More General Real FIR Filters

So far we have looked at the design of linear phase filters. In this case, $\mathbf {A}$ , ${\underline{h}}$ and ${\underline{d}}$ are all real. In some applications, we need to specify both the magnitude and phase of the frequency response. Examples include

• minimum phase filters [263],
• inverse filters (``deconvolution''),
• fractional delay filters [266],
• interpolation polyphase subfilters (Chapter 11)

In general, these all involve complex desired frequency-response samples ( ${\underline{d}}$ complex), and the matrix $\mathbf {A}$ remains a more general Fourier transform matrix that cannot be reduced to a matrix of cosines.