<p>In this dissertation, two filter banks optimization problems are studied. The first problem is the optimization of filter banks used in a subband coder under a bit constraint. In the second problem, a multiple input multiple output communication system is optimized under a power constraint. Three different cases on the filter lengths are considered: unconstrained length filter banks, transforms, and finite impulse response filter banks with arbitrary given filter lengths. </p><p>In source coding and multiple input multiple output communication systems, transforms and filter banks are used to decompose the source in order to generate samples that are partly decorrelated. Then, they are more suitable for source coding or transmission over a channel than the original source samples. Most transformers and filter banks that are studies in the literature have the perfect reconstruction property. In this dissertation, the perfect reconstruction condition is relaxed, so that the transforms and filter banks are allowed to belong to larger sets, which contain perfect reconstruction transforms and filter banks as subsets. </p><p>Jointly optimal analysis and synthesis filter banks and transforms are proposed under the bit and power constraints for all the three filter length cases. For a given number of bits used in the quantizers or for a given channel with a maximum allowable input power, the analysis and synthesis transforms and filter banks are jointly optimized such that the mean square error between the original and decoded signal is minimized. Analytical expressions are obtained for unconstrained length filter banks and transforms, and an iterative numerical algorithm is proposed in the finite impulse response filter bank case. </p><p>The channel in the communication problem is modelled as a known multiple input multiple output transfer matrix with signal independent additive vector noise having known second order statistics. A pre- and postprocessor containing modulation is introduced in the unconstrained length filter bank system with a power constraint. It is shown that the performance of this system is the same as the performance of the power constrained transform coder system when the dimensions of the latter system approach infinity.</p><p>In the source coding problem, the results are obtained with different quantization models. In the simplest model, the subband quantizers are modelled as additive white signal independent noise sources. The proposed unconstrained length filter banks, and it is shown that the proposed transform has better performance than the Karhunen-Loève transform. Also, the proposed transform coder has the same performance as a transform coder using a reduced rank Karhunen- Loève analysis transform with jointy optimal bit allocation and Wiener synthesis transform. The proposed finite impulse response filter banks have at least as good theoretical rate distortion performance as the perfect reconstruction filter banks and the finite impulse response Wiener filter banks used in the comparison. </p><p>A practical coding system is introduced where the coding of the subband signals is performed by uniform threshold quantizers using the centroids as representation levels. It is shown that there is a mismatch between the theoretical and practical results. Three methods for removing this mismatch are introduced. In the two first methods, the filter banks them selves are unchanged, but the coding method of the subband signals is changed. In the first of these two methods, quantizers are derived such that the additive coding noise and subband signals are uncorrelated. Subtractive dithering is the second method used for coding of the subband signals. In the third method, a signal dependent colored noise model is introduced, and this model is used to redesign the filter banks. In all three methods, good correspondence is achieved between the theoretical and practical results, and comparable or better practical rate distortion performance is achieved by the proposed methods compared to systems using perfect reconstruction filter banks and finite impulse response Wiener synthesis filter banks. </p><p>Finally, conditions for when finite impulse response filter banks are optimal are derived. </p>

In this dissertation, two filter banks optimization problems are studied. The first problem is the optimization of filter banks used in a subband coder under a bit constraint. In the second problem, a multiple input multiple output communication system is optimized under a power constraint. Three different cases on the filter lengths are considered: unconstrained length filter banks, transforms, and finite impulse response filter banks with arbitrary given filter lengths. In source coding and multiple input multiple output communication systems, transforms and filter banks are used to decompose the source in order to generate samples that are partly decorrelated. Then, they are more suitable for source coding or transmission over a channel than the original source samples. Most transformers and filter banks that are studies in the literature have the perfect reconstruction property. In this dissertation, the perfect reconstruction condition is relaxed, so that the transforms and filter banks are allowed to belong to larger sets, which contain perfect reconstruction transforms and filter banks as subsets. Jointly optimal analysis and synthesis filter banks and transforms are proposed under the bit and power constraints for all the three filter length cases. For a given number of bits used in the quantizers or for a given channel