Question

The linear filtering operation followed by down sampling on x(n) is not time invariant.

(a) True

(b) False

I have been asked this question by my college director while I was bunking the class.

I need to ask this question from Decimation by a Factor D in section Multirate Digital Signal Procesing of Digital Signal Processing

Answer 1

Right option is (a) True

Easy explanation: Given the fact that x(n) produces y(m), we note that x(n-n0) does not imply y(n-n0) unless n0 is a multiple of D. Consequently, the overall linear operation, that is linear filtering followed by down sampling on x(n) is not time invariant.