Introduction -- Single-Channel Noise Reduction with a Filtering Vector -- Single-Channel Noise Reduction with a Rectangular Filtering Matrix -- Multichannel Noise Reduction with a Filtering Vector -- Multichannel Noise Reduction with a Rectangular Filtering Matrix.

Additive noise is ubiquitous in acoustics environments and can affect the intelligibility and quality of speech signals. Therefore, a so-called noise reduction algorithm is required to mitigate the effect of the noise that is picked up by the microphones. This work proposes a general framework in the time domain for the single and multiple microphone cases, from which it is very convenient to derive, study, and analyze all kind of optimal noise reduction filters. Not only that all known algorithms can be deduced from this approach, shedding more light on how they function, but new ones can be discovered as well.