Question

Are downsampling and upsampling Linear Time Invariant (LTI) systems in Digital Signal Pocessing

Answer 1

up sampling and down sampling is basically depends on time and frequency domain.

the basic methodology behind the up sampling  is to decrease the time between two instances of time ...shown in the picture.

say one signal i am giving f(x) and it will be up sampled 2 times and then it will be f(y). so the relation should be like

f(y) = f(x) * 2

so like it can be up sampled N times ; so it will look like a linearly increased system.But the time is invariant as it comes under a discrete domain. as we are putting zero's to decrease time domain as frequency will increase.

same case for down sampling ; it is also a discrete signal . because to make the frequency lesser it skips instances of time one after another.

so it is also L T I system.