Design of complex polyphase IIR multi-flattop filters

This paper presents an extension to our previous work on multi-flattop filter design using polyphase IIR filter structures. The previous publication addressed only the real filter case giving only an indication that the complex filters could also be designed. This paper discusses in more detail problems associated with complex flattop filter design based on the polyphase IIR structure and suggests the possible design procedures. The complex flattop filters, similarly to their real versions, achieve extremely flat weighted passbands down to micro dBs and step-like magnitude responses with transition bands completely free of crossover oscillations. The complex frequency transformations employed to control the passband edges are much simpler than for the real designs allowing much simpler implementation of the overall filter structure.