Guess the Periodic Signal

  • $ \sum_{n = 0}^{1} x[n] = 8 $
  • $ \sum_{n = 0}^{1} (-1)^n x[n] = 3 $
  • $ a_k = 0 $ when |k| > 1
  • The period of the DT signal x[n] = 2



Answer

x[n] with Fourier series representation (pg. 230):
$ x[n] = \sum_{k = N}^{1}a_k * e $$ (jk(2\pi /N)n $

$ \,\ a_0 = 0.5 * 8 = 4 $

$ a_1 = \frac{1}{2} \sum_{n = 0}^{1} x[n] * e $$ (-j\pi n) $ $ = \frac{3}{2} $

Final Answer:

$ \,\ x[n] = 4 + \frac{3}{2} * e $$ (-j\pi n) $

Alumni Liaison

Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett