Chapter 1 Introduction. The magnetic field lines that emerge from the polar regions extend to great distances from the earth. The auroral zone closely approximate the boundary between those field lines that are closed within the magnetosphere and those that form the geomagnetic tail. the field lines int he tail may be open or possibly joined with the interplanetary field. this introduces considerable coupling between the polar ionosphere and the distant regions of the earth's atmosphere. High energy charged particles from the sun and disturbances in the magnetosphere, therefore cause large changes in the polar ionosphere, with auroral displays and regions of increased or irregular ionisation. Increasing attention is therefore, being paid to studies of the polar ionosphere to gain some insight into the changes occurring at great heights.

Work began in March 1967 with the design and construction of the fixed interferometer (described in Chapter 2) for measuring the elevation angle of arrival of 20MHz signals from the satellite Beacon-B. Also during this first year most of the computing was completed for the theoretical calculations on ray paths presented in Chapter 5; these results along with some previously obtained experimental results form the basis of a paper accepted by Radio Science. Records were obtained from the interferometer from April 1968 to the end of the transmitting life of Beacon-B in January 1970. The analysis of the phase traces from the two aperture interferometer was complicated by the automatic antenna switching procedures; each transit had to be annotated and the useful chart delineated manually before the analysts recorded the phase at intervals of a few seconds on a semi-automatic digital recording system. The antenna switching was designed to save electronics and one channel on the chart recorder, but lead to a computer programming effort which may have been more costly in time and lost transits than the saving achieved by avoiding two separate interferometers (Chapter 2). While this programming and analysis were going on, the computing delays on the University’s overworked IBM 1130 gave time to follow up the idea of recording the fast Faraday fading on 20 MHz signals from a satellite near to or even below the horizon. This project was simplified by the availability of an easily converted 20 MHz receiver and a digital recording system. The report on this project is given in Chapter 4 and also in a short paper. The elevation angle measurements from the interferometer were converted to virtual height increment versus equivalent vertical frequency plots and thence to electron density profiles (Chapter 3, Part I). This analysis was developed from ideas given originally by Titheridge (1964). The interpretation of the resulting values of the scale height at the peak (Chapter 3, Part II) in terms of ionosphere morphology depended heavily on the total content hourly values maintained on computer disk by Dr Titheridge. The results and discussion in Chapter 3 will be presented as a separated paper. Chapter 6 is a review of the effects of the ionosphere on transmitted satellite signals and in particular gives a wider view of Faraday fading than is normally taken. Because of its general nature Chapter 6 can serve as an introduction to satellite radio propagation techniques; it appears at the end of this thesis as common ground after the diversions of Chapters 4 and 5. Since this work falls into three separate projects of ray elevation angle measurements, fast Faraday fading, and second order Faraday rotation calculations, the reports on each have been written with minimal cross referencing; this should facilitate reading but has resulted in a small amount of repetition.

The single-polynomial method for ionogram analysis is adapted to give a least-squares procedure in which the number of scaled virtual heights is greater than the number of terms in the real-height polynomial. The general principles are described in detail and the procedure is applied to the valley problem in bottomside ionogram analysis. It is shown that only a single parameter, the integrated valley ionisation, is obtainable from typical ionograms. The least-squares technique is then applied to the problem of topside ionogram analysis where the facility for using any mixture of ordinary and extraordinary ray virtual depth data is very useful. The method is shown to offer many advantages over the more traditional methods. The effects of horizontal ionisation gradients on bottomside and topside ionograms are extensively investigated by a new technique for synthesising ionograms corresponding to a given model of a moving disturbance in the ionosphere. A number of interesting and important ionogram characteristics are identified and explained. Finally, the specific problem of a large disturbance seen on total electron content records during summer nights is briefly re-examined using topside ionogram data. It is suggested that the disturbance is not primarily a topside phenomenon as originally supposed.

Chapter 1 Introduction. The magnetic field lines that emerge from the polar regions extend to great distances from the earth. The auroral zone closely approximate the boundary between those field lines that are closed within the magnetosphere and those that form the geomagnetic tail. the field lines int he tail may be open or possibly joined with the interplanetary field. this introduces considerable coupling between the polar ionosphere and the distant regions of the earth's atmosphere. High energy charged particles from the sun and disturbances in the magnetosphere, therefore cause large changes in the polar ionosphere, with auroral displays and regions of increased or irregular ionisation. Increasing attention is therefore, being paid to studies of the polar ionosphere to gain some insight into the changes occurring at great heights.

