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  • Roxburgh, A.J., "On Computing the Discrete Fourier Transforms" A report submitted to fulfill the requirements of
    55:198 Individual Investigations: Electrical and Computer Engineering. University of Iowa, Iowa City, IA 52242
    Summer Session, 2009. Newly revised and updated, December 9, 2013

ABSTRACT:  The development of time-efficient small-N discrete Fourier transform (DFT) algorithms has received a lot of attention due to the ease with which they combine, “building block” style, to yield time-efficient large transforms. This paper reports on the discovery that efficient computational algorithms for small-N DFT developed during the 19th century bear more than a passing resemblance to similar-sized modern-day algorithms, including the same nested (+)(x)(+) structure, similar flow graphs, and a comparable number of arithmetic operations. This suggests that despite the formal sophistication of more recent approaches to the development of efficient small-N DFT algorithms, the key underlying principles are still the symmetry and periodicity properties of the sine and cosine basis functions of the Fourier transform. While the earlier methods explicitly manipulated the DFT operator on the level of these properties, the present-day methods (typically based on the cyclic convolution properties of the DFT operator) tend to hide this more basic level of reality from view. All reduced-arithmetic DFT algorithms take advantage of how easy it is to factor the DFT operator. From the matrix point of view, an efficient DFT algorithm results when we factor the DFT operator into a product of sparse matrices containing mostly ones and zeros. Given that there are innumerable factorizations, it is interesting that modern-day algorithms developed using number-theoretic techniques quite removed from the trigonometric identities and simple algebraic techniques used by the pioneers of discrete signal analysis, should be so similar in form to the early algorithms.


  • Infrared Repeater System. United States Patent Application Application US 2010/0258729 A1
    Published Oct 14, 2010. Filed April 13, 2009. Inventors: Alastair Roxburgh, Richard Lenser, Bill Cawlfield

ABSTRACT:  An infrared sensor includes a photodiode receiving an infrared signal. A first amplifier is connected to the photodiode. A second amplifier is connected to the first amplifier. A DC servo is connected in a feedback loop between the output of the second amplifier and the positive side of the first amplifier. An analog-to-digital signal converter is connected to the second amplifier. An output driver is connected to the analog-to-digital signal converter. The infrared sensor may receive and retransmit an infrared signal and may be incorporated in an infrared repeater system."

SUMMARY:  A reduced number of capacitors in the signal path lowers the "Q" and reduces phase distortion. This allows IR signals to be repeated with less ringing, overshoot, and distortion, all of which are important for accurately passing the new high-density IR codes. Examples of these codes are RC-MM and XMP, which respectively use 4-ary and 8-ary symbol coding, rather than the conventional binary (2-ary) format. The corresponding code symbols are respectively 2 and 3 bits long. Avoidance of intersymbol interference for these IR codes requires timing precision to be maintained 4x better than binary for RC-MM, and 8x better for XMP. It is difficult to maintain a sufficient degree of ringing- and overshoot-free accuracy in circuits that have a modulation passband response that has too high a "Q"-value (i.e., a response that has too high an order, primarily caused by too many coupling capacitor poles in the frequency response). This new "Hi-Fi" IR repeater architecture solves the problem.


  • Baker, A.B., McLeod, C.N., Roxburgh, A.J., and Bannister, P., "Descending aortic flow contribution to intrathoracic impedance-Development and preliminary testing of a dual impedance model," Journal of Clinical Monitoring and Computing, 22, pp. 11-22, 2008. 

OBJECTIVE: Impedance measurement of cardiac output has struggled to become established partly because there have been only a few attempts to establish a sound theoretical basis for this measurement. Our objective is to demonstrate that there is valuable aortic flow information available from an intrathoracic impedance signal which may eventually be useful in the measurement of cardiac output by impedance technology.

METHODS: A model, using dual impedance measurement electrodes and the change in impedance when blood flows, has been developed based on an intrathoracic impedance model of the descending aorta and esophagus. Using this model as the basis for measurement by an esophageal probe, we provide solutions to the velocity of blood flow in the descending aorta.

RESULTS: Five patients were studied. Only three patients had suitable signals for analysis but the aortic flow profiles from these three patients were consistent and realistic.

