2026-09-19T01:47:17Zhttps://dspace.mit.edu/server/oai/request

oai:dspace.mit.edu:1721.1/430292022-01-13T07:54:29Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022

Alan V. Oppenheim. Dey, Sourav Raj, 1980- Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science 2008-11-07T18:53:57Z 2008-11-07T18:53:57Z 2008 2008 http://hdl.handle.net/1721.1/43029 243603540 Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008. Includes bibliographical references (p. 151-153). This thesis considers the benefits of randomization in two fundamental signal processing techniques: sampling and filtering. The first part develops randomized non-uniform sampling as a method to mitigate the effects of aliasing. Randomization of the sampling times is shown to convert aliasing error due to uniform under-sampling into uncorrelated shapeable noise. In certain applications, especially perceptual ones, this form of error may be preferable. Two sampling structures with are developed in this thesis. In the first, denoted simple randomized sampling, non-white sampling processes can be designed to frequency-shape the error spectrum, so that its power is minimized in the band of interest. In the second model, denoted filtered randomized sampling, a pre-filter, post-filter, and the sampling process can be designed to further frequency-shape the error to improve performance. The thesis develops design techniques using parametric binary process models to optimize the performance of randomized non-uniform sampling. In addition, a detailed second-order error analysis, including performance bounds and results from simulation, is presented for each type of sampling. The second part of this thesis develops randomization as a method to improve the performance of multiplier-less FIR filters. Static multiplier-less filters, even when carefully designed, result in frequency distortion as compared to a desired continuous-valued filter. Replacing each static tap with a binary random process is shown to mitigate this distortion, converting the error into uncorrelated shapeable noise. As with randomized sampling, in certain applications this form of error may be preferable. This thesis presents a FIR Direct Form I randomized multiplier-less filter structure denoted binary randomized filtering (BRF). In its most general form, BRF incorporates over-sampling combined with a tapped delay-line that changes in time according to a binary vector process. (cont)The time and tap correlation of the binary vector process can be designed to improve the error performance. The thesis develops design techniques using parametric binary vector process models to do so. In addition, a detailed second-order error analysis, including performance bounds, error scaling with over-sampling, and results from simulation, is presented for the various forms of BRF. by Sourav R. Dey. Ph.D. 153 p. eng Massachusetts Institute of Technology M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 Electrical Engineering and Computer Science. Randomized sampling and multiplier-less filtering Thesis application/pdf false Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="c4045144-99cc-48b4-8c55-4ee7aa97c530"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Randomized sampling and multiplier-less filtering</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2008</PublicationDate> <Authors> <Author> <DisplayName>Dey, Sourav Raj, 1980-</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Electrical Engineering and Computer Science.</Keyword> <Abstract>This thesis considers the benefits of randomization in two fundamental signal processing techniques: sampling and filtering. The first part develops randomized non-uniform sampling as a method to mitigate the effects of aliasing. Randomization of the sampling times is shown to convert aliasing error due to uniform under-sampling into uncorrelated shapeable noise. In certain applications, especially perceptual ones, this form of error may be preferable. Two sampling structures with are developed in this thesis. In the first, denoted simple randomized sampling, non-white sampling processes can be designed to frequency-shape the error spectrum, so that its power is minimized in the band of interest. In the second model, denoted filtered randomized sampling, a pre-filter, post-filter, and the sampling process can be designed to further frequency-shape the error to improve performance. The thesis develops design techniques using parametric binary process models to optimize the performance of randomized non-uniform sampling. In addition, a detailed second-order error analysis, including performance bounds and results from simulation, is presented for each type of sampling. The second part of this thesis develops randomization as a method to improve the performance of multiplier-less FIR filters. Static multiplier-less filters, even when carefully designed, result in frequency distortion as compared to a desired continuous-valued filter. Replacing each static tap with a binary random process is shown to mitigate this distortion, converting the error into uncorrelated shapeable noise. As with randomized sampling, in certain applications this form of error may be preferable. This thesis presents a FIR Direct Form I randomized multiplier-less filter structure denoted binary randomized filtering (BRF). In its most general form, BRF incorporates over-sampling combined with a tapped delay-line that changes in time according to a binary vector process.</Abstract> <Abstract>(cont)The time and tap correlation of the binary vector process can be designed to improve the error performance. The thesis develops design techniques using parametric binary vector process models to do so. In addition, a detailed second-order error analysis, including performance bounds, error scaling with over-sampling, and results from simulation, is presented for the various forms of BRF.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>