Work began in March 1967 with the design and construction of the fixed interferometer (described in Chapter 2) for measuring the elevation angle of arrival of 20MHz signals from the satellite Beacon-B. Also during this first year most of the computing was completed for the theoretical calculations on ray paths presented in Chapter 5; these results along with some previously obtained experimental results form the basis of a paper accepted by Radio Science. Records were obtained from the interferometer from April 1968 to the end of the transmitting life of Beacon-B in January 1970. The analysis of the phase traces from the two aperture interferometer was complicated by the automatic antenna switching procedures; each transit had to be annotated and the useful chart delineated manually before the analysts recorded the phase at intervals of a few seconds on a semi-automatic digital recording system. The antenna switching was designed to save electronics and one channel on the chart recorder, but lead to a computer programming effort which may have been more costly in time and lost transits than the saving achieved by avoiding two separate interferometers (Chapter 2). While this programming and analysis were going on, the computing delays on the University’s overworked IBM 1130 gave time to follow up the idea of recording the fast Faraday fading on 20 MHz signals from a satellite near to or even below the horizon. This project was simplified by the availability of an easily converted 20 MHz receiver and a digital recording system. The report on this project is given in Chapter 4 and also in a short paper. The elevation angle measurements from the interferometer were converted to virtual height increment versus equivalent vertical frequency plots and thence to electron density profiles (Chapter 3, Part I). This analysis was developed from ideas given originally by Titheridge (1964). The interpretation of the resulting values of the scale height at the peak (Chapter 3, Part II) in terms of ionosphere morphology depended heavily on the total content hourly values maintained on computer disk by Dr Titheridge. The results and discussion in Chapter 3 will be presented as a separated paper. Chapter 6 is a review of the effects of the ionosphere on transmitted satellite signals and in particular gives a wider view of Faraday fading than is normally taken. Because of its general nature Chapter 6 can serve as an introduction to satellite radio propagation techniques; it appears at the end of this thesis as common ground after the diversions of Chapters 4 and 5. Since this work falls into three separate projects of ray elevation angle measurements, fast Faraday fading, and second order Faraday rotation calculations, the reports on each have been written with minimal cross referencing; this should facilitate reading but has resulted in a small amount of repetition.

The single-polynomial method for ionogram analysis is adapted to give a least-squares procedure in which the number of scaled virtual heights is greater than the number of terms in the real-height polynomial. The general principles are described in detail and the procedure is applied to the valley problem in bottomside ionogram analysis. It is shown that only a single parameter, the integrated valley ionisation, is obtainable from typical ionograms. The least-squares technique is then applied to the problem of topside ionogram analysis where the facility for using any mixture of ordinary and extraordinary ray virtual depth data is very useful. The method is shown to offer many advantages over the more traditional methods. The effects of horizontal ionisation gradients on bottomside and topside ionograms are extensively investigated by a new technique for synthesising ionograms corresponding to a given model of a moving disturbance in the ionosphere. A number of interesting and important ionogram characteristics are identified and explained. Finally, the specific problem of a large disturbance seen on total electron content records during summer nights is briefly re-examined using topside ionogram data. It is suggested that the disturbance is not primarily a topside phenomenon as originally supposed.

Chapter 1 Introduction. The magnetic field lines that emerge from the polar regions extend to great distances from the earth. The auroral zone closely approximate the boundary between those field lines that are closed within the magnetosphere and those that form the geomagnetic tail. the field lines int he tail may be open or possibly joined with the interplanetary field. this introduces considerable coupling between the polar ionosphere and the distant regions of the earth's atmosphere. High energy charged particles from the sun and disturbances in the magnetosphere, therefore cause large changes in the polar ionosphere, with auroral displays and regions of increased or irregular ionisation. Increasing attention is therefore, being paid to studies of the polar ionosphere to gain some insight into the changes occurring at great heights.

Work began in March 1967 with the design and construction of the fixed interferometer (described in Chapter 2) for measuring the elevation angle of arrival of 20MHz signals from the satellite Beacon-B. Also during this first year most of the computing was completed for the theoretical calculations on ray paths presented in Chapter 5; these results along with some previously obtained experimental results form the basis of a paper accepted by Radio Science. Records were obtained from the interferometer from April 1968 to the end of the transmitting life of Beacon-B in January 1970. The analysis of the phase traces from the two aperture interferometer was complicated by the automatic antenna switching procedures; each transit had to be annotated and the useful chart delineated manually before the analysts recorded the phase at intervals of a few seconds on a semi-automatic digital recording system. The antenna switching was designed to save electronics and one channel on the chart recorder, but lead to a computer programming effort which may have been more costly in time and lost transits than the saving achieved by avoiding two separate interferometers (Chapter 2). While this programming and analysis were going on, the computing delays on the University’s overworked IBM 1130 gave time to follow up the idea of recording the fast Faraday fading on 20 MHz signals from a satellite near to or even below the horizon. This project was simplified by the availability of an easily converted 20 MHz receiver and a digital recording system. The report on this project is given in Chapter 4 and also in a short paper. The elevation angle measurements from the interferometer were converted to virtual height increment versus equivalent vertical frequency plots and thence to electron density profiles (Chapter 3, Part I). This analysis was developed from ideas given originally by Titheridge (1964). The interpretation of the resulting values of the scale height at the peak (Chapter 3, Part II) in terms of ionosphere morphology depended heavily on the total content hourly values maintained on computer disk by Dr Titheridge. The results and discussion in Chapter 3 will be presented as a separated paper. Chapter 6 is a review of the effects of the ionosphere on transmitted satellite signals and in particular gives a wider view of Faraday fading than is normally taken. Because of its general nature Chapter 6 can serve as an introduction to satellite radio propagation techniques; it appears at the end of this thesis as common ground after the diversions of Chapters 4 and 5. Since this work falls into three separate projects of ray elevation angle measurements, fast Faraday fading, and second order Faraday rotation calculations, the reports on each have been written with minimal cross referencing; this should facilitate reading but has resulted in a small amount of repetition.

