Digital Signal Processing Basics
Which of the following is the energy E = Σ|x[n]|² of x[n] = (0.5)ⁿu[n] (0.5 to the power n for n ≥ 0, 0 for n < 0)?
- AAbout 1.33
- B2
- C4
Show answer and explanation
Answer: A. About 1.33
Energy is the sum of the squares of all samples. Since |x[n]|² = (0.25)ⁿ, the geometric series formula gives E = 1/(1 − 0.25) = 4/3 ≈ 1.33. The energy is finite, so this is an energy signal and its average power is 0.
- A. Correct. The square of (0.5)ⁿ is (0.25)ⁿ, and the sum is 1/(1 − 0.25) = 4/3.
- B. This adds the amplitudes without squaring them (1/(1 − 0.5) = 2).
- C. This squares the sum of the amplitudes, 2. The sum of squares and the square of the sum are different.