The most general case--a TDL having a tap after every delay element--is the general causal Finite Impulse Response (FIR) filter, shown in Fig.2.22. It is restricted to be causal because the output may not depend on ``future'' inputs , , etc. The FIR filter is also called a transversal filter. FIR filters are described in greater detail in .
The difference equation for the th-order FIR filter in Fig.2.22 is, by inspection,
and the transfer function is
The STK class for implementing arbitrary direct-form FIR filters is called Fir. (There is also a class for IIR filters named Iir.) In Matlab and Octave, the built-in function filter is normally used.