We review some computational aspects of motor control. The problem of trajectory control is phrased in terms of an efficient representation of the operator connecting joint angles to joint torques. Efficient look-up table solutions of the inverse dynamics are related to some results on the decomposition of function of many variables. In a biological perspective, we emphasize the importance of the constraints coming from the properties of the biological hardware for determining the solution to the inverse dynamic problem.

Test and evaluation (TandE) is a critically important step before in-the-field deployment of radio-frequency (RF) hardware in order to assure that the hardware meets its design requirements and specifications. Typically, TandE is performed either in a lab setting utilizing a software simulation environment or through real-world field testing. While the former approach is typically limited by the accuracy of the simulation models (particularly of the anticipated hardware effects) and by non-real-time data rates, the latter can be extremely costly in terms of time, money, and manpower. To build upon the strengths of these approaches and to mitigate their weaknesses, this work presents the development of an FPGA-based TandE tool that allows for real-time pseudo-random aggregate signal generation for testing RF receiver hardware (such as communication receivers, spectrum sensors, etc.). In particular, a framework is developed for an FPGA-based implementation of a test signal emulator that generates randomized aggregate spectral environments containing signals with random parameters such as center frequencies, bandwidths, start times, and durations, as well as receiver and channel effects such as additive white Gaussian noise (AWGN). To test the accuracy of the developed spectrum generation framework, the randomization properties of the framework are analyzed to assure correct probability distributions and independence. Additionally, FPGA implementation decisions, such as bit precision versus accuracy of the generated signal and the impact on the FPGA's hardware footprint, are analyzed.This analysis allows the test signal engineer to make informed decisions while designing a hardware-based RF test system. This framework is easily extensible to other signal types and channel models, and can be used to test a variety of signal-based applications. / Master of Science / Test and evaluation (TandE) is a critically important step before in-the-field deployment of radio-frequency signal hardware in order to assure that the hardware meets its design requirements and specifications. Typically, TandE is performed either in a lab setting utilizing a software simulation or through real-world field testing. While the former approach is typically limited by the accuracy of the simulation models and by slower data rates, the latter can be extremely costly in terms of time, money, and manpower. To address these issues, a hardware-based signal generation approach that takes the best of both methods mentioned above is developed in this thesis. This approach allows the user to accurately model a radio-frequency system without requiring expensive equipment. This work presents the development of a hardware-based TandE tool that allows for real-time random signal generation for testing radio-frequency receiver hardware (such as communication receivers). In particular, a framework is developed for an implementation of a test signal emulator that allows for user-defined randomization of test signal parameters such as frequencies, signal bandwidths, start times, and durations, as well as communications receiver effects. To test the accuracy of the developed emulation framework, the randomization properties of the framework are analyzed to assure correct probability distributions and independence. Additionally, hardware implementation decisions such as bit precision versus quality of the generated signal and the impact on the hardware footprint are analyzed. Ultimately, it is shown that this framework is easily extensible to other signal types and communication channel models.

