Understanding the Use of Variable Notation in the DTFT

In summary, Variable notation for DTFT is a mathematical representation used to analyze and process discrete-time signals in the frequency domain. It differs from other Fourier transforms by operating on discrete signals and being defined over a finite range of frequencies. The commonly used variables in DTFT are n, x[n], and X(e^jω). Variable notation is used in practical applications to represent the input signal and its frequency domain representation, allowing for easier manipulation and analysis. However, it has limitations such as only being applicable to discrete-time signals and becoming more complex with multi-dimensional or infinite duration signals.
  • #1
Jammin_James
49
0
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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  • #2
[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).
 

1. What is variable notation for DTFT?

Variable notation for DTFT stands for variable notation for Discrete Time Fourier Transform. It is a mathematical representation used to analyze and process discrete-time signals in the frequency domain.

2. How is DTFT different from other Fourier transforms?

DTFT differs from other Fourier transforms in that it operates on discrete signals, while other transforms are used for continuous signals. DTFT is also defined over a finite range of frequencies, while other transforms are defined over an infinite range.

3. What are the commonly used variables in DTFT?

The commonly used variables in DTFT are n for the discrete time index, x[n] for the discrete-time signal, and X(e) for the DTFT of x[n] at frequency ω.

4. How is variable notation used in practical applications of DTFT?

Variable notation is used in practical applications of DTFT to represent the input signal and its corresponding frequency domain representation. It allows for easier manipulation and analysis of the signal in the frequency domain, which can provide useful insights into the characteristics of the signal.

5. Are there any limitations of using variable notation for DTFT?

One limitation of using variable notation for DTFT is that it is only applicable to discrete-time signals and cannot be used for continuous-time signals. Additionally, the notation can become more complex when dealing with multi-dimensional signals or signals with infinite duration.

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