# Finite Impulse Response Farrow Filter (firfarrow)

liquid implements non-recursive Farrow filters using the firfarrow family of objects. The Farrow structure is convenient for varying the group delay of a filter. The filter coefficients themselves are not stored explicitly, but are represented as a set of polynomials each with an order \(Q\) . The coefficients can be computed dynamically from the polynomial by arbitrarily specifying the fractional sample delay \(\mu\) . Listed below is the full interface to the firfarrow family of objects. While each method is listed for firfarrow_crcf , the same functionality applies to firfarrow_rrrf .

- firfarrow_crcf_create(N,Q,fc,As) creates a firfarrow object with \(N\) coefficients using a polynomial of order \(Q\) with a cutoff frequency \(f_c\) and as stop-band attenuation of \(A_s\) dB.
- firfarrow_crcf_destroy(q) destroy object, freeing all internally-allocated memory.
- firfarrow_crcf_clear(q) clear filter internal memory buffer. This does not reset the delay.
- firfarrow_crcf_print(q) prints the filter's internal state to stdout .
- firfarrow_crcf_push(q,x) push a single sample \(x\) into the filter's internal buffer.
- firfarrow_crcf_set_delay(q,mu) set fractional delay \(\mu\) of filter.
- firfarrow_crcf_execute(q,*y) computes the output sample, storing the result in \(y\) .
- firfarrow_crcf_get_length(q) returns length of the filter (number of taps)
- firfarrow_crcf_get_coefficients(q,*h) returns the internal filter coefficients, storing the result in the output vector \(\vec{h}\) .
- firfarrow_crcf_freqresponse(q,fc,*H) computes the complex response \(H\) of the filter at the normalized frequency \(f_c\) .
- firfarrow_crcf_groupdelay(q,fc) returns the group delay of the filter at the normalized frequency \(f_c\) .

Listed below is an example of the firfarrow object's interface.

```
#include <liquid/liquid.h>
int main()
{
// options
unsigned int h_len=19; // filter length
unsigned int Q=5; // polynomial order
float fc=0.45f; // filter cutoff
float As=60.0f; // stop-band attenuation [dB]
// generate filter object
firfarrow_crcf q = firfarrow_crcf_create(h_len, Q, fc, As);
// set fractional sample delay
firfarrow_crcf_set_delay(q, 0.3f);
float complex x; // input sample
float complex y; // output sample
// execute filter (repeat as necessary)
{
firfarrow_crcf_push(q, x); // push input sample
firfarrow_crcf_execute(q,&y); // compute output
}
// destroy object
firfarrow_crcf_destroy(q);
}
```

An example of the Farrow filter's group delay can be found in [fig-filter-firfarrow-groupdelay]