with a maximum allowable input power, the analysis and synthesis transforms and filter banks are jointly optimized such that the mean square error between the original and decoded signal is minimized. Analytical expressions are obtained for unconstrained length filter banks and transforms, and an iterative numerical algorithm is proposed in the finite impulse response filter bank case. The channel in the communication problem is modelled as a known multiple input multiple output transfer matrix with signal independent additive vector noise having known second order statistics. A pre- and postprocessor containing modulation is introduced in the unconstrained length filter bank system with a power constraint. It is shown that the performance of this system is the same as the performance of the power constrained transform coder system when the dimensions of the latter system approach infinity. In the source coding problem, the results are obtained with different quantization models. In the simplest model, the subband quantizers are modelled as additive white signal independent noise sources. The proposed unconstrained length filter banks, and it is shown that the proposed transform has better performance than the Karhunen-Loève transform. Also, the proposed transform coder has the same performance as a transform coder using a reduced rank Karhunen- Loève analysis transform with jointy optimal bit allocation and Wiener synthesis transform. The proposed finite impulse response filter banks have at least as good theoretical rate distortion performance as the perfect reconstruction filter banks and the finite impulse response Wiener filter banks used in the comparison. A practical coding system is introduced where the coding of the subband signals is performed by uniform threshold quantizers using the centroids as representation levels. It is shown that there is a mismatch between the theoretical and practical results. Three methods for removing this mismatch are introduced. In the two first methods, the filter banks them selves are unchanged, but the coding method of the subband signals is changed. In the first of these two methods, quantizers are derived such that the additive coding noise and subband signals are uncorrelated. Subtractive dithering is the second method used for coding of the subband signals. In the third method, a signal dependent colored noise model is introduced, and this model is used to redesign the filter banks. In all three methods, good correspondence is achieved between the theoretical and practical results, and comparable or better practical rate distortion performance is achieved by the proposed methods compared to systems using perfect reconstruction filter banks and finite impulse response Wiener synthesis filter banks. Finally, conditions for when finite impulse response filter banks are optimal are derived.

<p>In a traditional communication system, the coding process is divided into source coding and channel coding. Source coding is the process of compressing the source signal, and channel coding is the process of error protection. It can be shown that with no delay or complexity constraints and with exact knowledge of the source and channel properties, optimal performance can be obtained with separate source and channel coding. However, joint source-channel coding can lead to performance gains under complexity or delay constraints and offer robustness against unknown system parameters.</p><p>Multiple description coding is a system for generating two (or more) descriptions of a source, where decoding is possible from either description, but decoding of higher quality is possible if both descriptions are available. This system has been proposed as a means for joint source-channel coding. In this dissertation, the multiple description coding is used to protect against loss of data in an error correcting code caused by a number of channel errors exceeding the correcting ability of the channel code. This is tried on three channel models: a packet erasure channel, a binary symmetric channel, and a block fading channel, and the results obtained with multiple description coding is compared against traditional single description coding. The results show that if a long-term average mean square error distortion measure is used, multiple description coding is not as good as single description coding, except when the delay or block error rate of the channel code is heavily constrained.</p><p>A direct source-channel mapping is a mapping from amplitude continuous source symbols to amplitude continuous channel symbols, often involving a dimension change. A hybrid scalar quantizer-linear coder (HSQLC) is a direct source-channel mapping where the memoryless source signal is quantized using a scalar quantizer. The quantized value is transmitted on an analog channel using one symbol which can take as many levels as the quantizer, and the quantization error is transmitted on the same channel by means of a simple linear coder. Thus, there is a bandwidth expansion, two channel symbols are produced per source symbol. The channel is assumed to have additive white Gaussian noise and a power constraint. The quantizer levels and the distribution of power between the two symbols are optimized for different source distributions. A uniform quantizer with an appropriate step size gives a performance close to the optimized quantizer both for a Gaussian, a Laplacian, and a uniform memoryless source. The coder performs well compared to other joint source-channel coders, and it is relatively robust against variations in the channel noise level.