# How to find out the farrow coefficients if FIR coefficients are given?

FIR filter coefficients are known. Then what is the matlab code or function that is used to determine the corresponding farrow structure coefficients?

• it's funny, i've done fractional-sample delay filters for a variety of audio applications. i have heard of the Farrow structure but haven't bothered to use it. i think that Julius Smith might have a good place to begin. check it out. – robert bristow-johnson Nov 16 '15 at 6:08
• I'm not sure what you want to achieve. The Farrow structure is basically an implementation of an adjustable FIR filter. Often the adjustable parameter is a fractional delay, but that's not necessary. If you have designed a fixed FIR filter, there is no standard way to convert it to a Farrow structure. Which parameter should be adjustable? – Matt L. Nov 17 '15 at 20:14
• I want to design a high order FIR filter using farrow structure, where the polyphase components are expressed using the farrow structure. The variable delay μ is adjustable. – mkrv Dec 29 '15 at 8:16

There is no standard way to determine the coefficients of the Farrow structure for a given FIR filter. The Farrow structure is an implementation of a whole class of FIR filters with transfer function(s) $H_{\mu}(z)$ with a continuous control parameter $\mu$. Often this parameter $\mu$ determines a fractional delay, but it could as well be any other adjustable filter property.

The transfer function $H_{\mu}(z)$ of the Farrow structure is given by

$$H_{\mu}(z)=\sum_{k=0}^{K-1}C_k(z)\mu^k\tag{1}$$

where $C_k(z)$ are FIR transfer functions. From $(1)$, the impulse response is

$$h_{\mu}[n]=\sum_{k=0}^{K-1}c_k[n]\mu^k\tag{2}$$

So each filter coefficient (of the corresponding transversal filter structure) $h_{\mu}[n]$ is implemented as a weighted sum of coefficients $c_k[n]$. This is why there is no one-to-one mapping from given FIR filter coefficients to the coefficients of the Farrow structure.

You need to specify which filter property the parameter $\mu$ is supposed to control, and then you need to design the coefficients $c_k[n]$ of the Farrow structure accordingly.

• Is it possible to select the coefficients of a set of FIR filters as ck[n] to get hμ[n] ? – mkrv Dec 30 '15 at 5:39
• How to design ck[n] using mat lab ? – mkrv Dec 30 '15 at 8:23