# dsp.FarrowRateConverter

Polynomial sample rate converter with arbitrary conversion factor

## Description

The `dsp.FarrowRateConverter`

System object™ implements a polynomial-fit sample rate conversion filter using a Farrow
structure. You can use this object to convert the sample rate of a signal up or down by an
arbitrary factor. This object supports fixed-point operations.

To convert the sample rate of a signal:

Create the

`dsp.FarrowRateConverter`

object and set its properties.Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

## Creation

### Syntax

### Description

creates a
polynomial filter-based sample rate converter System object, `frc`

= dsp.FarrowRateConverter`frc`

. For each channel of an input signal,
`frc`

converts the input sample rate to the output sample
rate.

sets properties using one or more name-value pairs. Enclose each property name in single
quotes. `frc`

= dsp.FarrowRateConverter(`Name,Value`

)

**Example:**

```
frc =
dsp.FarrowRateConverter('Specification','Coefficients','Coefficients',[1 2; 3
4])
```

returns a filter that converts from 44.1 kHz to 48 kHz using custom
coefficients that implement a 2nd-order polynomial filter.

returns a sample rate converter System object, `frc`

= dsp.FarrowRateConverter(`fsIn`

,`fsOut`

,`tol`

,`np`

)`frc`

, with InputSampleRate property set
to `fsIn`

, OutputSampleRate property set
to `fsOut`

, OutputRateTolerance
property set to `tol`

, and PolynomialOrder property set
to `np`

.

## Properties

## Usage

### Syntax

### Description

### Input Arguments

### Output Arguments

## Object Functions

To use an object function, specify the
System object as the first input argument. For
example, to release system resources of a System object named `obj`

, use
this syntax:

release(obj)

## Examples

## Algorithms

Farrow filters implement piecewise polynomial interpolation using Horner’s rule to compute samples from the polynomial. The polynomial coefficients used to fit the input samples correspond to the Lagrange interpolation coefficients.

Once a polynomial is fitted to the input data, the value of the polynomial can be calculated at any point. Therefore, a polynomial filter enables interpolation at arbitrary locations between input samples.

You can use a polynomial of any order to fit to the existing samples. However, since large-order polynomials frequently oscillate, polynomials of order 1, 2, 3, or 4 are used in practice.

The block computes interpolated values at the desired locations by varying only the
fractional delay, *µ*. This value is the interval between the previous
input sample and the current output sample. All filter coefficients remain constant.

The input samples are filtered using

*M*+ 1 FIR filters, where*M*is the polynomial order.The outputs of these filters are multiplied by the fractional delay,

*µ*.The output is the sum of the multiplication results.

## References

[1] Hentschel, T., and G. Fettweis. "Continuous-Time Digital Filters for Sample-Rate
Conversion in Reconfigurable Radio Terminals." *Frequenz*. Vol. 55,
Number 5-6, 2001, pp. 185–188.

## Extended Capabilities

## See Also

### Functions

`getPolynomialCoefficients`

|`getActualOutputRate`

|`getRateChangeFactors`

|`generatehdl`

|`freqz`

|`fvtool`

|`info`

|`cost`

### Objects

### Blocks

**Introduced in R2014b**