Denna avhandling behandlar analog-digitalomvandling. I synnerhet behandlas postkorrektion av analog-digitalomvandlare (A/D-omvandlare). A/D-omvandlare är i praktiken behäftade med vissa fel som i sin tur ger upphov till distorsion i omvandlarens utsignal. Om felen har ett systematiskt samband med utsignalen kan de avhjälpas genom att korrigera utsignalen i efterhand. Detta verk behandlar den form av postkorrektion som implementeras med hjälp av en tabell ur vilken korrektionsvärden hämtas. Innan en A/D-omvandlare kan korrigeras måste felen i den mätas upp. Detta görs genom att estimera omvandlarens överföringsfunktion. I detta arbete behandlas speciellt problemet att skatta kvantiseringsintervallens mittpunkter. Det antas härvid att en referenssignal finns tillgänglig som grund för skattningen. En skattare som baseras på sorterade data visas vara bättre än den vanligtvis använda skattaren baserad på sampelmedelvärde. Nästa huvudbidrag visar hur resultatet efter korrigering av en A/D-omvandlare kan predikteras. Omvandlaren antas här ha en viss differentiell olinjäritet och insignalen antas påverkad av ett slumpmässigt brus. Ett postkorrektionssystem, implementerat med begränsad precision, korrigerar utsignalen från A/D-omvandlaren. Ett utryck härleds som beskriver signal-brusförhållandet efter postkorrektion. Förhållandet visar sig bero på den differentiella olinjäritetens varians, det slumpmässiga brusets varians, omvandlarens upplösning samt precisionen med vilken korrektionstermerna beskrivs. Till sist behandlas indexering av korrektionstabeller. Valet av metod för att indexera en korrektionstabell påverkar såväl tabellens storlek som förmågan att beskriva och korrigera dynamiska fel. I avhandlingen behandlas i synnerhet tillståndsmodellbaserade metoder, det vill säga metoder där tabellindex bildas som en funktion utav flera på varandra följande sampel. Allmänt gäller att ju fler sampel som används för att bilda ett tabellindex, desto större blir tabellen, samtidigt som förmågan att beskriva dynamiska fel ökar. En indexeringsmetod som endast använder en delmängd av bitarna i varje sampel föreslås här. Vidare så påvisas hur valet av indexeringsbitar kan göras optimalt, och experimentella utvärderingar åskådliggör att tabellstorleken kan reduceras avsevärt utan att fördenskull minska prestanda mer än marginellt. De teorier och resultat som framförs här har utvärderats med experimentella A/D-omvandlardata eller genom datorsimuleringar. / Analog-to-digital conversion and quantization constitute the topic of this thesis. Post-correction of analog-to-digital converters (ADCs) is considered in particular. ADCs usually exhibit non-ideal behavior in practice. These non-idealities spawn distortions in the converters output. Whenever the errors are systematic, it is possible to mitigate them by mapping the output into a corrected value. The work herein is focused on problems associated with post-correction using look-up tables. All results presented are supported by experiments or simulations. The first problem considered is characterization of the ADC. This is in fact an estimation problem, where the transfer function of the converter should be determined. This thesis deals with estimation of quantization region midpoints, aided by a reference signal. A novel estimator based on order statistics is proposed, and is shown to have superior performance compared with the sample mean traditionally used. The second major area deals with predicting the performance of an ADC after post-correction. A converter with static differential nonlinearities and random input noise is considered. A post-correction is applied, but with limited (fixed-point) resolution in the corrected values. An expression for the signal-to-noise and distortion ratio after post-correction is provided. It is shown that the performance is dependent on the variance of the differential nonlinearity, the variance of the random noise, the resolution of the converter and the precision of the correction values. Finally, the problem of addressing, or indexing, the correction look-up table is dealt with. The indexing method determines both the memory requirements of the table and the ability to describe and correct dynamically dependent error effects. The work here is devoted to state-space--type indexing schemes, which determine the index from a number of consecutive samples. There is a tradeoff between table size and dynamics: more samples used for indexing gives a higher dependence on dynamic, but also a larger table. An indexing scheme that uses only a subset of the bits in each sample is proposed. It is shown how the selection of bits can be optimized, and the exemplary results show that a substantial reduction in memory size is possible with only marginal reduction of performance. / QC 20101019

A multi-precision function interpolator, which is fitted in with the IEEE-754 single precision floating point standard, is proposed in this paper. It provides logarithms, exponentials, reciprocal and square root reciprocal operations. Each operation is able to dynamically select four different precision modes in demand. The hardware architecture is designed with fully pipeline in order to comply with hardware architectures of general digital signal processors (DSPs) and graphics processors (GPUs). When considering the usefulness of each precision mode, it is designed to minimize the error among various modes as far as possible in the beginning. According to the precision from high to low, function interpolator can provide 23, 18, 13 and 8-bit accuracy respectively in spite of the rounding effect. This function interpolator is designed based on the look-up table method. It can get the approximation value of target function through the calculation of quadratic polynomial. The coefficient of quadratic polynomial is obtained by piecewise minimax approximation. Before implementing the hardware, we use the Maple algebra software to generate the quadratic polynomial coefficients of aforementioned four operations, and estimate whether these coefficients can meet IEEE-754 single precision floating point standard. In addition, we take the exhaustive search to check the results generated by our implementation to make sure that it can meet the requirements for various operations and precision modes. When performing one of the above four operations, only the tables of the operation are used to obtain the quadratic polynomial coefficient. Therefore, we can take the advantage of the tri-state buffer as a switch to reduce dynamic power consumption of tables for the other three operations. In addition, when performing lower precision modes, we can turn off a part of hardwares, which are used to calculate the quadratic polynomial, to save the power consumption more effectively. By providing multi-precision hardware, we hope users or developers, those who use the battery device, can choose a lower precision mode within the permissible error range to extend the battery life.

