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.