## Closing the gap: CPU and FPGA Trends in sustainable floating-point BLAS performance

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.

## BLAS Comparison on FPGA, CPU and GPU

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.

## Biosignal processing challenges in emotion recognition for adaptive learning

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.

## Gauss-Newton Based Learning for Fully Recurrent Neural Networks

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.

## Wavelet Denoising for TDR Dynamic Range Improvement

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.

## Bilinear Transformation Made Easy

A formula is derived and demonstrated that is capable of directly generating digital filter coefficients from an analog filter prototype using the bilinear transformation. This formula obviates the need for any algebraic manipulation of the analog prototype filter and is ideal for use in embedded systems that must take in any general analog filter specification and dynamically generate digital filter coefficients directly usable in difference equations.

## FUZZY LOGIC BASED CONVOLUTIONAL DECODER FOR USE IN MOBILE TELEPHONE SYSTEMS

Efficient convolutional coding and decoding algorithms are most crucial to successful operation of wireless communication systems in order to achieve high quality of service by reducing the overall bit error rate performance. A widely applied and well evaluated scheme for error correction purposes is well known as Viterbi algorithm [7]. Although the Viterbi algorithm has very good error correcting characteristics, computational effort required remains high. In this paper a novel approach is discussed introducing a convolutional decoder design based on fuzzy logic. A simplified version of this fuzzy based decoder is examined with respect to bit error rate (BER) performance. It can be shown that the fuzzy based convolutional decoder here proposed considerably reduces computational effort with only minor BER performance degradation when compared to the classical Viterbi approach.

## Method to Calculate the Inverse of a Complex Matrix using Real Matrix Inversion

This paper describes a simple method to calculate the invers of a complex matrix. The key element of the method is to use a matrix inversion, which is available and optimised for real numbers. Some actual libraries used for digital signal processing only provide highly optimised methods to calculate the inverse of a real matrix, whereas no solution for complex matrices are available, like in [1]. The presented algorithm is very easy to implement, while still much more efficient than for example the method presented in [2]. [1] Visual DSP++ 4.0 C/C++ Compiler and Library Manual for TigerSHARC Processors; Analog Devices; 2005. [2] W. Press, S.A. Teukolsky, W.T. Vetterling, B.R. Flannery; Numerical Recipes in C++, The art of scientific computing, Second Edition; p52 : “Complex Systems of Equations”;Cambridge University Press 2002.

## Fully Programmable LDPC Decoder Hardware Architectures

In recent years, the amount of digital data which is stored and transmitted for private and public usage has increased considerably. To allow a save transmission and storage of data despite of error-prone transmission media, error correcting codes are used. A large variety of codes has been developed, and in the past decade low-density parity-check (LDPC) codes which have an excellent error correction performance became more and more popular. Today, low-density parity-check codes have been adopted for several standards, and eﬃcient decoder hardware architectures are known for the chosen structured codes. However, the existing decoder designs lack ﬂexibility as only few structured codes can be decoded with one decoder chip. In consequence, diﬀerent codes require a redesign of the decoder, and few solutions exist for decoding of codes which are not quasi-cyclic or which are unstructured. In this thesis, three diﬀerent approaches are presented for the implementation of fully programmable LDPC decoders which can decode arbitrary LDPC codes. As a design study, the ﬁrst programmable decoder which uses a heuristic mapping algorithm is realized on an ﬁeld-programmable gate array (FPGA), and error correction curves are measured to verify the correct functionality. The main contribution of this thesis lies in the development of the second and the third architecture and an appropriate mapping algorithm. The proposed fully programmable decoder architectures use one-phase message passing and layered decoding and can decode arbitrary LDPC codes using an optimum mapping and scheduling algorithm. The presented programmable architectures are in fact generalized decoder architectures from which the known decoders architectures for structured LDPC codes can be derived.

## Design of a Scalable Polyphony-MIDI Synthesizer for a Low Cost DSP

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.

## An Experimental Multichannel Pulse Code Modulation System of Toll Quality + Electron Beam Deflection Tube For Pulse Code Modulation

See this blog post for context. Pulse Code Modulation offers attractive possibilities for multiplex telephony via such media as the microwave radio relay. The various problems involved in its use have been explored in terms of a 96-channel system designed to meet the transmission requirements commonly imposed upon commercial toll circuits. Twenty-four of the 96 channels have been fully equipped in an experimental model of the system. Coding and decoding devices are described, along with other circuit details. The coder is based upon a new electron beam tube, and is characterized by speed and simplicity as well as accuracy of coding. These qualities are matched in the decoder, which employs pulse excitation of a simple reactive network.

## Towards Efﬁcient and Robust Automatic Speech Recognition: Decoding Techniques and Discriminative Training

Automatic speech recognition has been widely studied and is already being applied in everyday use. Nevertheless, the recognition performance is still a bottleneck in many practical applications of large vocabulary continuous speech recognition. Either the recognition speed is not sufﬁcient, or the errors in the recognition result limit the applications. This thesis studies two aspects of speech recognition, decoding and training of acoustic models, to improve speech recognition performance in different conditions.

