## Documentation Center |

Upsample IIR filter by integer factor

`[Num,Den,AllpassNum,AllpassDen] =
iirrateup(B,A,N)`

`[Num,Den,AllpassNum,AllpassDen] =
iirrateup(B,A,N)` returns the numerator and denominator
vectors, `Num` and `Den` respectively,
of the target filter being transformed from any prototype by applying
an `N`th-order rateup frequency transformation, where `N` is
the upsample ratio. Transformation creates `N` equal
replicas of the prototype filter frequency response.

It also returns the numerator, `AllpassNum`,
and the denominator, `AllpassDen`, of the allpass
mapping filter. The prototype lowpass filter is given with a numerator
specified by `B` and a denominator specified by `A`.

The relative positions of other features of an original filter
do not change in the target filter. This means that it is possible
to select two features of an original filter, F_{1} and
F_{2}, with F_{1} preceding
F_{2}. Feature F_{1} will
still precede F_{2} after the transformation.
However, the distance between F_{1} and F_{2} will
not be the same before and after the transformation.

Design a prototype real IIR halfband filter using a standard elliptic approach:

[b, a] = ellip(3, 0.1, 30, 0.409); [num, den] = iirrateup(b, a, 4);

Verify the result by comparing the prototype filter with the target filter:

fvtool(b, a, num, den);

As shown in the figure produced by FVTool, the transformed filter appears as expected.

Variable | Description |
---|---|

B | Numerator of the prototype lowpass filter |

A | Denominator of the prototype lowpass filter |

N | Frequency multiplication ratio |

Num | Numerator of the target filter |

Den | Denominator of the target filter |

AllpassNum | Numerator of the mapping filter |

AllpassDen | Denominator of the mapping filter |

Was this topic helpful?