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Allpass filter for integer upsample transformation


[AllpassNum,AllpassDen] = allpassrateup(N)


[AllpassNum,AllpassDen] = allpassrateup(N) returns the numerator, AllpassNum, and the denominator, AllpassDen, of the Nth-order allpass mapping filter for performing the rateup frequency transformation, which creates N equal replicas of the prototype filter frequency response.

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, F1 and F2, with F1 preceding F2. Feature F1 will still precede F2 after the transformation. However, the distance between F1 and F2 will not be the same before and after the transformation.


Design the allpass filter creating the effect of upsampling the digital filter four times:

Choose any feature from an original filter, say at Wo=0.2:

N = 4;
Wo = 0.2; Wt = Wo/N + 2*[0:N-1]/N;
[AllpassNum, AllpassDen] = allpassrateup(N);

Calculate the frequency response of the mapping filter in the full range:

[h, f] = freqz(AllpassNum, AllpassDen, 'whole');



Frequency replication ratio (upsampling ratio)


Numerator of the mapping filter


Denominator of the mapping filter

Introduced in R2011a

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