The single-polynomial method for ionogram analysis is adapted to give a least-squares procedure in which the number of scaled virtual heights is greater than the number of terms in the real-height polynomial. The general principles are described in detail and the procedure is applied to the valley problem in bottomside ionogram analysis. It is shown that only a single parameter, the integrated valley ionisation, is obtainable from typical ionograms. The least-squares technique is then applied to the problem of topside ionogram analysis where the facility for using any mixture of ordinary and extraordinary ray virtual depth data is very useful. The method is shown to offer many advantages over the more traditional methods. The effects of horizontal ionisation gradients on bottomside and topside ionograms are extensively investigated by a new technique for synthesising ionograms corresponding to a given model of a moving disturbance in the ionosphere. A number of interesting and important ionogram characteristics are identified and explained. Finally, the specific problem of a large disturbance seen on total electron content records during summer nights is briefly re-examined using topside ionogram data. It is suggested that the disturbance is not primarily a topside phenomenon as originally supposed.

This thesis provides a thorough analysis of the theoretical foundations and properties of the Spectral Warping Transform. The spectral warping transform is defined as a time-domain-to-time-domain digital signal processing transform that shifts the frequency components of a signal along the frequency axis. The z -transform coefficients of a warped signal correspond to z -domain ‘samples’ of the original signal that are unevenly spaced along the unit circle (equivalently, frequency-domain coefficients of the warped signal correspond to frequency-domain samples of the original signal that are unevenly spaced along the frequency axis). The location of these unevenly spaced frequency-domain samples is determined by a z -domain mapping function. This function may be arbitrary, except that it must map the unit circle to the unit circle. It is shown that, in addition to the frequency location, the bandwidth, duration and amplitude of each frequency component of a signal are affected by spectral warping. Specifically, frequency components within bands that are expanded in frequency have shortened durations and larger amplitudes (conversely, components in compressed frequency bands become longer with smaller amplitudes). A property related to the expansion and compression of the duration of frequency components is that if a signal is time delayed (its digital sequence is prepended with zeroes) then each of the frequency components will have a different delay after warping. This time-domain separation phenomenon is useful for separating in time the frequency components of a signal. Such separation is employed in the generation of spectrally flat chirp signals. Because spectral warping will generally expand the duration of some frequency components within a signal, the transform must produce more output samples than there are (non-zero) input samples in order to avoid time-domain aliasing. A discussion of the necessary output signal length is presented. Particular attention is given to spectral warping using all-pass mapping function, which can be realised as a cascade of all-pass filters. There exists an efficient hardware implementation for this all-pass SW realisation [1, 2]. A proof-of-concept application-specific integrated circuit that performs the core operations required by this algorithm was developed. Another focus of the presented research is spectral warping using a piecewise- linear mapping function. This type of spectral warping has the advantage that the changes in frequency, duration and amplitude between the non-warped and warped signals are constant factors over fixed frequency bands. A matrix formulation of the spectral warping transformation is developed. It presents the spectral warping transform as a single matrix multiplication. The transform matrix is the product of the three matrices that represent three conceptual steps. The first step is to apply a discrete Fourier transform to the time-domain signal, providing the frequency-domain representation. Step two is an interpolation to produce the signal content at the desired new frequency samples. This interpolation effectively provides the frequency warping. The final step is an inverse DFT to transform the signal back into the time domain. A special case of the spectral warping transform matrix has the same result as a linear (finite-impulse-response) filter, showing that spectral warping is a generalisation of linear filtering. The conditions for the invertibility of the spectral warping transformation are derived. Several possible realisation of the SW transform are discussed. These include two realisation using parallel finite-impulse-response filter banks and a realisation that uses a cascade of infinite-impulse-response filters. Finally, examples of applications for the spectral warping transform are given. These include: non-uniform spectral analysis (and signal generation), approximate spectral analysis in the time domain, and filter design. This thesis concludes that the SW transform is a useful tool for the manipulation of the frequency content of digital signals, and is particularly useful when the frequency content of a signal (or the frequency response of a system) over a limited band is of interest. It is also claimed that the SW transform may have valuable applications for embedded mixed-signal testing.