Polyphase filter matrix for rational sampling rate conversions

The polyphase filter array has been used for efficient implementations of filters with integer sampling rate conversions. [1] The filter in the high sampling rate side is decomposed into its polyphase filters which can be moved to the lower sampling rate side without changing their functions. For FIR filters the computational complexity is reduced by a factor equal to the sampling rate ratio. A rational (L/M) sampling rate conversion system realized with a 1-to-L interpolator followed by an M-to-1 decimator has three sampling rates F, LF and (L/M)F involved. By using the polyphase filter array a filter operating at the sampling rate of LF can be implemented in either the input side or the output side with lower sampling rates. The polyphase filter matrix structure will operate at the sampling rate of F/M, which does not show in the above model and is lower than any one of those three rates. For FIR filters the computational complexity is reduced by a factor of LM compared to the direct realization of the integral filter or by a factor of M (or L) compared to the polyphase filter array realization while the system input-output relation is maintained.