Streaming orthogonal prediction filter in - domain for random noise attenuation |

The Sherman-Morrison formula can be derived directly by solving the linear problem as

where is a column vector and is a row vector. Assuming is already known, we pre-multiply equation A-1 by and denote and to give

Because is a scalar quantity, we can denote it as . To find , we pre-multiply the equation A-2 by to give

Since and in the equation A-3 are scalars, one can easily solve for to get

Thus the solution can be written as

We then obtain the Sherman-Morrison formula

Streaming orthogonal prediction filter in - domain for random noise attenuation |

2019-05-06