Understanding the Use of Variable Notation in the DTFT

AI Thread Summary
The discussion clarifies the use of variable notation in the Discrete-Time Fourier Transform (DTFT), specifically the distinction between capital omega (Ω) and e^(jω). Ω represents continuous frequency, which is suitable for the DTFT, while e^(jω) emphasizes the evaluation of frequency response on the unit circle. The z-transform is also mentioned as a crucial tool in digital signal processing (DSP), covering the entire complex plane. This notation helps in understanding the relationship between frequency and the DTFT. Overall, the choice of notation enhances clarity in analyzing frequency responses.
Jammin_James
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Can someone explain to me why sometimes I see the DTFT as functions of capital omegas or e^(jomega).

I'm failing to see the reason.
 
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\Omega usually refers to continuous frequency, which is often appropriate for the DTFT. The z transform is also used heavily in DSP, and it covers the full complex plane. Use of exp(j\omega) makes it very clear that you are evaluating the frequency response (which is on the unit circle).
 

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