DT Fourier Transform Properties

    DT Fourier Transform Time Reversal $  x[-n] \longleftrightarrow X(e^{-j \omega})  $ 
    DT Fourier Transform Duality $  F(x(t)) = X(w) \longleftrightarrow F(X(t)) = 2\pi x(-w)  $ 
    DT Fourier Transform Multiplication $  x[n]y[n]\longleftrightarrow \frac{1}{2\pi} \int_{2\pi} X(e^{j\theta})Y(e^{j(\omega-\theta)})d\theta  $
    DT Fourier Transform Convolution $  x[n]*y[n] = X(e^{jw})Y(e^{jw}) \!  $