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-johnsonCommented Nov 16, 2015 at 6:08
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$\begingroup$ 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.Commented Nov 17, 2015 at 20:14
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$\begingroup$ 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. $\endgroup$– mkrvCommented Dec 29, 2015 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] ? $\endgroup$– mkrvCommented Dec 30, 2015 at 5:39
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