parameters is shown to dramatically improve results for speech mixtures. Experimental results are pre- sented, and sample sound files can be found on the authors' web site (1). In this paper, our goal is to understand when there is enough infor- mation contained in the audio signals received at two microphones to produce the audio that would have actually been heard had a third microphone been present in the environment. We show that for anechoic environments, when the virtual microphone is located along ...
Sparse representations are being used to solve problems pre- viously thought insolvable. For exam... more Sparse representations are being used to solve problems pre- viously thought insolvable. For example, we can separate more sources than sensors using an appropriate transforma- tion of the mixtures into a domain where the sources are sparse. But what do we mean by sparse? What attributes should a sparse measure have? And how can we use this sparsity to separate sources? We investigate these questions and, as a result, conclude that sparse sources are separated sources, as long as you use the correct measure.
Page 1. NMF of Compressively Sampled Non-Negative Signals Paul O'Grady & Scott Rickard .... more Page 1. NMF of Compressively Sampled Non-Negative Signals Paul O'Grady & Scott Rickard ... Compressive Sampling Paul O'Grady & Scott Rickard Sparse Signal Processing Group, Complex & Adaptive Systems Laboratory, University College Dublin, Ireland. ...
The new emerging theory of Compressive Sampling has demonstrated that by exploiting the structure... more The new emerging theory of Compressive Sampling has demonstrated that by exploiting the structure of a signal, it is possible to sample a signal below the Nyquist rate and achieve perfect reconstruction.
The new emerging theory of Compressive Sampling has demonstrated that by exploiting the structure... more The new emerging theory of Compressive Sampling has demonstrated that by exploiting the structure of a signal, it is possible to sample a signal below the Nyquist rate and achieve perfect reconstruction.
It is hard to avoid ASCII Art in today's digital world, from the ubiquitous emoticons-;)-to the e... more It is hard to avoid ASCII Art in today's digital world, from the ubiquitous emoticons-;)-to the esoteric artistic creations that reside in many people's e-mail signatures, everybody has come across ASCII art at some stage. The origins of ASCII art can be traced back to the days when computers had a high price, slow operating speeds and limited graphics capabilities, which forced computer programmers and enthusiasts to develop some innovative ways to render images using the limited graphics blocks available, viz., text characters. Here, we treat automatic ASCII art conversion of binary images as an optimisation problem, and present an application of our work on Non-Negative Matrix Factorisation to this task-where a basis constructed from monospace font glyphs is fitted to a binary image using a winner-takes-all assignment.
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Papers by Scott Rickard