Discrete-time Fourier Analysis

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SUMMARY

The discussion focuses on computing the Discrete-Time Fourier Transform (DTFT) of the signal x[n] = n(0.5)^n u[n]. The user presents their solution as 0.5 e^(-jw)/((1-0.5e^(-jw))^2), which is confirmed as correct by other participants. This topic appears to challenge many, indicating a common difficulty in understanding DTFT calculations in discrete-time signals.

PREREQUISITES
  • Understanding of Discrete-Time Signals
  • Familiarity with the Discrete-Time Fourier Transform (DTFT)
  • Knowledge of the unit step function u[n]
  • Basic complex exponential functions
NEXT STEPS
  • Study the properties of the Discrete-Time Fourier Transform (DTFT)
  • Learn about the unit step function and its applications in signal processing
  • Explore examples of DTFT calculations for various discrete-time signals
  • Investigate the relationship between DTFT and Z-transform
USEFUL FOR

Students and professionals in signal processing, electrical engineering, and applied mathematics who are looking to deepen their understanding of Fourier analysis in discrete-time systems.

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I am trying to compute the DTFT of x[n]=n(.5)^n u[n].

This is my work so far.
1.JPG


Is this correct?
 
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I see that this topic totally stumps everyone! LOL

I have solved ths with an answer of

0.5 e^(-jw)/((1-0.5e^(-jw))^2)
 

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