Finite Impulse Response (FIR) Filter

An FIR filter can be implemented using the IIR filter described the above.

Since an FIR filter can be expressed as:

$$y_n = \sum_{k=0}^{M-1}{b_k x_{n-k}},$$ (4.4)

or equivalently,

$$H(z) = \frac{Y(z)}{X(z)} = \sum_{k=0}^{M-1}{b_k z^{-k}}.$$ (4.5)

So in fact, the FIR filter implementation is:

 gsl_vector* y = cl_filter_iir(b,&a.vector,x);

where a.vector is an all-one vector with length 1, e.g., $a_0=1$ , $a_k = 0,k>0$ .