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THE FEUTEX TOOLKIT

Four-Sample Fourier Transform

Transform four equally spaced real samples into their discrete Fourier frequency components.

Math workspace● Runs in your browser
01 Your input
02 Your result
View or copy raw result data
FormulaDc = x0+x1+x2+x3; Bin1 Real = x0-x2; Bin1 Imag = x3-x1; Nyquist = x0-x1+x2-x3; Bin3 Real = x0-x2; Bin3 Imag = x1-x3
Sources and model references

Worked example

Inputs

Sample 0
1 amplitude
Sample 1
0 amplitude
Sample 2
-1 amplitude
Sample 3
0 amplitude

Expected results

Dc
0 number
Bin1 Real
2 number
Bin1 Imag
0 number
Nyquist
0 number
Bin3 Real
2 number
Bin3 Imag
0 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter the labeled inputs using consistent units.
  2. Check the stated assumptions and calculate.
  3. Review each output and compare another input scenario.

Try this example

{
  "x0": 1,
  "x1": 0,
  "x2": -1,
  "x3": 0
}

Accuracy and scope

Unnormalized forward DFT with negative exponential sign. Samples are equally spaced and real. Finite floating-point arithmetic; results can lose precision near singular or extreme inputs.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.