Understanding the Use of Variable Notation in the DTFT

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SUMMARY

The discussion clarifies the use of variable notation in the Discrete-Time Fourier Transform (DTFT), specifically the distinction between capital omega (Ω) and the exponential notation e^(jω). Ω represents continuous frequency, which is suitable for the DTFT, while e^(jω) explicitly indicates evaluation on the unit circle, emphasizing frequency response. The z-transform's relevance in Digital Signal Processing (DSP) is also highlighted, as it encompasses the entire complex plane.

PREREQUISITES
  • Understanding of Discrete-Time Fourier Transform (DTFT)
  • Familiarity with complex frequency representation
  • Knowledge of z-transform in Digital Signal Processing (DSP)
  • Basic concepts of frequency response analysis
NEXT STEPS
  • Explore the properties of the Discrete-Time Fourier Transform (DTFT)
  • Study the implications of using capital omega (Ω) in frequency analysis
  • Learn about the z-transform and its applications in DSP
  • Investigate frequency response evaluation using e^(jω)
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Students and professionals in electrical engineering, signal processing practitioners, and anyone interested in understanding frequency analysis in digital systems.

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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[tex]\Omega[/tex] 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 [tex]exp(j\omega)[/tex] makes it very clear that you are evaluating the frequency response (which is on the unit circle).
 

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