</p><p>A previous image coder using direct source-channel mappings is improved. This coder is a subband coder where a classification following the decorrelating filter bank assigns mappings of different rates to different subband samples according to their importance. Improvements are made to practically all the parts of the coder, but the most important one is that the mappings are changed, and particularly, the bandwidth expanding HSQLC is introduced. The coder shows large improvements compared to the previous version, especially at channel qualities near the design quality. For poor channels or high rates, the HSQLC provides a large portion of the improvement. The coder is compared against a combination of a JPEG 2000 coder and a good channel code, and the performance is competitive with the reference, while the robustness against an unknown channel quality is largely improved. This kind of robustness is very important in broadcasting and mobile communications. </p> / <p>I tradisjonelle kommunikasjonssystemer kan kodingen deles inn i kildekoding (kompresjon) og kanalkoding (feilbeskyttelse). Disse operasjonene kan ses i sammenheng, og kombinert kilde- og kanalkoding kan gi forbedringer ved begrenset kompleksitet eller forsinkelse, og øke robustheten mot ukjente systemparametre. I avhandlingen vurderes to metoder. I den første er kilde- og kanalkodingen fortsatt delvis separat, men kildekoden er gjort robust mot dekodingsfeil i kanalkoden. Dette gjøres ved flerbeskrivelseskoding (multiple description coding), der kildesignalet representeres med to beskrivelser. Dekoding er mulig fra hver beskrivelse isolert, men høyere kvalitet kan oppnås hvis begge beskrivelsene er tilgjengelig. Ved sammenligning med et tradisjonelt system viser det seg at med hensyn på midlere kvadratisk avvik er flerbeskrivelseskoding som regel mindre bra enn et tradisjonelt system. Direkte kilde-til-kanal-avbildninger er avbildninger fra amplitudekontinuerlige kildesymboler direkte til amplitudekontinuerlige kanalsymboler. En slik metode blir lansert. Der skalarkvantiseres kildesignalet, som antas minneløst, og overføres med ett symbol på en analog kanal, mens kvantiseringsfeilen overføres analogt på den samme kanalen. Systemparametrene blir optimalisert for forskjellige kilder og kanalkvaliteter. Denne koderen gir bra ytelse sammenlignet med andre kombinerte kilde- og kanalkodere, og den er relativt robust mot variasjoner i støynivået på kanalen. Direkte kilde-til-kanal-avbildninger anvendes i en delbåndskoder for stillbilder. Denne koderen, som er basert på tidligere arbeider, blir sammenlignet med en kombinasjon av en JPEG 2000-koder og en god kanalkode, og ytelsen er omtrent like bra som referansen, samtidig som robustheten mot ukjent kanalkvalitet har økt kraftig. Denne typen robusthet er svært viktig i kringkasting og mobilkommunikasjon.</p>

In a traditional communication system, the coding process is divided into source coding and channel coding. Source coding is the process of compressing the source signal, and channel coding is the process of error protection. It can be shown that with no delay or complexity constraints and with exact knowledge of the source and channel properties, optimal performance can be obtained with separate source and channel coding. However, joint source-channel coding can lead to performance gains under complexity or delay constraints and offer robustness against unknown system parameters. Multiple description coding is a system for generating two (or more) descriptions of a source, where decoding is possible from either description, but decoding of higher quality is possible if both descriptions are available. This system has been proposed as a means for joint source-channel coding. In this dissertation, the multiple description coding is used to protect against loss of data in an error correcting code caused by a number of channel errors exceeding the correcting ability of the channel code. This is tried on three channel models: a packet erasure channel, a binary symmetric channel, and a block fading channel, and the results obtained with multiple description coding is compared against traditional single description coding. The results show that if a long-term average mean square error distortion measure is used, multiple description coding is not as good as single description coding, except when the delay or block error rate of the channel code is heavily constrained. A direct source-channel mapping is a mapping from amplitude continuous source symbols to amplitude continuous channel symbols, often involving a dimension change. A hybrid scalar quantizer-linear coder (HSQLC) is a direct source-channel mapping where the memoryless source signal is quantized using a scalar quantizer. The quantized value is transmitted on an analog channel using one symbol which can take as many levels as the quantizer, and the quantization error is transmitted on the same channel by means of a simple linear coder. Thus, there is a bandwidth expansion, two channel symbols are produced per source symbol. The channel is assumed to have additive white Gaussian noise and a power constraint. The quantizer levels and the distribution of power between the two symbols are optimized for different source distributions. A uniform quantizer with an appropriate step size gives a performance close to the optimized quantizer both for a Gaussian, a Laplacian, and a uniform memoryless source. The coder performs well compared to other joint source-channel coders, and it is relatively robust against variations in the channel noise level. A