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

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  • $\begingroup$ 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. $\endgroup$ – robert bristow-johnson Nov 16 '15 at 6:08
  • $\begingroup$ 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? $\endgroup$ – Matt L. Nov 17 '15 at 20:14
  • $\begingroup$ 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. $\endgroup$ – mkrv Dec 29 '15 at 8:16
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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.

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

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