Relations between thek-dimensional unconstrained and linear phase FIR Wiener filters

In this note, we show that thek-dimensional linear phase FIR Wiener filter can be obtained from the unconstrained filter with a simple reverse and add operation. The relation between the linear phase and unconstrained phase filters is obtained also in the case of a multichannelk-dimensional system. In this case, the properties of the autocorrelation matrix do not allow the simplifications noted for the single channel case.