The discrete-time Fourier transform is a [[frequency domain representation]] for both periodic a non-periodic signals. A discrete-time Fourier transform (DTFT) pair can be represented as: $x(n) \xrightarrow[\cal DTFT]{}X(e^{j\omega})$ The [[DTFT analysis]] equation computes the discrete-time Fourier transform $X(e^{j\omega})$ from the discrete-time signal $x(n)$: $X(e^{j \omega}) = \sum_{n=-\infty}^{+\infty} x(n) e^{-j \omega n}$ The [[DTFT synthesis]] equation recreates the discrete-time signal from the discrete-time Fourier transform: $x(n) = \frac{1}{2\pi} \int_{2\pi} X(e^{j \omega}) e^{j \omega n} d\omega$