Normalized DTFT Basis

The Discrete Time Fourier Transform (DTFT) is similar to the Fourier transform case:

$$\varphi _\omega (n) \isdef e^{j\omega n}/\sqrt{2\pi},\quad \omega \in (-\pi,\pi], \quad n\in (-\infty,\infty)$$ (12.114)

The inner product $\left<\varphi _\omega ,x\right>$ and reconstruction of $x(n)$ in terms of $\{\varphi _\omega \}$ are left as exercises.