Simple Fourier transform problem

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Discussion Overview

The discussion revolves around a homework problem involving the Fourier transform of a specific sequence defined as x1[n] = [0.9ncos(0.6*pi*n)] * x[n-2]. Participants are attempting to determine the Fourier transform in terms of a given transform X(ejw), while grappling with the implications of the sequence's properties.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant suggests that the problem may not have a solution because the term 0.9n is not summable, implying that it does not have a Fourier transform.
  • Another participant expresses confusion about the problem, questioning whether it involves calculating the Fourier transform of a constant or a sequence of constants.
  • A later reply clarifies the wording of the problem, emphasizing that it asks for the Fourier transform of sequences in terms of X(ejw).
  • Further, another participant reiterates their confusion regarding the problem's phrasing and its implications.

Areas of Agreement / Disagreement

Participants generally express confusion about the problem statement and its requirements. There is no consensus on how to approach the problem or whether it is well-defined.

Contextual Notes

Participants highlight potential limitations in understanding the problem due to the nature of the sequence and its Fourier transform properties, particularly regarding summability and the interpretation of the sequence involved.

asdf12312
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Homework Statement


Given x[n] with transform X(ejw), find the Fourier transform in terms of X(ejw).

x1[n]=[0.9ncos(0.6*pi*n)] * x[n-2]

Homework Equations


time shift: x[n-k] -> e-jwkX(ejw)
convolution: x[n] * h[n] -> X(w)H(w)
freq. shift: x[n]ejwcn -> X(ew-wc)

The Attempt at a Solution


I think that this problem has no solution because 0.9n has no Fourier transform (not summable). 0.9nu[n] on the other hand does but not the same case here. am i doing this right?
 
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I am at a loss to understand the problem. It seems to me as if the problem is to calculate the Fourier transform of a constant - or a sequence of constants. Is that correct?
 
yeah, I guess i didn't word it correctly. what it reads exactly is 'given a sequence x[n] with Fourier transform Xejw, determine the Fourier transform of the sequences in terms of Xejw.
 
asdf12312 said:
'given a sequence x[n] with Fourier transform Xejw, determine the Fourier transform of the sequences in terms of Xejw.
Still does not make any sense to me...
 

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