Design of Frequency Sampling Rational Rate Polyphase FIR Converter.

Frequency sampling structures are being effectively used in different signal processing applications, especially for higher filter lengths with a few non-zero samples in the passband. Although a few time domain-based polyphase Rational Sampling Rate Converter (RSRC) design approaches are available, a Frequency Sampling-based polyphase RSRC design approach has not yet been developed, and hence, it is analyzed in this presented work. In the proposed work, initially, we have derived a mathematical expression of the transfer function with real-valued parameters for the polyphase component of the FIR filter in the frequency domain. Stability analysis of the proposed filter with a radius r<1 gives better results. The work also discusses the usage of derived expressions to indicate the effect of different values of ‘r’. Thereafter, it is established that the proposed structure has a lower requirement of Multiplications Per Output Sample (MPOS). For example, in the case of M=3, L=2 and N=420 configuration by allowing 38 more Additions Per Output Sample (APOS), 24 MPOS are reduced, whereas, for M=10, L=9 and N=900 configuration just 9 more APOS enables the proposed structure eliminating 20 MPOS. Finally, the synthesis result validates the efficacy of the proposed structure.