Benefits of DFT over FFT in MATLAB

In summary, the FFT is generally faster than the DFT, but the DFT may be faster if only a small number of Fourier coefficients are needed from a large amount of data points. Precision is not expected to be a significant difference between the two methods.
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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.
 

What is DFT and FFT?

DFT (Discrete Fourier Transform) and FFT (Fast Fourier Transform) are both mathematical algorithms used to convert a signal from its original domain (usually time or space) to a representation in the frequency domain. They are commonly used in signal processing and data analysis.

What are the benefits of using DFT over FFT in MATLAB?

One of the main benefits of DFT over FFT in MATLAB is that it allows for more control and customization. DFT can be easily modified to fit specific needs and can handle non-uniformly spaced data, whereas FFT is limited to uniformly spaced data. Additionally, DFT is more accurate for signals with a small number of data points.

Can DFT be used for real-time processing?

Yes, DFT can be used for real-time processing in MATLAB. However, it may not always be the most efficient option for real-time applications due to its higher computational complexity compared to FFT.

Is there a significant difference in speed between DFT and FFT in MATLAB?

In most cases, FFT will be faster than DFT in MATLAB due to its more efficient implementation. However, the difference in speed may not be noticeable for smaller data sets.

Can I use both DFT and FFT in MATLAB for signal processing?

Yes, you can use both DFT and FFT in MATLAB for signal processing. It is common to use DFT for data analysis and visualization, and then use FFT for more efficient processing and calculations. Knowing when to use each algorithm can greatly improve the accuracy and efficiency of signal processing in MATLAB.

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