A new class of nonlinear phase FIR digital filters and its application to efficient design of multirate digital filters

An iterative design algorithm for the design of a new class of nonlinear phase FIR filters, with transfer function of the form
H_{s}(z)H_{p}(z^{D})
, is presented. The order estimation of
H_{s}(z)
and
H_{p}(z^{D})
is discussed. By introducing this class of nonlinear phase FIR filters into the design of multistage decimators and interpolators for narrow band filter implementation, it is found that an efficient narrow band filter requiring considerably fewer multiplications than the conventional linear phase FIR design can be obtained due to the fact that the filter
H_{p}(z^{D})
can be realized at a lower sampling rate and due to its spectrum shaping in the stopband. It is also found that the amount of storages is reduced with respect to its linear phase counterparts. Examples are given and the performance is compared to the conventional linear phase FIR design and discussed.