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Digital Signal Processing Basics

Which of the following is the average power (the mean of |x[n]|² over one period) of x[n] = 2cos(πn/4)?

  1. A2
  2. B4
  3. C16
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Answer: A. 2

The average power of a sine wave of amplitude A is A²/2, so for A = 2 it is 4/2 = 2. Averaging the squares of the 8 samples in one period (2, √2, 0, −√2, −2, −√2, 0, √2) also gives (4 + 2 + 0 + 2 + 4 + 2 + 0 + 2)/8 = 2. A periodic signal has infinite energy, so its size is expressed by its average power instead (a power signal).

  • A. Correct. A²/2 = 4/2 = 2.
  • B. This is the peak value squared (A² = 4). The mean of a squared sine wave is half the peak value squared.
  • C. This is the sum of the squares of the 8 samples in one period. The average power is this divided by the 8 samples.
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