<p>Denna avhandling behandlar analog-digitalomvandling. I synnerhet behandlas postkorrektion av analog-digitalomvandlare (A/D-omvandlare). A/D-omvandlare är i praktiken behäftade med vissa fel som i sin tur ger upphov till distorsion i omvandlarens utsignal. Om felen har ett systematiskt samband med utsignalen kan de avhjälpas genom att korrigera utsignalen i efterhand. Detta verk behandlar den form av postkorrektion som implementeras med hjälp av en tabell ur vilken korrektionsvärden hämtas.</p><p>Innan en A/D-omvandlare kan korrigeras måste felen i den mätas upp. Detta görs genom att estimera omvandlarens överföringsfunktion. I detta arbete behandlas speciellt problemet att skatta kvantiseringsintervallens mittpunkter. Det antas härvid att en referenssignal finns tillgänglig som grund för skattningen. En skattare som baseras på sorterade data visas vara bättre än den vanligtvis använda skattaren baserad på sampelmedelvärde.</p><p>Nästa huvudbidrag visar hur resultatet efter korrigering av en A/D-omvandlare kan predikteras. Omvandlaren antas här ha en viss differentiell olinjäritet och insignalen antas påverkad av ett slumpmässigt brus. Ett postkorrektionssystem, implementerat med begränsad precision, korrigerar utsignalen från A/D-omvandlaren. Ett utryck härleds som beskriver signal-brusförhållandet efter postkorrektion. Förhållandet visar sig bero på den differentiella olinjäritetens varians, det slumpmässiga brusets varians, omvandlarens upplösning samt precisionen med vilken korrektionstermerna beskrivs.</p><p>Till sist behandlas indexering av korrektionstabeller. Valet av metod för att indexera en korrektionstabell påverkar såväl tabellens storlek som förmågan att beskriva och korrigera dynamiska fel. I avhandlingen behandlas i synnerhet tillståndsmodellbaserade metoder, det vill säga metoder där tabellindex bildas som en funktion utav flera på varandra följande sampel. Allmänt gäller att ju fler sampel som används för att bilda ett tabellindex, desto större blir tabellen, samtidigt som förmågan att beskriva dynamiska fel ökar. En indexeringsmetod som endast använder en delmängd av bitarna i varje sampel föreslås här. Vidare så påvisas hur valet av indexeringsbitar kan göras optimalt, och experimentella utvärderingar åskådliggör att tabellstorleken kan reduceras avsevärt utan att fördenskull minska prestanda mer än marginellt.</p><p>De teorier och resultat som framförs här har utvärderats med experimentella A/D-omvandlardata eller genom datorsimuleringar.</p> / <p>Analog-to-digital conversion and quantization constitute the topic of this thesis. Post-correction of analog-to-digital converters (ADCs) is considered in particular. ADCs usually exhibit non-ideal behavior in practice. These non-idealities spawn distortions in the converters output. Whenever the errors are systematic, it is possible to mitigate them by mapping the output into a corrected value. The work herein is focused on problems associated with post-correction using look-up tables. All results presented are supported by experiments or simulations.</p><p>The first problem considered is characterization of the ADC. This is in fact an estimation problem, where the transfer function of the converter should be determined. This thesis deals with estimation of quantization region midpoints, aided by a reference signal. A novel estimator based on order statistics is proposed, and is shown to have superior performance compared with the sample mean traditionally used.</p><p>The second major area deals with predicting the performance of an ADC after post-correction. A converter with static differential nonlinearities and random input noise is considered. A post-correction is applied, but with limited (fixed-point) resolution in the corrected values. An expression for the signal-to-noise and distortion ratio after post-correction is provided. It is shown that the performance is dependent on the variance of the differential nonlinearity, the variance of the random noise, the resolution of the converter and the precision of the correction values.</p><p>Finally, the problem of addressing, or indexing, the correction look-up table is dealt with. The indexing method determines both the memory requirements of the table and the ability to describe and correct dynamically dependent error effects. The work here is devoted to state-space--type indexing schemes, which determine the index from a number of consecutive samples. There is a tradeoff between table size and dynamics: more samples used for indexing gives a higher dependence on dynamic, but also a larger table. An indexing scheme that uses only a subset of the bits in each sample is proposed. It is shown how the selection of bits can be optimized, and the exemplary results show that a substantial reduction in memory size is possible with only marginal reduction of performance.</p>

