Question

In a signal \( x(n) \), if ‘n’ is replaced by \( \frac{n}{3} \), then it is called ________.

• A. upsampling
• B. folded version
• C. downsampling
• D. shifted version

Hint:

If time index is divided by \( k \), it’s upsampling. If multiplied, it’s downsampling.

Answer 1

The Correct Option is A

Step 1: In discrete-time systems:
\( x(n) \rightarrow x(kn) \): downsampling
\( x(n) \rightarrow x\left(\frac{n}{k}\right) \): upsampling
Step 2: Here, replacing \( n \) by \( \frac{n}{3} \) increases the number of samples — that’s upsampling.
Step 3: For example: \[ x(n) = [1, 2, 3] \Rightarrow x\left(\frac{n}{2}\right) = [1, 0, 2, 0, 3] \] Hence, this is upsampling by 3.