CONCLUSION: Aortic blood flow information may be obtained from the intrathoracic impedance signal using this dual impedance method.


  • Roxburgh, A.J., On computing the discrete Fourier transform. Research paper (55:198 Individual Investigations: Electronic and Computer Engineering, University of Iowa), 1990 (pp. i-viii, 1-30).

ABSTRACT: The development of time-efficient small-N discrete Fourier transform (DFT) algorithms has received a lot of attention due to the ease with which they may be combined, “building block” style, to yield time-efficient large transforms. This paper reports on the discovery that efficient computational algorithms for small-N DFT developed during the 19th century bear more than a passing resemblance to similar-sized modern-day algorithms, including the same nested (+)(´)(+) structure, similar flow graphs, and a comparable number of arithmetic operations. This suggests that despite the formal sophistication of more recent approaches to the development of efficient small-N DFT algorithms, the key underlying principles are still the symmetry and periodicity properties of the sine and cosine basis functions. While the earlier methods explicitly manipulated the DFT operator on the level of these properties, the present-day methods (typically based on the cyclic convolution properties of the DFT operator) tend to hide this more basic level of reality from view. All reduced-arithmetic DFT algorithms take advantage of how easy it is to factor the DFT operator. From the matrix point of view, an efficient DFT algorithm results when we factor the DFT operator into a product of sparse matrices containing ones and zeros. Given that there are innumerable factorizations, it is interesting that modern-day algorithms developed using number-theoretic techniques quite removed from the trigonometric identities and simple algebraic techniques used by the pioneers of discrete signal analysis, should be so similar in form to the early algorithms.


  • Roxburgh, A.J. (team leader), Aminzay S.Q., Khumalo, T., Nguyen, D., Binary Lookahead Carry Adder (BLCA). Project Final Report (55:142 Introduction to VLSI Design, Electronic and Computer Engineering Department, University of Iowa), 1988 (pp. i-iii, 1-20).

    OBJECTIVE: Create a floor plan and interconnections for cell design layouts (Magic).
                           Pad design: input protection, output buffering.
                           Types of BLCA:  4-bit, 8-bit, 16-bit, 32-bit. Simulation: functional verification (Esim); timing analysis (Crystal).

    DESIGN:       Carry expression: Ci = Gi,      (Gi, Pi) = (gi, pi) o (Gi-1, Pi-1)      if  2 ≤  i  ≤ n
                                                                                          = (gi, pi)                           if  i = 1,
                                                                        where (g, p) o (g', p') = (g + (p.g'), p.p')
                           Floor plan generation: Used corrected and verified C program (appendix A).
                           Theoretical equations:  time ~ log2(n),   n = adder size;    area ~ n log2(n).

     RESULT:      Completed simulation of 4-, 8-, 16-, and 32-bit BCLA. Achieved reasonable propagation time (table 1, appendix D),
                           and showed that time delay closely followed log2(n). Chip area is ~ 2n log2(n)+n  (table 2).


  • Roxburgh, A.J., The simple Fourier transform, Thesis, M.Sc., University of Otago, 1987 (249 pp.).

ABSTRACT: A new algorithm for numerically evaluating the discrete Fourier transform (DFT) is developed. The algorithm, which yields results of high precision, is also computationally efficient in the context of typical 8-bit microprocessor instruction sets. Because it gives a particularly simple DFT implementation for such microprocessors, the algorithm has been named the simple Fourier transform, or SFT. Central to the SFT algorithm is the implementation of multiplication using a lookup table of squares. However, due to a mathematical simplification the number of squarings required is smaller than might be expected, each multiplication essentially being reduced to a single ADD-and-SQUARE macro-operation. Thus, even though most simple microprocessors lack a built-in multiply instruction, the slower alternative of software multiplication need not be considered for DFT processing. The SFT algorithm is extended with a Hann (sine-squared) data window applied as a spectral convolution, which due to further simplification of the arithmetic requires no additional computation time. This modified form of the SFT has been named the SFT-Hann algorithm. Good performance for real-input narrow-band spectral analysis makes the SFT and SFT-Hann algorithms useful for a variety of low-end signal processing applications. Versions of these algorithms written for the z80 microprocessor are examined, and compared with several other discrete Fourier transform programs. In order to verify the methods used, as well as to make them more widely accessible, several illustrative programs written in BASIC are also presented.


