discrete time interpolation

[ran_out]

i am stuck on some exercise from computer explorations in signals and systems ex. 7.2, i uploaded the relevant pages.

where can i find info about this subject, i mean taking a discrete signal, upsample it and then interpolate with a digital filter.

i am trying to implement a bandlimited interpolation of some signal sampled at
Ts = 1/2

Now i upsample it by 4, which means that i insert 3 zeros between each sample

and then i need to interpolate.

if i use linear interpoaltor (triangle wave) - no problem

my problem is with the ideal lowpass digital interpoaltor

i must be wrong somewhere - but according to my understanding - that's why i do:

1. i take hlp = (sin(Ws*t/2))/(Ws*t/2)

2. i sample it with Ti = 1/8, because after i upsample the input signal the sample time became 0.5/4 = 1/8

3. i trancate it between -2 and 2, because thats what ive been asked to do (its taken from computer exploration in signals and systems ex. 7.2)

4. my problem is that hlp = 0 for t = nTi by definition, so when i convolve it with the upsampled input, it does nothing

how should i do it right?

what am i missing here?

thanks