How Do You Compute the DFT of Periodic Signals?

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SUMMARY

The discussion focuses on computing the Discrete Fourier Transform (DFT) of periodic signals, specifically for sequences defined by x[n] = x[n - N] with period N. The examples provided include the Dirac delta function, a difference of unit step functions, and a cosine function. Participants emphasize the importance of understanding the DFT definition and suggest using Wikipedia as a reliable resource for foundational knowledge. The need for additional tutorials or hints is highlighted due to the absence of a textbook in the digital processing class.

PREREQUISITES
  • Understanding of Discrete Fourier Transform (DFT)
  • Familiarity with periodic sequences and their properties
  • Basic knowledge of digital signal processing concepts
  • Ability to interpret mathematical notation related to signals
NEXT STEPS
  • Study the mathematical definition of the Discrete Fourier Transform (DFT) on Wikipedia
  • Explore periodic signal properties and their implications in DFT calculations
  • Learn about the relationship between time-domain signals and their frequency-domain representations
  • Investigate tutorials on digital signal processing for practical applications of DFT
USEFUL FOR

Students in digital signal processing courses, educators teaching Fourier analysis, and anyone seeking to understand the computation of DFT for periodic signals.

ankh
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Homework Statement


Find the discrete Fourier transform X[k] = DFTn {x[n]} of the following
periodic sequences x[n] = x[n - N] with period N:

(a) For n = 0 . . .N - 1 we have x[n] =\delta[n].
(b) For n = 0 . . .N - 1 we have x[n] = \mu[n] -\mu[n - K] with K < N.
(c) x[n] = cos( (2*pi*M*n)/N ).

Homework Equations


We don't have a book for my digital processing class and i missed couple of classes so i have no idea how to start these problems. A little hint or a link to a good tutorial/source would be greatly appreciated.

The Attempt at a Solution

 
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