  • Baker, A.B. and Roxburgh, A.J., "Computerised EEG monitoring for carotid endarterectomy," Anaesthesia and Intensive Care, 14(1), pp. 32-36, Feb., 1986.

ABSTRACT: A prospective study was undertaken in twenty patients undergoing carotid endarterectomy using computerised EEG monitoring in the form of a density-modulated spectral array, spectral edge frequency and integrated EEG power for monitoring cerebral ischaemia. This form of monitoring proved to be easy to use and understand. Because ischaemic EEG events longer than one minute were not necessarily followed by postoperative deficits, the definition of significant events that would cause ischaemia may need to be modified.


  • Roxburgh, A.J., Baker, A.B., Bannister, P., and McLeod, C., "Aortic blood flow from intra-thoracic impedance," Proc. Univ. Otago Med. Sch., 63, pp. 73-74, 1985.

ABSTRACT: Intra-thoracic electrical impedance change may be caused as much by aortic blood flow as by aortic movement, contradicting a statement by Mitchell and Newbower (1979) that all of the impedance change is due to movement alone.  With two impedance analyzers, however, the aortic movement component of the intra-thoracic impedance may be cancelled out enabling a more accurate measurement of the aortic blood flow. Dual impedance data was analyzed for one cardiac cycle from a patient following cardiac surgery, which using a simplified anatomical model, gave a stroke volume of 57 ml. Cardiac output measured simultaneously by thermal dilution gave a stroke volume of 59 ml.


  • Baker, A.B., Roxburgh, A.J., and McLeod, C., "Intra-thoracic impedance plethysmography and aortic blood flow," Proc. Univ. Otago Med. Sch., 62, pp. 69-70, 1984.

ABSTRACT: Mitchell and Newbower (1979) produced a theoretical model which shows that any change in the intra-thoracic electrical impedance is unlikely to be correlated with stroke volume, due to the inability to distinguish aortic movement from blood flow. Their model did not take into account the increase in the electrical conductivity of blood that occurs when blood flows, which can be as high as 25%, as reported by Coulter (1949), and Visser (1981) and others. This study has refined these models to generate an equation that defines the relationship between blood velocity and other components of the intra-thoracic impedance. From blood velocity , stroke volume may be derived.  


  • Baker, A.B. and Roxburgh, A.J., "Intra-thoracic impedance plethysmography and cardiac output," Proc. Univ. Otago Med. Sch., 62, pp. 12-14, 1984.

ABSTRACT: Oesophageal catheter probes provide an established method of measuring variables such as ECG, temperature, heart and breath sounds, diaphramatic EMG, and electrical impedance. One advantage for the trans-thoracic electrical impedance measured by the oesophageal probe is that it gives a pulsatile component of 5-10% compared with 0.2% for the trans-thoracic method. The aim of this study was to document the better cardiac-related signal-to-noise ratio from the intra-thoracic method, as a first step in allowing better impedance-based measurements of cardiac output.


  • Roxburgh, A.J. and Baker, A.B., "The use of disposable ECG electrodes for intraoperative electroencephalography," Proc. Univ. Otago Med. Sch., 61, pp. 51-53, 1983.

ABSTRACT: Following on from the suggestion to use disposable electrocardiograph (ECG) electrodes for intraoperative electroencephalography (EEG), as a time-saving and reliability measure, and a recent theoretical prediction that two widely-spaced EEG electrodes attached to the frontal and mastoid regions of the scalp will be sufficiently sensitive to detect diffuse events, as well as major focal events such as ischaemia, we decided to compare the suitability of various electrodes for EEG by measuring the electrical impedance of such a widely-space pair of electrodes. Low impedance is an important factor in EEG measurements, but is not typically specified for ECG electrodes. Standard gold cup electrodes were compared with two varieties of disposable Ag/AgCl ECG electrodes, and stainless steel 27 gauge needles. In terms of electrical impedance at EEG frequencies, one brand of disposable ECG electrodes performed as well as the traditional gold cup EEG electrodes. 


  • Roxburgh, A.J., "Spectral edge frequency: a comparison of methods," Proc. Univ. Otago Med. Sch., 61, pp. 49-51, 1983.