previous image coder using direct source-channel mappings is improved. This coder is a subband coder where a classification following the decorrelating filter bank assigns mappings of different rates to different subband samples according to their importance. Improvements are made to practically all the parts of the coder, but the most important one is that the mappings are changed, and particularly, the bandwidth expanding HSQLC is introduced. The coder shows large improvements compared to the previous version, especially at channel qualities near the design quality. For poor channels or high rates, the HSQLC provides a large portion of the improvement. The coder is compared against a combination of a JPEG 2000 coder and a good channel code, and the performance is competitive with the reference, while the robustness against an unknown channel quality is largely improved. This kind of robustness is very important in broadcasting and mobile communications. / I tradisjonelle kommunikasjonssystemer kan kodingen deles inn i kildekoding (kompresjon) og kanalkoding (feilbeskyttelse). Disse operasjonene kan ses i sammenheng, og kombinert kilde- og kanalkoding kan gi forbedringer ved begrenset kompleksitet eller forsinkelse, og øke robustheten mot ukjente systemparametre. I avhandlingen vurderes to metoder. I den første er kilde- og kanalkodingen fortsatt delvis separat, men kildekoden er gjort robust mot dekodingsfeil i kanalkoden. Dette gjøres ved flerbeskrivelseskoding (multiple description coding), der kildesignalet representeres med to beskrivelser. Dekoding er mulig fra hver beskrivelse isolert, men høyere kvalitet kan oppnås hvis begge beskrivelsene er tilgjengelig. Ved sammenligning med et tradisjonelt system viser det seg at med hensyn på midlere kvadratisk avvik er flerbeskrivelseskoding som regel mindre bra enn et tradisjonelt system. Direkte kilde-til-kanal-avbildninger er avbildninger fra amplitudekontinuerlige kildesymboler direkte til amplitudekontinuerlige kanalsymboler. En slik metode blir lansert. Der skalarkvantiseres kildesignalet, som antas minneløst, og overføres med ett symbol på en analog kanal, mens kvantiseringsfeilen overføres analogt på den samme kanalen. Systemparametrene blir optimalisert for forskjellige kilder og kanalkvaliteter. Denne koderen gir bra ytelse sammenlignet med andre kombinerte kilde- og kanalkodere, og den er relativt robust mot variasjoner i støynivået på kanalen. Direkte kilde-til-kanal-avbildninger anvendes i en delbåndskoder for stillbilder. Denne koderen, som er basert på tidligere arbeider, blir sammenlignet med en kombinasjon av en JPEG 2000-koder og en god kanalkode, og ytelsen er omtrent like bra som referansen, samtidig som robustheten mot ukjent kanalkvalitet har økt kraftig. Denne typen robusthet er svært viktig i kringkasting og mobilkommunikasjon.

<p>This study was initiated to investigate if it could be feasible to supply offshore oil installations in the North Sea with electrical power from land. A prestudy of alternative converter topologies indicated that the most promising solution would be to investigate a conventional system with reduced synchronous compensator rating.</p><p>The study starts with a summary of the state of power supply to offshore installations today, and a short review of classical HVDC transmission. It goes on to analyse how a passive network without sources influences the inverter. The transmission, with its current controlled rectifier and large inductance, is simulated as a current source. Under these circumstances the analysis shows that the network frequency has to adapt in order to keep the active and reactive power balance until the controllers are able to react. The concept of firing angle for a thyristor is limited in a system with variable frequency, the actual control parameter is the firing delay time.</p><p>Sensitivity analysis showed some astonishing consequences. The frequency rises both by an increase in the active and in the reactive load. The voltage falls by an increase in the active load, but rises by an increase in the inductive load.</p><p>Two different control principles for the system of inverter, synchronous compensator and load are defined. The first takes the reference for the firing delay time from the fundamental voltage at the point of common coupling. The second takes the reference for the firing delay time from the simulated EMF of the synchronous compensator. Of these, the second is the more stable and should be chosen as the basis for a possible control system.</p><p>Two simulation tools are applied. The first is a quasi-phasor model running on Matlab with Simulink. The other is a time domain model in KREAN. The time domain model is primarily used for the verification of the quasi-phasor model, and shows that quasi-phasors is still a valuable tool for making a quick analysis of the main features when the details of the transients are of less importance.</p><p>The study indicates that power supply by HVDC transmission from land to offshore oil installations could be technically feasible, even without the large synchronous compensators normally required. It has been shown that in a network only supplied by an inverter, variations of active and reactive loads have significant influence on both voltage and frequency. Particularly it should be noted that the frequency shows a positive sensitivity to increases in load. This could make the system intrinsically unstable in the case of a frequency dependent load such as motors.