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## Series and Parallel Transfer Functions

The transfer function conveniently captures the algebraic structure of a filtering operation with respect to series or parallel combination:

• Transfer functions of filters in series multiply together
If the output of filter is given as input to filter (series combination), as shown in Fig.6.1, the overall transfer function is . Thus, the transfer functions of two filters connected in series simply multiply together.7.1

• Transfer functions of parallel filters sum together
If two filters and are driven by the same input signal, and if their outputs are summed, as depicted in Fig.6.2, this is called a parallel combination of filters and . The transfer function of the parallel combination is then . This result follows immediately from linearity of the z transform.

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