ABSTRACT: Owing to its value in the detection of cerebral ischaemia, spectral edge frequency (SEF) stands out as the single most useful univariate descriptor of the electroencephalogram (EEG) power spectrum. Previous work used the cumulative power method to define a significant upper spectral edge, however this correlates poorly with visual estimates.  Rampil et al (1980) improved the detection of the spectral edge by using a recursively-filtered, template-matching algorithm, but found that is did not provide reliable detection for the human EEG.


  • Roxburgh, A.J. and Baker, A.B., "A standard for display of EEG data using the density modulated spectral array," Proc. Univ. Otago Med. Sch., 60, pp. 81-83, 1982.

ABSTRACT: The density-modulated spectral array (DSA) is one of the more recently developed techniques for automated processing and display of clinical EEG data. Compared with earlier display methods. the DSA offers improved legibility of spectral patterns, yet is more easily integrated into existing patient monitoring systems. This report presents a concise description of the DSA system currently in use at Dunedin Hospital.


  • Roxburgh, A.J., Dobbinson, T.L., and Baker, A.B., "Monitoring ischaemic EEG events with the DSA display," Proc. Univ. Otago Med. Sch., 60, pp. 46-47, 1982.XXXX

ABSTRACT: The density-modulated spectral array (DSA) is a relatively new techniques for displaying the EEG power spectrum in a compact pictorial form which seems useful for detecting cerebral ischaemic and hypoxic events. This report describes preliminary trials using the DSA at Dunedin Hospital.


  • Roxburgh, A.J. and Baker, A.B., "Linear grey-scale raster displays on a thermal strip-chart recorder," Proc. Univ. Otago Med. Sch., 60, pp. 16-18, 1982.

ABSTRACT: The term "raster" derives from the scanning pattern used in television. Density-modulated raster displays plotted on a thermal strip-chart recorder have for several years been used to display EEG spectral data (the density-modulated spectral array, or DSA). The DSA shows frequency and power (pen position and grey-density, respectively) versus time. The raster grey-density is varied by changing the pen scanning speed, thereby varying the amount of heat applied to the chart paper. An inherent non-linearity in the grey scale is compensated for with a simple correction that is derived in the paper, and is found to obey a square-law. Retrace speed limitations limit the available contrast ratio to about 5:1, which causes some loss of data at small values of the density variable, however the parabolic density map can be offset to compensate.


  • Holmes, C.McK. and Roxburgh, A.J., "A computer simulation of gas concentrations in the circle system," Proc. Computing in Anesthesia Symposium, Santa Monica, CA, 1982.

ABSTRACT: The complex interaction of factors governing the concentration of gases in an anesthetic circle system are not easily understood by medical students, interns and residents. Even when the inhalational components of an anesthetic are nitrous oxide and oxygen only, it is not a simple two-component model, due to the presence initially of air in the lungs and circuit. The interacting factors are many, however, in the clinical situation some of these factors cannot be varied, and others can be altered only within safety limits. To this end a computer simulation has been devised, in which all of the variables may be changed at will, and the effects observed by the student. The program, which uses the nitrous oxide uptake rate found by Severinghaus, is written in Applesoft BASIC. The user can initially set the flows of the nitrous oxide and oxygen, the oxygen consumption, and stop time. Further, the initial values of circuit volume and nitrous oxide uptake may each be halved or doubled. At the stop time the use may exit the program or continue with the same or altered variables. The results are displayed in numerical and graphical form. 


  • Roxburgh, A.J. and Holmes, C.McK., "A computerized anesthesia record for the smaller hospital," Proc. Computing in Anesthesia Symposium, Santa Monica, CA, 1982.

    ABSTRACT:  Placeholder (under construction).


  • Smith, N.T., Roxburgh, A.J., and Quinn, M.L., "Continual measurement of airway resistance; use of a microprocessor controlled ventilator," Anesthesiology, 53:s389, 1980.

ABSTRACT: A microcomputer-controlled ventilator which can generate virtually any type of waveform has been developed. To allow the continual measurement of  airway resistance during ventilation, it was programmed it to superimpose high frequency square waves upon the regular flow pattern: a square wave,  half sine wave, ramp, or reverse ramp. We determined that the maximum difference in the high frequency amplitude, between high and low resistance, was seen with a high frequency of 5 Hz. Normal changes in compliance did not change the high frequency amplitude. 


