The proposed optimal algorithm for the digitizing of analog filters is based on two existing filter design methods: the extended window design (EWD) and the matched–pole (MP) frequency sampling design. The latter is closely related to the filter design with iterative weighted least squares (WLS). The optimization is performed with an original MP design that yields an equiripple digitizing error. Then, a drastic reduction of the digitizing error is achieved through the introduction of a fractional time shift that minimizes the magnitude of the equiripple error within a given frequency interval. The optimal parameters thus obtained can be used to generate the EWD equations, together with a variable fractional delay output, as described in an earlier paper. Finally, in contrast to the WLS procedure, which relies on a “good guess” of the weighting function, the MP optimization is straightforward.
Sequential Monte Carlo particle ﬁlters (PFs) are useful for estimating nonlinear non-Gaussian dynamic system parameters. As these algorithms are recursive, their real-time implementation can be computationally complex. In this paper, we analyze the bottlenecks in existing parallel PF algorithms, and we propose a new approach that integrates parallel PFs with independent Metropolis-Hastings (PPF-IMH) algorithms to improve root mean-squared estimation error performance. We implement the new PPF-IMH algorithm on a Xilinx Virtex-5 ﬁeld programmable gate array (FPGA) platform. For a onedimensional problem and using 1,000 particles, the PPF-IMH architecture with four processing elements utilizes less than 5% Virtex-5 FPGA resources and takes 5.85 μs for one iteration. The algorithm performance is also demonstrated when designing the waveform for an agile sensing application.
A new procedure is presented for designing second-order parametric equalizer filters. In contrast to the traditional approach, in which the design is based on a bilinear transform of an analog filter, the presented procedure allows for designing the filter directly in the digital domain. A rather intuitive technique known as pole-zero placement, is treated here in a quantitative way. It is shown that by making some meaningful approximations, a set of relatively simple design equations can be obtained. Design examples of both notch and resonance filters are included to illustrate the performance of the proposed method, and to compare with state-of-the-art solutions.
An adaptive distributed noise reduction algorithm for speech enhancement is considered, which operates in a wireless acoustic sensor network where each node collects multiple microphone signals. In previous work, it was shown theoretically that for a stationary scenario, the algorithm provides the same signal estimators as the centralized multi-channel Wiener filter, while significantly compressing the data that is transmitted between the nodes. Here, we present simulation results of a fully adaptive implementation of the algorithm, in a non-stationary acoustic scenario with a moving speaker and two babble noise sources. The algorithm is implemented using a weighted overlap-add technique to reduce the overall input-output delay. It is demonstrated that good results can be obtained by estimating the required signal statistics with a long-term forgetting factor without downdating, even though the signal statistics change along with the iterative filter updates. It is also demonstrated that simultaneous node updating provides a significantly smoother and faster tracking performance compared to sequential node updating.
Modern microprocessor technology is migrating from simply increasing clock speeds on a single processor to placing multiple processors on a die to increase throughput and power performance in every generation. To utilize the potential of such a system, signal processing algorithms have to be efficiently parallelized so that the load can be distributed evenly among the multiple processing units. In this paper, we study several advanced deterministic and stochastic signal processing algorithms and their computation using multiple processing units. Specifically, we consider two commonly used time-frequency signal representations, the short-time Fourier transform and the Wigner distribution, and we demonstrate their parallelization with low communication overhead. We also consider sequential Monte Carlo estimation techniques such as particle filtering, and we demonstrate that its multiple processor implementation requires large data exchanges and thus a high communication overhead. We propose a modified mapping scheme that reduces this overhead at the expense of a slight loss in accuracy, and we evaluate the performance of the scheme for a state estimation problem with respect to accuracy and scalability.
Field programmable gate arrays (FPGAs) have long been an attractive alternative to microprocessors for computing tasks — as long as floating-point arithmetic is not required. Fueled by the advance of Moore’s Law, FPGAs are rapidly reaching sufficient densities to enhance peak floating-point performance as well. The question, however, is how much of this peak performance can be sustained. This paper examines three of the basic linear algebra subroutine (BLAS) functions: vector dot product, matrix-vector multiply, and matrix multiply. A comparison of microprocessors, FPGAs, and Reconfigurable Computing platforms is performed for each operation. The analysis highlights the amount of memory bandwidth and internal storage needed to sustain peak performance with FPGAs. This analysis considers the historical context of the last six years and is extrapolated for the next six years.