</p><p>It was not a part of the study to optimize controllers, but even with simple controllers it was possible to keep the frequency within limits given by norms and regulations, but the voltages were dynamically outside the limits, though not very far. These voltage overswings take place in the first few instances after a disturbance, so it takes unrealistically fast controllers to handle them. They are partly due to the model, where the land based rectifier and the DC reactors are simulated by a constant current source, but partly they have to be handled by overdimensioning of the system.</p><p>The simulations indicate that it should be technically possible to supply an oil platform with electrical power from land by means of HVDC transmission with small synchronous compensators. Whether this is financially feasible has not been investigated. Neither has it been considered whether the necessary equipment can actually be installed on an oil platform.</p><p>Recently both ABB and Siemens have presented solutions for HVDC transmission in the lower and medium power range based on voltage source converters based on IGBTs. Fully controllable voltage source HVDC converters have properties that may be better suited than conventional line commutated current source thyristor inverters, to supply weak or passive networks, such as offshore oil installations, with electrical power. But they also have some disadvantages, and a complete technical and financial comparison must be performed in order to decide about any potential project.</p>

This study was initiated to investigate if it could be feasible to supply offshore oil installations in the North Sea with electrical power from land. A prestudy of alternative converter topologies indicated that the most promising solution would be to investigate a conventional system with reduced synchronous compensator rating. The study starts with a summary of the state of power supply to offshore installations today, and a short review of classical HVDC transmission. It goes on to analyse how a passive network without sources influences the inverter. The transmission, with its current controlled rectifier and large inductance, is simulated as a current source. Under these circumstances the analysis shows that the network frequency has to adapt in order to keep the active and reactive power balance until the controllers are able to react. The concept of firing angle for a thyristor is limited in a system with variable frequency, the actual control parameter is the firing delay time. Sensitivity analysis showed some astonishing consequences. The frequency rises both by an increase in the active and in the reactive load. The voltage falls by an increase in the active load, but rises by an increase in the inductive load. Two different control principles for the system of inverter, synchronous compensator and load are defined. The first takes the reference for the firing delay time from the fundamental voltage at the point of common coupling. The second takes the reference for the firing delay time from the simulated EMF of the synchronous compensator. Of these, the second is the more stable and should be chosen as the basis for a possible control system. Two simulation tools are applied. The first is a quasi-phasor model running on Matlab with Simulink. The other is a time domain model in KREAN. The time domain model is primarily used for the verification of the quasi-phasor model, and shows that quasi-phasors is still a valuable tool for making a quick analysis of the main features when the details of the transients are of less importance. The study indicates that power supply by HVDC transmission from land to offshore oil installations could be technically feasible, even without the large synchronous compensators normally required. It has been shown that in a network only supplied by an inverter, variations of active and reactive loads have significant influence on both voltage and frequency. Particularly it should be noted that the frequency shows a positive sensitivity to increases in load. This could make the system intrinsically unstable in the case of a frequency dependent load such as motors. It was not a part of the study to optimize controllers, but even with simple controllers it was possible to keep the frequency within limits given by norms and regulations, but the voltages were dynamically outside the limits, though not very far. These voltage overswings take place in the first few instances after a disturbance, so it takes unrealistically fast controllers to handle them. They are partly due to the model, where the land based rectifier and the DC reactors are simulated by a constant current source, but partly they have to be handled by overdimensioning of the system. The simulations indicate that it should be technically possible to supply an oil platform with electrical power from land by means of HVDC transmission with small synchronous compensators. Whether this is financially feasible has not been investigated. Neither has it been considered whether the necessary equipment can actually be installed on an oil platform. Recently both ABB and Siemens have presented solutions for HVDC transmission in the lower and medium power range based on voltage source converters based on IGBTs. Fully controllable voltage source HVDC converters have properties that may be better suited than conventional line commutated current source thyristor inverters, to supply weak or passive networks, such as offshore oil installations, with electrical power. But they also have some disadvantages, and a complete technical and financial comparison must be performed in order to decide about any potential project.