Benefits of DFT over FFT in MATLAB

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SUMMARY

The discussion highlights the advantages of using Discrete Fourier Transform (DFT) over Fast Fourier Transform (FFT) in MATLAB under specific conditions. While FFT is generally faster, DFT can outperform FFT when only a small number of Fourier coefficients are required from a large dataset. Additionally, the conventional FFT algorithms are efficient only when the number of data points can be completely factorized into small integers, which may not always be the case. Precision differences between DFT and FFT are not a significant concern based on the current findings.

PREREQUISITES
  • Understanding of Discrete Fourier Transform (DFT)
  • Familiarity with Fast Fourier Transform (FFT) algorithms
  • Basic knowledge of MATLAB programming
  • Concept of Fourier coefficients
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  • Explore the limitations of FFT algorithms regarding data point factorization
  • Investigate scenarios where DFT may provide performance benefits over FFT
  • Learn about precision considerations in Fourier analysis
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From what I have read, FFT seems to simply be faster than DFT, thus making DFT redundant. However, if computational speed is not an issue, are there any advantages of using DFT over FFT (such as increased precision, for example)?
 
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The conventional FFT algorithms are only "fast" if the number of data points can be factorized completely into small integers. (That is less restrictive than the first FFT algorithms, where the number of data points had to be a power of 2).

A DFT may be faster if you only want a small number of Fourier coefficients from a large number of data points.

I wouldn't expect precision to be an issue either way, though I haven't investigated that in any detail.
 

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