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With the increasing growth and sophistication of information technology, personal information is easily accessible electronically. This flood of released personal data raises important privacy concerns. However, electronic data sources exist to be used and have tremendous value (utility) to their users and collectors, leading to a tension between privacy and utility. This article aims to quantify that tension by means of an information-theoretic framework and motivate signal processing approaches to privacy problems. The framework is applied to a number of case studies to illustrate concretely how signal processing can be harnessed to provide data privacy.