Traditionally large format displays have been achieved using software. A new technique of using hardware based anywhere pixel routing is explored in this thesis. Information stored in a Look Up Table (LUT) in the hardware can be used to tile two image streams to produce a seamless image display. This thesis develops a 1 input-image 1 output-image system that implements arbitrary image warping on the image, based a LUT stored in memory. The developed system control mechanism is first validated using simulation results. It is next validated via implementation to a Field Programmable Gate Array (FPGA) based hardware prototype and appropriate experimental testing. It was validated by changing the contents of the LUT and observing that the resulting changes on the pixel mapping were always correct.

The present study proposes to use a Conrad probe for transient growth study by measuring the two-dimensional velocity behind an array of roughness elements in the Blasius boundary layer. A look-up table approach is proposed to increase the accuracy of the data reduction process at low velocities, based on the results of the calibration performed in a round jet. A velocity correction method is proposed to minimize the errors due to high velocity shear and wall-proximity in the Blasius boundary layer by comparing Conrad probe results to previous hot-wire data. Measurements of the steamwise velocity perturbation obtained with the Conrad probe agree with previous studies. The measured spanwise perturbation confirms the transport process suggested by simulation. The results show that the perturbation amplitude increases by increasing both the freestream velocity and roughness elements height. However, the mechanism for changing the perturbation amplitude of influence differs for these two parameters.

The present study proposes to use a Conrad probe for transient growth study by measuring the two-dimensional velocity behind an array of roughness elements in the Blasius boundary layer. A look-up table approach is proposed to increase the accuracy of the data reduction process at low velocities, based on the results of the calibration performed in a round jet. A velocity correction method is proposed to minimize the errors due to high velocity shear and wall-proximity in the Blasius boundary layer by comparing Conrad probe results to previous hot-wire data. Measurements of the steamwise velocity perturbation obtained with the Conrad probe agree with previous studies. The measured spanwise perturbation confirms the transport process suggested by simulation. The results show that the perturbation amplitude increases by increasing both the freestream velocity and roughness elements height. However, the mechanism for changing the perturbation amplitude of influence differs for these two parameters.

In modern wireless communication systems, advanced modulation techniques are used to support more users by handling high data rates and to increase the utilization efficiency of the limited RF spectrum. These techniques are sensitive to the nonlinear distortions due to their high peak to average power ratios. Main source of nonlinear distortion in transmitter topologies are power amplifiers that determine the overall efficiency and linearity of the transmitter. To increase linearity without sacrificing efficiency, power amplifier linearization techniques may be a choice. Baseband predistortion technique is known to be one of the optimum methods due to its relatively low complexity and its convenience for adaptation. In this thesis, different memoryless baseband signal predistortion methods are investigated and analyzed by simulations. Look-Up Table(LUT) and Polynomial approaches are compared and LUT approach is found to be better in performance. Parameters, like indexing, training sequences and training duration are evaluated. An open loop testbench is built with a real amplifier and a different LUT predistortion method that is based on amplifier modeling is offered. It is evaluated by using two tone test and adjacent channel power suppression with 8PSK data. Also, some Look-Up Table parameters are re-investigated with the proposed method. The performances of the proposed method in dierent amplifier classes are observed. Along with these studies, a list of prerequisites for design of a predistortion system is determined.

This master’s thesis deals with an analysis of digital security with CRC. In the thesis there is described a principle of coding theory, especially then digital security with CRC, for which there is explained a mathematical principle of their encoding and decoding, software implementation and a description of frequently used generator polynomials. The main aim of the thesis is a testing of undetected errors and a finding of number of these errors. After that it is used for the computation of probability with which undetected errors can occur. The thesis is supplemented with several programs which are programmed in the software Matlab.