University of Waterloo
http://hdl.handle.net/10012/1
The University of Waterloo institution-wide UWSpace community.Sun, 14 Oct 2018 11:43:30 GMT2018-10-14T11:43:30ZLearning Sparse Orthogonal Wavelet Filters
http://hdl.handle.net/10012/13998
Learning Sparse Orthogonal Wavelet Filters
Recoskie, Daniel
The wavelet transform is a well studied and understood analysis technique used in signal processing. In wavelet analysis, signals are represented by a sum of self-similar wavelet and scaling functions. Typically, the wavelet transform makes use of a fixed set of wavelet functions that are analytically derived. We propose a method for learning wavelet functions directly from data. We impose an orthogonality constraint on the functions so that the learned wavelets can be used to perform both analysis and synthesis. We accomplish this by using gradient descent and leveraging existing automatic differentiation frameworks. Our learned wavelets are able to capture the structure of the data by exploiting sparsity. We show that the learned wavelets have similar structure to traditional wavelets.
Machine learning has proven to be a powerful tool in signal processing and computer vision. Recently, neural networks have become a popular and successful method used to solve a variety of tasks. However, much of the success is not well understood, and the neural network models are often treated as black boxes. This thesis provides insight into the structure of neural networks. In particular, we consider the connection between convolutional neural networks and multiresolution analysis. We show that the wavelet transform shares similarities to current convolutional neural network architectures. We hope that viewing neural networks through the lens of multiresolution analysis may provide some useful insights.
We begin the thesis by motivating our method for one-dimensional signals. We then show that we can easily extend the framework to multidimensional signals. Our learning method is evaluated on a variety of supervised and unsupervised tasks, such as image compression and audio classification. The tasks are chosen to compare the usefulness of the learned wavelets to traditional wavelets, as well as provide a comparison to existing neural network architectures. The wavelet transform used in this thesis has some drawbacks and limitations, caused in part by the fact that we make use of separable real filters. We address these shortcomings by exploring an extension of the wavelet transform known as the dual-tree complex wavelet transform. Our wavelet learning model is extended into the dual-tree domain with few modifications, overcoming the limitations of our standard model. With this new model we are able to show that localized, oriented filters arise from natural images.
Fri, 12 Oct 2018 00:00:00 GMThttp://hdl.handle.net/10012/139982018-10-12T00:00:00ZSuite Talk: The Barriers and Opportunities of Providing Secondary Suites in Rural Metro-Adjacent Regions of Eastern Ontario
http://hdl.handle.net/10012/13997
Suite Talk: The Barriers and Opportunities of Providing Secondary Suites in Rural Metro-Adjacent Regions of Eastern Ontario
Caletti, Montana
Providing an adequate supply of affordable housing has become an increasing challenge for Ontario municipalities. As a result, changes were made to the Planning Act requiring all Ontario municipalities to implement provisions to permit secondary suites within their zoning bylaws, and official plans. While the implementation of these changes expanded the opportunities for municipalities to increase the supply of affordable housing, several barriers were also encountered.
The topic of secondary suites is most frequently studied from an urban perspective. However, given the unique characteristics, and prevailing conditions commonly found in rural communities, these areas impose distinct planning considerations that must be approached differently than urban areas. Therefore, this study examined the opportunities and constraints experienced throughout the implementation of secondary suites by rural metro-adjacent municipalities in Eastern Ontario.
The opportunities revealed through the study included: diversifying the existing housing stock, providing supplementary income to homeowners, making better use of existing infrastructure, providing a means for homeowners to aide family members, and increasing municipal control over secondary suite rental housing. Barriers were identified as: servicing issues, the older age and existing condition of homes, a lack of education among the community, limited planning resources, community resistance to change, personnel changes, difficulties adhering to building codes, and a lack of demand for rental purposes. Additionally, the research uncovered several measures that rural communities can use to increase the presence of secondary suites moving forward. These include: the creation of educational materials, continuing to explore funding opportunities, maintaining positive community relationships, increasing communication between departments, sharing best practices, and the continued promotion of secondary suites throughout communities.
Fri, 12 Oct 2018 00:00:00 GMThttp://hdl.handle.net/10012/139972018-10-12T00:00:00ZElectromagnetic Energy Harvesting Surfaces
http://hdl.handle.net/10012/13996
Electromagnetic Energy Harvesting Surfaces
Ashoor, Ahmed Z.
The concept of wireless power transfer (WPT) was successfully demonstrated in the early years of the 20th century. One promising application of using the WPT concept is the WPT transmission utilizing a large array of solar cells outside the earth's atmosphere to collect solar energy and then converts it to microwave power for transmission to earth using highly directive antennas. Space solar power SSP transmission concept may play an important role in the near future in harvesting clean and sustainable energy from space. The SSP concept calls for the large rectenna (i.e., antennas and rectifying circuitry) arrays farms that receive the microwave power that is transmitted from space and convert it into usable DC power. To obtain high power and high output voltage, the use of a large rectenna array is necessary, and hence the focus of this thesis is on improving the harvesting efficiency of rectenna systems.
The two main figures of merit to evaluate a WPT rectenna system are the radiation to AC efficiency, and the radiation to DC efficiency. The latter combines the efficiencies of the electromagnetic energy collectors or antenna, and that of the rectifying circuitry. In the progress towards improving the efficiency of a rectenna array system, efforts were heavily focused on improving the AC to DC conversion efficiencies. However, in most previous works, efforts to improve the efficiency of the antennas were not pursued. The majority of rectennas were in fact designed using conventional antennas because of their wide use in modern communications technologies but not for their particular ability or suitability to efficiently harvest electromagnetic radiation.
