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This is done in a general framework where the speech enhancement problem is stated as a signal vector estimation problem, i.e., with a filter matrix, where the estimate is obtained by means of a matrix-vector product of the filter matrix and the noisy signal vector. In this framework, minimum distortion, minimum variance distortionless response (MVDR), tradeoff, maximum signal-to-noise ratio (SNR), and Wiener filters are derived from the conventional speech enhancement approach and the recently introduced orthogonal decomposition approach. For each of the filters, we derive their properties in terms of output SNR and speech distortion. We then demonstrate how the ideas can be applied to single- and multichannel noise reduction in both the time and frequency domains as well as binaural noise reduction.<\/jats:p>","DOI":"10.1186\/1687-6180-2014-162","type":"journal-article","created":{"date-parts":[[2014,11,13]],"date-time":"2014-11-13T16:01:32Z","timestamp":1415894492000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A brief overview of speech enhancement with linear filtering"],"prefix":"10.1186","volume":"2014","author":[{"given":"Jacob","family":"Benesty","sequence":"first","affiliation":[]},{"given":"Mads Gr\u00e6sb\u00f8ll","family":"Christensen","sequence":"additional","affiliation":[]},{"given":"Jesper Rindom","family":"Jensen","sequence":"additional","affiliation":[]},{"given":"Jingdong","family":"Chen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,11,13]]},"reference":[{"issue":"4","key":"718_CR1","doi-asserted-by":"publisher","first-page":"1218","DOI":"10.1109\/TSA.2005.860851","volume":"14","author":"J Chen","year":"2006","unstructured":"Chen J, Benesty J, Huang Y, Doclo S: New insights into the noise reduction Wiener filter. 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