Filter Design Toolbox™

allpassrateup - Allpass filter for integer upsample transformation

Syntax

[AllpassNum,AllpassDen] = allpassrateup(N)

Description

[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.

Examples

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

N = 4;

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

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');

Plot the phase response normalized to π, which is in effect the mapping function W_o(W_t):

plot(f/pi, angle(h)/pi, Wt, Wo, 'ro');
title('Mapping Function Wo(Wt)');
xlabel('New Frequency, Wt');
ylabel('Old Frequency, Wo');

While this creates the effect of upsampling your prototype filter, compare the results to cicinterp for another approach to upsampling.

Arguments

See Also

iirrateup, zpkrateup

allpasslp2xn

allpassshift