# Finite Impulse Response Filter (firfilt)

API *Keywords: *finite impulse response FIR filter firfilt firfilt_cccf firfilt_crcf firfilt_rrrf

Finite impulse response (FIR) filters are implemented in liquid with the firfilt family of objects. FIR filters (also known as **non-recursive filters** ) operate on discrete-time samples, computing the output \(y\) as the convolution of the input \(\vec{x}\) with the filter coefficients \(\vec{h}\) as

where \(\vec{h} = [h(0),h(1),\ldots,h(N-1)]\) is the filter impulse response. Notice that the output sample in the above equation is simply the vector dot product (see dotprod ) of the filter coefficients \(\vec{h}\) with the time-reversed sequence\(\vec{x}\) .

An example of the firfilt can be seen in[ref:fig-filter-firfilt_crcf] in which a low-pass filter is applied to a signal to remove a high-frequency component. An example of the firfilt interface is listed below.

```
#include <liquid/liquid.h>
int main() {
// options
unsigned int h_len=21; // filter order
float h[h_len]; // filter coefficients
// ... initialize filter coefficients ...
// create filter object
firfilt_crcf q = firfilt_crcf_create(h,h_len);
float complex x; // input sample
float complex y; // output sample
// execute filter (repeat as necessary)
{
firfilt_crcf_push(q, x); // push input sample
firfilt_crcf_execute(q,&y); // compute output
}
// destroy filter object
firfilt_crcf_destroy(q);
}
```

The full list of interfaces to the firfilt family of objects can be found in its API page .