Ideal interpolation filter

When using the technique of zero insertion for interpolation, one can choose any suitable filter to remove spectral copies. But there is an ideal filter for this purpose. Matlab provides the function intfilt to get this ideal.

The following code snippet compares intfilt ideal filter with a general purpose fir1 filter of same order.

clear all; close all;

%example bandlimited random input & parameters
x = filter(fir1(70,.1),1,randn(1,1024));

up = 3;             %Interpolation factor
cutoff = .3;

intorder = 6;
h1 = intfilt(up, intorder, cutoff); %ideal filter
h1 = up*h1/sum(h1);

h2 = fir1(2*up*intorder-2,cutoff);  %ordinary LPF 
h2 = up*h2/sum(h2);

%upsample
x_up = zeros(1,length(x)*up);
x_up(1:up:end) = x;

x_f1 = filter(h1,1,x_up);
x_f2 = filter(h2,1,x_up);

figure;
subplot(3,1,1);hold
plot(x_f1,'o--');
plot(x_f2,'r.-');
legend('ideal output','fir1 output');

subplot(3,1,2);
plot(x_f1-x_f2);
legend('error');

subplot(3,1,3);hold
plot(h1,'.-');
plot(h2,'r.-');
legend('ideal filter','fir1 filter');