Could someone explain the intuition behind the variables of the FT and DTFT? Do I understand it correctly ?(adsbygoogle = window.adsbygoogle || []).push({});

For FT being [itex]X(f)[/itex], I understand that [itex]f[/itex] is a possible argument the frequency, as in number of cycles per second.

FT can be alternatively parameterized by [itex]\omega = 2 \pi f [/itex] which specified the number of cycles in radians, which results in also appending a division by [itex]2 \pi [/itex] to the transform.

For DTFT, I am told that we use the "digital frequency" [itex]\Omega[/itex] which ranges from 0 to [itex]2\pi[/itex] (or from[itex]-\pi [/itex] to [itex]\pi[/itex]). I vaguely understand that this is because of the periodicity, since [itex]X(\Omega)[/itex] is a periodic expansion of the FT.

Is that all there is? If so, why do the fourier pairs differ in the case of the FT and the DTFT?

(For example, see http://www.mechmat.ethz.ch/Lectures/tables.pdf [Broken]

I have also come accross the DTFT in the form of [itex]X(e^{j\omega})[/itex]. What's that about?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Arguments of the FT and DTFT

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**