  • Edwards, P.J., Hurst, R.B., Roxburgh, A.J., and Stanley, G.R., Data acquisition and processing. Otago Wind Energy Resource Survey Phase II. Report No. 2, New Zealand Research and Development Committee. April 1979. NZERDC P13, ISSN 0110-5388.

ABSTRACT: This report describes methods of data acquisition, processing and analysis used in implementing the NZ Wind Energy Resource Survey in Otago. Field operation of wind-run and wind-speed anemometers, electronic wind speed integrators and wind speed recorders is described. The recovery of field recorded data in computer compatible form and its subsequent analysis to provide wind energy parameters is also described. Examples of these analyses are given. Computer program listings are given in the internal version of this report, available from the Department of Physics, University of Otago, Dunedin, New Zealand.


  • Roxburgh, A.J., Edwards, P.J., and Hurst, R.B., "Acquisition and analysis of Otago wind energy data," Proc. N.Z. Meteorological Service Symposium on Meteorology and Energy, Wellington, New Zealand, Oct 11-12, 1977. Proc. New Zealand Meteorological Service, May 25, 1978.

ABSTRACT: This paper describes the acquisition and analysis of wind data by the University of Otago as part of the Wind Energy Resource Survey of New Zealand. Field operation of both wind-run and wind-speed anemometers by the Otago University Physics Department is detailed, together with calibration data. A wind speed recording system is described with particular reference to the continuous data format used. The format allows flexible readout in computer compatible form, in analog and numeric printer chart form, or allows direct analysis of the recovered analog wind-speed variable using special hardware.


  • Hurst, R.B., Edwards, P.J., and Roxburgh, A.J., "Characterisation of wind energy sites," Proc. N.Z. Meteorological Service Symposium on Meteorology and Energy, Wellington, New Zealand, Oct 11-12, 1977. Proc. New Zealand Meteorological Service, May 25, 1978. p.57-68.

ABSTRACT: The Otago University Physics Department, as part of its involvement in a national survey of wind energy resources, has logged a large quantity (approximately 10 logger-years) of wind speed data on magnetic tape from a selection of Otago sites. The blocks of data are continuous and up to a time 30 days in length. The recording format allows digitization with time resolutions of 2 s chosen when the tape is read out. Times of 64 seconds and 112 seconds have often been used, to give convenient speed resolutions of 0.1 or 0.2 m/s (depending on the variety of logger). However, time resolution down to a few seconds is attainable. Access to computing facilities is available directly (PDP11) or via punched paper tape. This paper describes some of the analysis carried out to date on this data to extract statistical information relevant to wind power generation.


  • Edwards, P.J., Hurst, R.B., and Roxburgh, A.J., "Aerogenerator performance at representative Otago sites," Proc. N.Z. Meteorological Service Symposium on Meteorology and Energy, Wellington, New Zealand, Oct 11-12, 1977. Proc. New Zealand Meteorological Service, May 25, 1978. p.85-92.

ABSTRACT: Electricity supply authorities in New Zealand have more difficulty in meeting load demands in late winter and early spring than at other times in the year. Thus, aerogeneration on a large scale will be of most value if it can provide a reliable source during this period. Of course, it is unrealistic to expect to be able to provide a full-time base load from the area covered by the Otago survey, measuring approximately 150 km by 100 km, but when similar studies become available from other parts of New Zealand then the ability of wind energy to provide winter base load can be assessed. Six special aspects of winter winds in Otago are examined in this report. 


  • Edwards, P.J. and Roxburgh, A.J., "A low cost meteorological data logging system for remote sites," Proc. World Meteorological Organization TECIMO Conf., Hamburg, July 1977. University of Otago Physics Department publication Astrophys 77/4

    SUMMARY: This paper describes the design of a low cost, low power magnetic tape cassette data recorder, its use at remote sites, and the associated data readout facilities. A conventional magnetic cassette transport system with low power slow speed DC motor is used. In the single data mode, clock pulses derived from a crystal controlled oscillator are recorded on one track, and event pulses on the second track. A four channel  head may be used to provide three data channels with a time resolution of one second, channel bandwidth 3 Hz, for one month recording period on a standard C-90 cassette. Power drain is 60 mW. The recorder has been successfully used with solarimeters, anemometers, and tipping buck rain gauges. Longer record duration is obtained with proportionally reduced time resolution and frequency response. The read-out facilities include analog chart recording, paper tape punching, and character printing as well as direct access to a minicomputer.


