Equivalence of block and N-path implementations of digital filters

It is established that the block implementation and the multipath realizations of digital filters are equivalent. This is done by showing that the matrix transfer functions of both implementations are identical. An example to demonstrate this is provided. It is shown that the direct implementation of block realization requires considerably less hardware compared to that of multipath realizations for the same throughput rate. The second multipath scheme, even though it consists of only N transfer functions, requires much more hardware than the delayed multipath realization partly because the order of each transfer function in the second multipath realization is much higher than that in the delayed multipath realization