Topic: Digital Signal Processing
Consider a sequence x(n) = [2, 4, 6, 8, 0, 1, 3, 5, 7, 9]. Down-sample the sequence by 3 and then up-sample by 2. The resulting sequence is:
- A. [2,0,0,0,7,0]
- B. [2,0,0,0,0,7,0,0]
- C. [2,0,8,0,3,0,9,0]
- D. [2,2,8,8,3,3,9,9]
Answer: C. [2,0,8,0,3,0,9,0]
Explanation: Given x(n) = {2, 4, 6, 8, 0, 1, 3, 5, 7, 9}. Down-sampling by 3 gives x(3n) = {2, 8, 3, 9}. Up-sampling by 2 gives x(3n/2) = {2, 0, 8, 0, 3, 0, 9}.