## How Discrete Signal Interpolation Improves D/A Conversion

Earlier this year, for the Linear Audio magazine, published in the Netherlands whose subscribers are technically-skilled hi-fi audio enthusiasts, I wrote an article on the fundamentals of interpolation as it's used to improve the performance of analog-to-digital conversion. Perhaps that article will be of some value to the subscribers of dsprelated.com. Here's what I wrote: We encounter the process of digital-to-analog conversion every day—in telephone calls (land lines and cell phones), telephone answering machines, CD & DVD players, iPhones, digital television, MP3 players, digital radio, and even talking greeting cards. This material is a brief tutorial on how sample rate conversion improves the quality of digital-to-analog conversion.

## STUDY OF DIGITAL MODULATION TECHNIQUES

Modulation is the process of facilitating the transfer of information over a medium. Typically the objective of a digital communication system is to transport digital data between two or more nodes. In radio communications this is usually achieved by adjusting a physical characteristic of a sinusoidal carrier, either the frequency, phase, amplitude or a combination thereof . This is performed in real systems with a modulator at the transmitting end to impose the physical change to the carrier and a demodulator at the receiving end to detect the resultant modulation on reception. Hence, modulation can be objectively defined as the process of converting information so that it can be successfully sent through a medium. This thesis deals with the current digital modulation techniques used in industry. Also, the thesis examines the qualitative and quantitative criteria used in selection of one modulation technique over the other. All the experiments, and realted data collected were obtained using MATLAB and SIMULINK

## A pole-zero placement technique for designing second-order IIR parametric equalizer filters

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.

## Adaptive distributed noise reduction for speech enhancement in wireless acoustic sensor networks

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.

## Active Noise Control of a Forest Machine Cabin

Today, a high noise level is considered a problem in many working environments. The main reason is that it contributes to stress and fatigue. Traditional methods using passive noise control is only practicable for high frequencies. As a complement to passive noise control, active noise control (ANC) can be used to reduce low frequency noise. The main idea of ANC is to use destructive interference of waves to cancel disturbing noises. The purpose of this thesis is to design and implement an ANC system in the driver's cabin of a Valmet 890 forest machine. The engine boom is one of the most disturbing noises and therefore the main subjective for the ANC system to suppress. The ANC system is implemented on a Texas Instrument DSP development starter kit. Different FxLMS algorithms are evaluated with feedback and feedforward configurations. The results indicate that an ANC system significantly reduces the sound pressure level (SPL) in the cabin. Best performance of the evaluated systems is achieved for the feedforward FxLMS system. For a commonly used engine speed of 1500 rpm, the SPL is reduced with 17 dB. The results show fast enough convergence and global suppression of low frequency noise.

## Voice Codec for Floating Point Processor

As part of an ongoing project at the department of electrical engineering, ISY, at Linköping University, a voice decoder using floating point formats has been the focus of this master thesis. Previous work has been done developing an mp3-decoder using the floating point formats. All is expected to be implemented on a single DSP.The ever present desire to make things smaller, more efficient and less power consuming are the main reasons for this master thesis regarding the use of a floating point format instead of the traditional integer format in a GSM codec. The idea with the low precision floating point format is to be able to reduce the size of the memory. This in turn reduces the size of the total chip area needed and also decreases the power consumption.One main question is if this can be done with the floating point format without losing too much sound quality of the speech. When using the integer format, one can represent every value in the range depending on how many bits are being used. When using a floating point format you can represent larger values using fewer bits compared to the integer format but you lose representation of some values and have to round the values off.From the tests that have been made with the decoder during this thesis, it has been found that the audible difference between the two formats is very small and can hardly be heard, if at all. The rounding seems to have very little effect on the quality of the sound and the implementation of the codec has succeeded in reproducing similar sound quality to the GSM standard decoder.

## Efficient arithmetic for high speed DSP implementation on FPGAs

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.

## Restoration of Nonlinearly Distorted Optical Soundtracks Using Regularized Inverse Characteristics

This dissertation is concerned with the possibilities of restoration of degraded film-sound. The sound-quality of old films are often not acceptable, which means that the sound is so noisy and distorted that the listener have to take strong efforts to understand the conversations in the film. In this case the film cannot give artistic enjoyment to the listener. This is the reason that several old films cannot be presented in movies or television. The quality of these films can be improved by digital restoration techniques. Since we do not have access to the original signal, only the distorted one, therefore we cannot adjust recording parameters or recording techniques. The only possibility is to post-compensate the signal to produce a better estimate about the undistorted, noiseless signal. In this dissertation new methods are proposed for fast and efficient restoration of nonlinear distortions in the optically recorded film soundtracks. First the nonlinear models and nonlinear restoration techniques are surveyed and the ill-posedness of nonlinear post-compensation (the extreme sensitivity to noise) is explained. The effects and sources of linear and nonlinear distortions at optical soundtracks are also described. A new method is proposed to overcome the ill-posedness of the restoration problem and to get an optimal result. The effectiveness of the algorithm is proven by simulations and restoration of real film-sound signals.