in Calculus recategorized by
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Let $x[n]=a^{\lfloor n \mid}$, ( $a$ is real, $0<a<1$ ) and the discrete time Fourier transform $\text{(DTFT)}$ of $x[n]$ is given by $X(\omega)=\sum_{n=-\infty}^{\infty} x[n] e^{-j \omega n}$. Then the $\text{DTFT}$ of $x[n]$ has which of the following properties?

  1. It goes to zero at infinite number of values of $\omega \in[-\pi, \pi]$
  2. It goes to zero only at one value of $\omega \in[-\pi, \pi]$
  3. Its maximum value is larger than $1$
  4. Its minimum value is less than $-1$
  5. None of the above
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