High Performance Computing (HPC) or scientific codes are being executed across a wide variety of computing platforms from embedded processors to massively parallel GPUs. We present a comparison of the Basic Linear Algebra Subroutines (BLAS) using double-precision floating point on an FPGA, CPU and GPU. On the CPU and GPU, we utilize standard libraries on state-of-the-art devices. On the FPGA, we have developed parameterized modular implementations for the dot product and Gaxpy or matrix-vector multiplication. In order to obtain optimal performance for any aspect ratio of the matrices, we have designed a high-throughput accumulator to perform an efficient reduction of floating point values. To support scalability to large data-sets, we target the BEE3 FPGA platform. We use performance and energy efficiency as metrics to compare the different platforms. Results show that FPGAs offer comparable performance as well as 2.7 to 293 times better energy efficiency for the test cases that we implemented on all three platforms.
User-centered computer based learning is an emerging field of interdisciplinary research. Research in diverse areas such as psychology, computer science, neuroscience and signal processing is making contributions to take this field to the next level. Learning systems built using contributions from these fields could be used in actual training and education instead of just laboratory proof-of-concept. One of the important advances in this research is the detection and assessment of the cognitive and emotional state of the learner using such systems. This capability moves development beyond the use of traditional user performance metrics to include system intelligence measures that are based on current theories in neuroscience. These advances are of paramount importance in the success and wide spread use of learning systems that are automated and intelligent. Emotion is considered an important aspect of how learning occurs, and yet estimating it and making adaptive adjustments are not part of most learning systems. In this research we focus on one specific aspect of constructing an adaptive and intelligent learning system, that is, estimation of the emotion of the learner as he/she is using the automated training system. The challenge starts with the definition of the emotion and the utility of it in human life. The next challenge is to measure the co-varying factors of the emotions in a non-invasive way, and find consistent features from these measures that are valid across wide population. In this research we use four physiological sensors that are non-invasive, and establish a methodology of utilizing the data from these sensors using different signal processing tools. A validated set of visual stimuli used worldwide in the research of emotion and attention, called International Affective Picture System (IAPS), is used. A dataset is collected from the sensors in an experiment designed to elicit emotions from these validated visual stimuli. We describe a novel wavelet method to calculate hemispheric asymmetry metric using electroencephalography data. This method is tested against typically used power spectral density method. We show overall improvement in accuracy in classifying specific emotions using the novel method. We also show distinctions between different discrete emotions from the autonomic nervous system activity using electrocardiography, electrodermal activity and pupil diameter changes. Findings from different features from these sensors are used to give guidelines to use each of the individual sensors in the adaptive learning environment.
The thesis discusses a novel off-line and on-line learning approach for Fully Recurrent Neural Networks (FRNNs). The most popular algorithm for training FRNNs, the Real Time Recurrent Learning (RTRL) algorithm, employs the gradient descent technique for finding the optimum weight vectors in the recurrent neural network. Within the framework of the research presented, a new off-line and on-line variation of RTRL is presented, that is based on the Gauss-Newton method. The method itself is an approximate Newton’s method tailored to the specific optimization problem, (non-linear least squares), which aims to speed up the process of FRNN training. The new approach stands as a robust and effective compromise between the original gradient-based RTRL (low computational complexity, slow convergence) and Newton-based variants of RTRL (high computational complexity, fast convergence). By gathering information over time in order to form Gauss-Newton search vectors, the new learning algorithm, GN-RTRL, is capable of converging faster to a better quality solution than the original algorithm. Experimental results reflect these qualities of GN-RTRL, as well as the fact that GN-RTRL may have in practice lower computational cost in comparison, again, to the original RTRL.
A technique is presented for removing large amounts of noise present in time-domain-reflectometry (TDR) waveforms to increase the dynamic range of TDR waveforms and TDR based s-parameter measurements.
I recently learned an interesting rule of thumb regarding the use of an amplifier to drive the input of an analog to digital converter (ADC). The rule of thumb describes how to specify the maximum allowable noise power of the amplifier.
Section 1: reviews the mathematical deﬁnition of Hilbert transform and various ways to calculate it.
Sections 2 and 3: review applications of Hilbert transform in two major areas: Signal processing and system identiﬁcation.
Section 4: concludes with remarks on the historical development of Hilbert transform
A technique is presented for removing large amounts of noise present in time-domain-reflectometry (TDR) waveforms to increase the dynamic range of TDR waveforms and TDR based s-parameter measurements.
In this thesis, the design of a music synthesizer implementing the Scalable Polyphony-MIDI soundset on a low cost DSP system is presented. First, the SP-MIDI standard and the target DSP platform are presented followed by review of commonly used synthesis techniques and their applicability to systems with limited computational and memory resources. Next, various oscillator and ﬁlter algorithms used in digital subtractive synthesis are reviewed in detail. Special attention is given to the aliasing problem caused by discontinuities in classical waveforms, such as sawtooth and pulse waves and existing methods for bandlimited waveform synthesis are presented. This is followed by review of established structures for computationally efﬁcient time-varying ﬁlters. A novel digital structure is presented that decouples the cutoff and resonance controls. The new structure is based on the analog Korg MS-20 lowpass ﬁlter and is computationally very efﬁcient and well suited for implementation on low bitdepth architectures. Finally, implementation issues are discussed with emphasis on the Differentiated Parabole Wave oscillator and MS-20 ﬁlter structures and the effects of limited computational capability and low bitdepth. This is followed by designs for several example instruments.
The author was sponsored by EnTegra Ltd, a company who develop hardware and software products and services for the real time implementation of DSP and RF systems. The field programmable gate array (FPGA) is being used increasingly in the field of DSP. This is due to the fact that the parallel computing power of such devices is ideal for today’s truly demanding DSP algorithms. Algorithms such as the QR-RLS update are computationally intensive and must be carried out at extremely high speeds (MHz). This means that the DSP processor is simply not an option. ASICs can be used but the expense of developing custom logic is prohibitive. The increased use of the FPGA in DSP means that there is a significant requirement for efficient arithmetic cores that utilises the resources on such devices. This thesis presents the research and development effort that was carried out to produce fixed point division and square root cores for use in a new Electronic Design Automation (EDA) tool for EnTegra, which is targeted at FPGA implementation of DSP systems. Further to this, a new technique for predicting the accuracy of CORDIC systems computing vector magnitudes and cosines/sines is presented. This work allows the most efficient CORDIC design for a specified level of accuracy to be found quickly and easily without the need to run lengthy simulations, as was the case before. The CORDIC algorithm is a technique using mainly shifts and additions to compute many arithmetic functions and is thus ideal for FPGA implementation.
Modern digital signal processing makes use of a variety of mathematical techniques. These techniques are used to design and understand efficient filters for data processing and control.
The Author began this Engineering Doctorate (EngD) in Autumn 1999, whilst already in full-time employment as a DSP software engineer at Nortel Networks, Harlow. This EngD comprises a set of three projects. The first project was focused on the development of dual-tone multi-frequency (DTMF) signal detection software. DTMF signals are currently used for operating menu-driven services such as voice-mail, telephone banking and share-dealing. The need for detection software in a packet networking environment exists because such signals become degraded when they travel through speech compression circuits. In addition, if they appear as echoes on a telephone line, they can affect the operation of echo cancellation systems. In this thesis a number of DSP algorithms are discussed where fast detection and minimum complexity are key characteristics. A key contribution here was the development of a novel detection algorithm based on the extraction of parameters that model the DTMF signal. The thesis reports a method combining parameter extraction with the technique of maximum likelihood to perform DTMF detection, resulting in very short time-frames when compared to standard approaches. Reducing the complexity of detection techniques is also important in today’s communication systems. To this end a key contribution here was the development of the ‘split Goertzel algorithm’, which permitted an overlapping of analysis windows without the need for reprocessing input data. Besides being applied to voice-band signals, such as in the case of DTMF, the Author also had the opportunity during the EngD to apply the skills and knowledge acquired in signal processing to higher-rate data-streams. This involved work concerning the equalisation of channel distortion commonly found in wireless communication systems. This covers two projects, with the first being conducted at Verticalband Ltd. (now no longer operational) in the area of digital television receivers. In this part of the thesis a real-time DSP implementation is discussed for enhancing a simulation system developed for wireless channels. A number of channel equalisation approaches are studied. The work concludes that for high-rate signals, non-linear algorithms have the best error rate performance. On the basis of the studies carried out, the thesis considers development and implementation issues of designs based on the decision feedback equaliser. The thesis reports on a software design which applies the method of least squares to carry out filter coefficient adaptation. The Verticalband studies reported lead on to further research within the context of channel equalisation, in the context of the detection of data in multiple-input multiple-output (MIMO) wireless local area network (WLAN) systems. This work was undertaken at Philips Research in Eindhoven, The Netherlands. The thesis discusses implementation scenarios of multi-element antenna arrays that aim to provide bit-rates orders of magnitude higher than today’s WLAN offerings, as those required by emerging standards such as 802.11n. The complexity of optimal detection techniques, such as maximum likelihood, scales exponentially with the number of transmit antennas. This translates to high processing costs and power consumption, rendering such techniques unsuitable for use in battery-powered devices. The initial main contribution here was the analysis of the complexity of algorithms whose performance had already been tested, such as the non-linear maximum likelihood approach and also less complex methods utilising linear filtering. This resulted in the development of new formulae to predict processing costs of algorithms based on the number of transmit and receive antennas. Other key contributions were defining a method to reduce the complexity of matrix inversion when using the Moore-Penrose pseudo-inverse, and the application of matrix decomposition to obviate the need for costly matrix inversion at all. Some on-going research into sub-optimal detection is also discussed, which describes methods to reduce the search-space for the maximum likelihood algorithm.
