Meaning of continuous frequency domain

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SUMMARY

The discussion focuses on the meaning of "continuous frequency domain" in the context of discrete-time transforms, specifically the Discrete-Time Fourier Transform (DTFT) and the Z-transform. In a discrete domain, functions are defined only at integer values, while in a continuous domain, they are defined at real or complex values. The conversation highlights the distinction between the DTFT and the Discrete Fourier Transform (DFT), emphasizing the mapping from discrete to discrete domains. The participants also express interest in the applications of various transform methods in signal processing.

PREREQUISITES
  • Understanding of Discrete-Time Fourier Transform (DTFT)
  • Familiarity with Z-transform concepts
  • Basic knowledge of signal processing principles
  • Mathematical foundations related to frequency domains
NEXT STEPS
  • Research the applications of the Discrete-Time Fourier Transform (DTFT) in signal analysis
  • Explore the Z-transform and its role in system stability analysis
  • Study the differences between the Discrete Fourier Transform (DFT) and the DTFT
  • Investigate various transform methods listed on the Wikipedia page for transforms
USEFUL FOR

This discussion is beneficial for students and professionals in signal processing, mathematicians interested in transforms, and anyone seeking to deepen their understanding of discrete-time analysis methods.

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Homework Statement



Discrete-time transforms

What does it mean when it says this :
These transforms have a continuous frequency domain:

Discrete-time Fourier transform
Z-transform


What is the meaning of continuous frequency domain..?
 
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So in a discrete domain the functions are only defined at integer values of the independent variables.

For the continuous domain the functions are defined at real number values (or complex values in the case of the z-domain).

For an example of a transformation that maps from a discrete domain to another discrete domain read about the Discrete Fourier Transform (as oppose to the Discrete TIME Fourier Transform).

Does that help at all? Sorry, I am not very good at explaining stuff.

I bet the math guys/gals in here are going to get onto me for trying to explain this so sloppily!

Are you studying signal processing or just math?
 
Last edited:
I am studying both. But I like the answer to be inclined more towards Signals.
Also I looked at different transform methods. Can anybody tell me where all http://en.wikipedia.org/wiki/List_of_transforms" transform methods are used?
 
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