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An iterative design algorithm for the design of a new class of nonlinear phase FIR filters, with transfer function of the form , is presented. The order estimation of and 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 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.