The first part of this thesis introduces, for the first time, the use of dielectric resonator antenna (DRA) in an array form as an energy harvester. A single DRA and a 1x3 array were used to build foundation profiles for using DRAs in an array form as an energy harvester. The proposed structures were designed and fabricated to maximize energy reception around 5.5 GHz. The size of the ground plane and coupling between dielectric resonator (DR) elements in an array were studied with special focus on the overall efficiency of the antenna structure for different incident polarizations. A 5x5 array was built and tested numerically and experimentally. Measurements showed that energy absorption efficiency as high as 67% can be achieved using an array of DRAs. Then an extension of this finding was carried out considering the DRA's fabrication challenges. A complementary DRAs structure consisting of DR blocks backed by cut grounds is proposed. It was shown through numerical simulations that the complementary DR blocks resonator can efficiently deliver the incident power carried by an electromagnetic wave to a load with an efficiency of 80%.
The concept of using an electromagnetic energy harvesting surface (EHS) structure is introduced in the second part of this thesis. A design of an electromagnetic EHS inspired by an array of printed metallic dipolar elements is introduced. The unit cell of the EHS is based on two printed asymmetric off-center fed dipoles. As a proof of concept, a finite array of 9x3 unit cells was analyzed numerically and experimentally to work at 3 GHz. The array was first analyzed for maximizing radiation to AC absorption where each dipole was terminated by a resistor across its gap. An overall radiation to DC harvesting efficiency of 76% was obtained experimentally.
The third part of this dissertation presents a design for a multi-polarization electromagnetic EHS inspired by a multi-layer unit cell of printed asymmetrical metallic dipolar elements. The harvesting array features two layers that collectively capture the incident energy from various incident angles. The harvester was first analyzed for maximizing the radiation to AC absorption at 3 GHz where each dipole was terminated by a resistor across its energy-collecting gap. As a proof of concept, a multi-layer array consisting of 3x3 asymmetrical dipolar elements of the multi-layer unit cell was fabricated and measured experimentally. The experimental results yielded an overall radiation to DC harvesting efficiency of 70%for multiple incident polarizations.
Next, an EHS is introduced for receiving multiple polarizations while using only one metallization layer. The EHS unit cell is based on two cross-dipoles that enable capturing the energy from various angles of illuminations at an operating frequency of 3 GHz. The simulation results yielded a radiation to AC efficiency of 94% at multiple angles of polarization. For validation, a finite array of 7x7 unit cells was fabricated and tested experimentally. The experimental results of the EHS energy harvesting array show an overall radiation to DC harvesting efficiency of 74% at various polarization angles. A critical design feature of the proposed cross-dipole EHS array is that it allows direct matching to a rectifying circuitry at the dipoles plane.
The thesis concludes by introducing an efficient dual-band EHS array using two stacked-layer of cross-dipole elements for efficient harvesting at two frequency bands for multiple polarizations. The proposed EHS array introduces the concept of stacked surfaces that can be directly integrated with the rectification circuitry. The multilayer EHS array allows direct matching to a rectifying circuitry such that DC power is collected at the elements' plane for each layer. The total achieved harvested DC power is the collective contribution of the rectified DC power from the EHS's layers. A finite multi-layer array of 7x7 unit cells was fabricated and tested experimentally. The experimental results of the dual-band EHS energy harvesting array show an overall radiation to DC harvesting efficiencies of 77% and 70%, respectively, at various polarization angles at the desired operating frequencies of 2.7 GHz and 3.4 GHz.
Thu, 11 Oct 2018 00:00:00 GMThttp://hdl.handle.net/10012/139962018-10-11T00:00:00ZMultiscale GARCH Modeling and Inference
http://hdl.handle.net/10012/13995
Multiscale GARCH Modeling and Inference
Chen, Lichen
The motivation behind this thesis is the shortage of formal statistical inference methods in the literature for testing whether a time series model is consistent with a sample at multiple sampling frequencies simultaneously. Most existing statistical methods for time series data focuses on a particular frequency of sample. However, in the statistical modeling of financial time series and applications, having a modeling being consistent with data at multiple frequencies can provide better interpretation of the underlying phenomenon and provide convenience in practical applications.
Mantegna and Stanley (1995, 1996) and Ghashghaie, et.al.(1996)are among the pioneers in pointing out the distinctive scaling behavior in financial asset return distributions. Mandelbrot, et.al. (1997) explicitly pointed out the need to look at financial time series at multiple frequencies and use the scaling property of the data to help identify a model. Engle and Patton (2001) raised the question of whether a GARCH(1,1) model, acceptable for modeling return volatility at each single time scale from 1-day to 1-week, is consistent across scales.
It is the purpose of this thesis to propose formal statistical inference methods for testing whether a given time series of ARMA and GARCH type is consistent with a sample at multiple frequencies simultaneously. To do so, we first examine the problem of model temporal aggregation. Then, based on temporal aggregation relations, we propose a novel statistical inference methods based on empirical likelihood with estimating equations. The proposed method can be used to formally test hypotheses of the following types: (i) whether a model with a fixed set of parameter values is consistent with sample at multiple frequencies; (ii) whether the model itself is capable of being consistent with the sample at multiple frequencies. Some related problems on GARCH model parameterization and parameter estimation with temporally aggregated data are also addressed.
Thu, 11 Oct 2018 00:00:00 GMThttp://hdl.handle.net/10012/139952018-10-11T00:00:00Z