MATLAB: VariableFractionalDelay object, what is the order of Farrow Interpolation

Question

For the "dsp.VariableFractionalDelay" object, you can select the Farrow method of interpolation. The documentation states that this uses Lagrange interpolation. What order polynomial does the Farrow method use for interpolation?

Answer 1

The Lagrange Interpolation method uses a polynomial of order (n-1) where "n" is the number of data points used for interpolation. The "dsp.VariableFractionalDelay" object has a property "FilterLength" which allows the user to specify the number of points that are used in the Lagrange interpolation. Thus if the "FilterLength" is 2 the interpolation is linear, if the "FilterLength" is 3 the interpolation is quadratic, and so on.

For background on Lagrange interpolation see the following link:

http://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html

For information on the "FilterLength" property, see the documentation page for the "dsp.VariableFractionalDelay" object below:

https://www.mathworks.com/help/dsp/ref/dsp.variablefractionaldelay-system-object.html#bsfy7ph-FilterLength