  • Hurst R.B., Roxburgh A.J., and Edwards P.J., Computer program for atmospheric turbidity determination, University of Otago Physics Department publication Astrophys 77/5, (Document produced as part-fulfillment of N.Z. Meteorological Service Turbidity Contract), 1977.

ABSTRACT: It has been proposed (Edwards, P.J. and Othman, M., Southern Stars, Journal of the Royal Astronomical Society of New Zealand, 26:8, p.184, 1976) that measurements be made of atmospheric stellar extinction at selected astronomical observatories, for the purpose of estimating atmospheric turbidity. This report describes data reduction and a Burroughs 6700 computer programme developed to process the data from these astronomical observations.

The astronomical observations consist of photoelectric measurements at several wavelengths of light from a known star (i.e., with known right ascension and declination, and known spectral characteristics). These measurements, made for a range of zenith angles (and hence for a range of air-path lengths) allow determination of the atmospheric extinction, at the wavelength in question. The principal processes contributing to this extinction are Rayleigh scattering, ozone absorption, and aerosol scattering. The extinction due to Rayleigh scattering and ozone absorption alone may be estimated for a model atmosphere.  Such an estimate is generally less than the extinction actually measured, the difference being attributed to turbidity. 


  • Cherry N.J., Edwards P.J., and Roxburgh A.J., "Low-cost instrumentation for a wind energy survey," Proc. 22nd International Instrumentation Symposium, San Diego, May 25-27, 1976.

ABSTRACT: An observational programme for a wind energy survey is being carried out in several areas of New Zealand. The instrumentation required, excluding the anemometer assembly, was developed locally. Wind-run, or mean wind speed, is obtained by counting one pulse per revolution of the anemometer on a modified pocket calculator. Power requirements are reduced to less than an average of 5 mA by turning the display off when it is not being read. This is a low cost system with the additional advantage of being able to run hundreds of meters of cable to the display in a location remote from the mast.

Mean wind speeds over averaging periods of an hour or submultiples of an hour down to a minute or less are recorded electronically on standard reel-to-reel or cassette tape decks or recorders. Two systems are in use. The first records a frequency proportional to the wind speed on channel one and a clock pulse train on channel two. Mean wind speeds over time intervals as short as three to five seconds or as long as one month can be retrieved. The second system uses a standard cassette tape recorder to record data in an incremental digital form, using 12-bit binary numbers recorded in biphase audio tones. Averaging periods of 1, 2, 5, 15, 30, or 60 minutes may be selected. The density of data on the tape is increased by recording the data in blocks of 100 numbers out of a memory unit. All systems can be powered from the mains or from 12 V dc batteries.  


  • Roxburgh, A.J., The construction of apparatus producing kilowatt nanosecond pulses at 337.1 nm for the study of organic laser dye characteristics. Thesis, Post Grad. Dip. Sci., University of Otago, 1972 (54 pp.). (Short title: N2 Laser at 337.1 nm for the Study of Organic Laser Dyes.)

ABSTRACT: This work concerns the modification of a superradiant nitrogen laser built by Manson (1972). Project stages: 1) Redesign the laser discharge channel using demountable glass components with integral metal shield casing and cutoff waveguide for beam exit, to reduce RFI in nearby equipment by 40 to 50 dB; 2) Optimize the power output of the laser using a high-pressure (6 Atm.) spark gap instead of the original atmospheric-pressure one, together with a more powerful 60 kV 120 W adjustable power supply and end-tapered 30 MW 60 W charging resistor chain; 3) Verify power output using a self-built microstripline PIN photo diode UV detector with 1 ns sampling oscilloscope, and a commercial radiometer (peak powers of 1.4 kW at 25 Hz repetition rates were obtained); 4) Attempt to pump quartz cell filled with 0.0001 M rhodamine 6G dye into lasing.