Interpolation of Bandpass signal

Hi all,

I'm trying to figure out a way resample data points using an interpolation filter, but I want to make sure that the interpolated point is within some bandwidth range. The specific problem is as follows:

I have a bandpass noise signal:

% Design Filter
fpass = [0.4 0.6];
fstop = fpass+[-0.05 0.05];
att   = 60;
d     = fdesign.bandpass(fstop(1),fpass(1),fpass(2),fstop(2),att,1,att);
D     = design(d,'equiripple');

% Make Signal
N     = 1e3;
t     = 0:N-1;
s     = filter(D,randn(1,numel(t)));

and I want interpolate s to a new time vector:

t1    = t + 0.1*randn(size(t));
s1    = awesomeNoiseInterpFunction(s,t,t1);

For example, I want to make sure that in the interpolation of point s1(5), which is at a random place between points s(4) and s(5), the bandwidth is with the range of fstop. Basically, a random point between s(4) and s(5) such that fstop is obeyed.

Also, if anybody knows of a way to do that kind of random time vector interpolation without timeseries.m, please let me know.

Any thoughts or documents that can point me in the correct direction is greatly appreciated.