DTFT of x[n]

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1582251394
1582251394 2017-2-20
评论： Walter Roberson 2021-3-26
Hi, I have a given a sequence x[n] = [1 2 3 5 6 7];
I'm trying to perform a DTFT on this sequence. I can't seem to find any DTFT functions online. Should I just make my own with a for loop or something. Just multiply each value in the sequence by e^-jwn. Thanks!

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回答（3 个）

Walter Roberson
Walter Roberson 2017-2-20
Christian David
Christian David 2018-10-24
Hi, The result of the DTFT is a continuous function, so it not can be determined in a computer. The alternative is DTF, which can be calculated using FFT algorithm (available in Matlab).
  2 个评论
Walter Roberson
Walter Roberson 2018-10-25
No, by definition DTFT is Discrete Time Fourier Transform, which is a discrete function rather than a continuous function.
Christian David
Christian David 2018-10-26
编辑：Walter Roberson 2018-10-26
Dear Walter, I forgot to reference my answer:
"This is the DTFT, the procedure that changes a discrete aperiodic signal in the time domain into a frequency domain that is a continuous curve. In mathematical terms, a system's frequency response is found by taking the DTFT of its impulse response. Since this cannot be done in a computer, the DFT is used to calculate a sampling of the true frequency response. This is the difference between what you do in a computer (the DFT) and what you do with mathematical equations (the DTFT)" [1]
"The DTFT itself is a continuous function of frequency, but discrete samples of it can be readily calculated via the discrete Fourier transform (DFT) (see Sampling the DTFT)" [2]
[1] S. W. Smith, Digital signal processing, pp. 180, Second Edition. San Diego - California: California Technical Publiching, 1999. https://users.dimi.uniud.it/~antonio.dangelo/MMS/materials/Guide_to_Digital_Signal_Process.pdf [2] https://en.wikipedia.org/wiki/Discrete-time_Fourier_transform

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Siddhant Sharma
Siddhant Sharma 2021-3-26
But if I want to use it without using FFT function how can we approach it? Have you developed the code for that?
  1 个评论
Walter Roberson
Walter Roberson 2021-3-26
A number of people have posted fft implementations based upon summation of complex exponentials.

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