Saturday, April 7, 2018

fourier transform - why do we use X(ejomega) instead of X(jomega) in Discrete Time FT


I am studying DT-FT. But I cannot figure out why we use X(ejω) instead of X(jω) in DT FT



Thanks in advance..



Answer



The argument ejω emphasizes the 2π-periodicity of the discrete-time Fourier transform (DTFT) of a sequence. Furthermore, if the Z-transform X(z) of the sequence x[n] exists and if the unit circle |z|=1 is inside the region of convergence, then the DTFT of the sequence is simply obtained by evaluating X(z) on the unit circle z=ejω.


That's the same thing as with the continuous Fourier transform and the Laplace transform, referred to in your previous question.


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