This book introduces readers to the novelconcept of variable span speech enhancement filters, and demonstrates how itcan be used for effective noise reduction in various ways. Further, the bookprovides the accompanying Matlab code, allowing readers to easily implement themain ideas discussed. Variable span filters combine the ideas of optimal linearfilters with those of subspace methods, as they involve the jointdiagonalization of the correlation matrices of the desired signal and thenoise. The book shows how some well-known filter designs, e.g. the minimumdistortion, maximum signal-to-noise ratio, Wiener, and tradeoff filters (includingtheir new generalizations) can be obtained using the variable span filterframework. It then illustrates how the variable span filters can be applied invarious contexts, namely in single-channel STFT-based enhancement, inmultichannel enhancement in both the time and STFT domains, and, lastly, intime-domain binaural enhancement. In these contexts, the properties of thesefilters are analyzed in terms of their noise reduction capabilities and desiredsignal distortion, and the analyses are validated and further explored insimulations.