Motivation: A man was interested in knowing of unknown from the very beginning of the human history. Our human eyes help us to investigate our environment by reflection of light. However, wavelengths of visible light allows transparent view through only a very small kinds of materials. On the other hand, Ultra WideBand (UWB) electromagnetic waves with frequencies of few Gigahertz are able to penetrate through almost all types of materials around us. With some sophisticated methods and a piece of luck we are able to investigate what is behind opaque walls. Rescue and security of the people is one of the most promising fields for such applications. Rescue: Imagine how useful can be information about interior of the barricaded building with terrorists and hostages inside for a policemen. The tactics of police raid can be build up on realtime information about ground plan of the room and positions of big objects inside. How useful for the firemen can be information about current interior state of the room before they get inside? Such hazardous environment, full of smoke with zero visibility, is very dangerous and each additional information can make the difference between life and death. Security: Investigating objects through plastic, rubber, dress or other nonmetallic materials could be highly useful as an additional tool to the existing x-ray scanners. Especially it could be used for scanning baggage at the airport, truckloads on borders, dangerous boxes, etc.
The Global Positioning System (GPS) is now in operation, and many improvements to its performance are being sought. One such improvement is Differential GPS (DGPS), where known errors in the GPS broadcast are identified and the corrections broadcast to the end user. One implementation of DGPS being considered is the use of coastal marine radio direction finding (RDF) radiobeacons in the 285-325kHz band as transmitters for the DGPS broadcast. The normal RDF beacon signal consists of a continuous carrier on a one kilohertz boundary plus a Morse-code identification signal 1025Hz above the carrier. In the DGPS/radiobeacon implementation proposed for the US coastal regions, the differential data link signal uses minimum shift keying (MSK) at a data rate of 25, 50, 100, 200 or 400 baud (the exact baud rat has not yet been decided). This MSK signal is centered between the RDF beacon carrier and identification signal. At the frequencies that these radiobeacons are operated, the prevailing atmospheric noise is both non-Gaussian and very strong. This noise characteristic makes the design of a long-range data link difficult. One solution that has been proposed is the use of forward error correction (FEC) coding of the data. The performance of FEC decoders can be improved by the used of a soft decision receiver, which delivers both bit decisions and information about the validity of the bit decisions. This work describes the design of a radio receiver for DGPS/Radiobeacon servics which is capable of reception of 400 baud MSK in the DGPS/Radiobeacon band. The receiver is designed to be easily augmented to provide soft decisions and easily modified to recieve MSK at data rates of 25 to 400 baud. The radio is a microprocessor controlled dual conversion superheterodyne with an audio frequency of 1kHz. The demodulator runs on the same microprocessor that controls the radio. The weak-signal performance of the demodulator is very good: the Eb/No vs. bit error rate performance of the demodulator is only a couple of dB worse than the theoretical performance of differential phase-shift keying. The radio has a noise floor of -114dBm referenced to it's 500Hz wide audio bandwidth and a 3rd order intermodulation intercept of +7dBm for a dynamic range of 83dB. This work concludes with a thumbnail analysis of the operations needed to implement a soft bit decision estimator, and some suggestions for the implementation of said soft bit decision estimator.
This thesis addresses the problem of estimating a random process from two observed signals sampled at different rates. The case where the low–rate observation has a higher signal–to– noise ratio than the high–rate observation is addressed. Both adaptive and non–adaptive filtering techniques are explored. For the non–adaptive case, a multirate version of the Wiener–Hopf optimal filter is used for estimation. Three forms of the filter are described. It is shown that using both observations with this filter achieves a lower mean–squared error than using either sequence alone. Furthermore, the amount of training data to solve for the filter weights is comparable to that needed when using either sequence alone. For the adaptive case, a multirate version of the LMS adaptive algorithm is developed. Both narrowband and broadband interference are removed using the algorithm in an adaptive noise cancellation scheme. The ability to remove interference at the high rate using observations taken at the low rate without the high–rate observations is demonstrated.