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Discrete Fourier Transform Calculator

Calculate the forward DFT of a bounded real-valued sequence.

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Calculate the forward DFT of a bounded real-valued sequence. Use this for the specific transformation described above. Start with the fixed sample and compare its result before replacing it with your own representative input.

How to use it

Enter a value or text in the format shown in the example. Choose Calculate. Review the output, then copy or download it.

Worked examples

Use this for the specific transformation described above. Start with the fixed sample and compare its result before replacing it with your own representative input.

Reproducible worked example

Settings: No additional settings.

Input:

1,0,-1,0

With the input and settings above, the tool produces:

Output:

[
  {
    "bin": 0,
    "real": 0,
    "imaginary": 0,
    "magnitude": 0
  },
  {
    "bin": 1,
    "real": 2,
    "imaginary": 1.2246467991473532e-16,
    "magnitude": 2
  },
  {
    "bin": 2,
    "real": 0,
    "imaginary": -2.4492935982947064e-16,
    "magnitude": 2.4492935982947064e-16
  },
  {
    "bin": 3,
    "real": 2,
    "imaginary": 3.6739403974420594e-16,
    "magnitude": 2
  }
]

The example returns 4 top-level items in an array. Each item is a record; the first record contains “bin”, “real”, “imaginary”, “magnitude”.

Limitations and common mistakes

  • Calculations use your supplied assumptions and floating-point arithmetic. Check input order, units and the worked example before relying on a result.
  • Combined input is bounded to 150,000 characters; output text is bounded to 1.2 million characters. Some algorithms impose smaller limits, stated in their error messages.

Frequently asked questions

What format should I enter?

Enter a value or text in the format shown in the example. The worked example shows the supported structure and actual output.

How can I compute the forward DFT of a bounded real-valued sequence online?

Enter a value or text in the format shown in the example. Choose Calculate. Review the output, then copy or download it.

Where is my input processed?

The bundled tool processes input in your browser. It does not upload tool input to a conversion service. Other site plugins, analytics, advertising and browser extensions may have separate behavior.

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