A parallel transfer rate converter inputs first parallel data with number of samples being S1 pieces in synchronism with a first clock, and outputs second parallel data with number of samples being S2=S1(m/p) pieces (p is an integer equal to or larger than 1) in synchronism with a second clock having a frequency which is p/m times of a frequency of the first clock. A convolution operation device inputs the second parallel data in synchronism with the second clock, generates third parallel data with number of samples being S3=S2(n/m) pieces (S3 is an integer equal to or larger than 1) by executing a convolution operation with a coefficient indicating a transmission characteristic to the second parallel data, and outputs the third parallel data in synchronism with the second clock.

A parallel transfer rate converter inputs first parallel data with number of samples being S1 pieces in synchronism with a first clock, and outputs second parallel data with number of samples being S2=S1(m/p) pieces (p is an integer equal to or larger than 1) in synchronism with a second clock having a frequency which is p/m times of a frequency of the first clock. A convolution operation device inputs the second parallel data in synchronism with the second clock, generates third parallel data with number of samples being S3=S2(n/m) pieces (S3 is an integer equal to or larger than 1) by executing a convolution operation with a coefficient indicating a transmission characteristic to the second parallel data, and outputs the third parallel data in synchronism with the second clock.

Data samples are filtered by using a digital filter where the length of an impulse response of the digital filter is finite, an impulse response of the digital filter is symmetric and the operation of the digital filter is multi-rate. The method uses a polyphase decomposition to break down the input data stream into N parallel substreams and the multi-rate digital filter is separated by a polyphase decomposition into multiple lower-rate sub-filters where each of the sub-filters is separated into a set of simpler sub-sub-filters which operate upon the same set of input samples and which have impulse responses which are jointly centro-symmetric, a set of pre-filtering arithmetic structures, and a set of post-filtering arithmetic structures and performing each such pair of sub-sub-filtering operations using a single shared filter structure, a set of pre-filtering combining adders, and a set of post-filtering separating adders.